A Riemannian Deployment-Based Network Security Waveform Design Method for Smart Reflector-Assisted Communication

Abstract

This invention proposes a Riemann expansion network security waveform design method for intelligent reflector-assisted communication, belonging to the field of wireless communication technology. This invention innovatively reconstructs the security rate maximization problem, which involves jointly optimizing the normalized transmit beamforming matrix and the reflection coefficient vector, into an unconstrained optimization problem on a product Riemann manifold. This invention designs an efficient product Riemann gradient descent algorithm to solve this problem, and further expands the iterative physical process of this algorithm into a trainable neural network layer. Specifically, this expanded network adaptively optimizes the descent step size of each iteration through unsupervised learning, not only strictly preserving the inherent geometric structure of the constant modulus constraint of the intelligent reflector, but also possessing clear interpretability. This invention has extremely fast convergence speed and extremely low online computational complexity, meeting real-time requirements. This invention avoids local optima traps and significantly improves the security rate performance of the system.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a Riemann expansion network security waveform design method for intelligent reflector-assisted communication. Background Technology

[0002] Due to the open nature of wireless channels, transmitted signals are highly susceptible to interception and eavesdropping by unauthorized individuals. Therefore, physical layer security has become a crucial technological evolution direction for ensuring information security in the current wireless communication field. In recent years, intelligent reflectors have been introduced into this field as a promising new technology. Intelligent reflectors can actively reconstruct the wireless propagation environment by dynamically adjusting the reflection coefficients of a large number of array elements on their surface, thereby improving channel conditions for legitimate users while effectively degrading the channel quality for eavesdroppers.

[0003] To fully leverage the security gains offered by intelligent reflectors, the system cannot rely solely on unilateral adjustments; instead, it requires coordinated design of the base station's active transmission beam and the intelligent reflector's passive reflection coefficient. Therefore, given the limitations of base station transmission power and intelligent reflector hardware, how to jointly optimize the transmission beamforming matrix and the intelligent reflector's reflection coefficient to maximize the system's security rate has become a core issue of great interest to both academia and industry.

[0004] However, due to the strict hardware limitations of the phase-shifting array elements of the intelligent reflector and the high coupling effect between the base station beam and the reflection matrix of the intelligent reflector, the problem of maximizing the security rate is a highly challenging non-convex optimization problem. Currently, researchers mainly use traditional mathematical methods such as alternating optimization and block coordinate descent, or purely data-driven deep learning methods such as deep neural networks to solve it. Traditional methods usually face bottlenecks of high computational complexity and extremely slow convergence, making it difficult to meet the real-time requirements of practical systems; while conventional deep learning methods exhibit "black box" characteristics, lack interpretability, and require a large amount of computational resources.

[0005] On the other hand, while the emerging deep deployment technology combines the advantages of mathematical models and deep learning, current research is mainly limited to conventional multi-antenna scenarios such as signal detection and resource allocation. For the complex manifold geometric constraints (such as strict constant modulus constraints) in smart reflector-assisted secure communication, existing technologies still lack effective solutions, and their potential to improve physical layer security has not been fully explored. Summary of the Invention

[0006] The purpose of this invention is to provide a Riemann expansion network security waveform design method for intelligent reflector-assisted communication. This invention delves into the geometric characteristics of the system's physical constraints, innovatively reconstructing the problem of maximizing the security rate by jointly optimizing the transmitted beam and reflection coefficient into an unconstrained optimization problem on a product Riemann manifold. This invention designs an efficient product Riemann gradient descent algorithm to solve this problem, and further expands the iterative physical process of this algorithm into a trainable neural network layer. Specifically, this expanded network adaptively optimizes the descent step size of each iteration through unsupervised learning, not only strictly preserving the inherent geometric structure of the constant modulus constraint of the intelligent reflector, but also significantly improving the convergence speed and system security rate while maintaining clear interpretability. This addresses the technical problem that most existing security rate maximization problems rely on highly complex traditional iterative optimization (facing slow convergence) or pure data-driven deep learning (facing "black box" and uninterpretable issues).

[0007] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0008] A Riemann expansion network security waveform design method for smart reflector-assisted communication is proposed. The method is applied to a multi-input multi-output downlink network assisted by a smart reflector, the downlink network comprising a device equipped with… The transmitter with the root antenna attempts to be equipped with In the case of an eavesdropper with a root antenna, for equipped The root antenna provides secure communication services to legitimate users and utilizes... The method utilizes intelligent reflective surfaces of individual reflective units to enhance physical layer security; the method includes the following steps:

[0009] Step S1: Construct a secret rate maximization problem on a product Riemannian manifold; represented as follows:

[0010]

[0011] in, This represents the secret rate maximization problem on a product Riemannian manifold. Represents the cost function; This represents the normalized transmit beamforming matrix; Represents the reflection coefficient vector; Represents a product Riemannian manifold; Represents the determinant operation of a matrix; Represents the conjugate transpose of a matrix; Representing dimensions The identity matrix; Representing dimensions The identity matrix; Indicates the maximum transmission power; and These represent the equivalent channel for a legitimate user and the equivalent channel for an eavesdropper, respectively. , , , , These represent the number of transmitter antennas, the number of legitimate user antennas, the number of eavesdropper antennas, the number of data streams, and the number of smart reflector units, respectively.

[0012] Step S2: Construct the Riemann expansion network. The Riemann expansion network is based on the single iteration process of the product Riemann gradient descent algorithm. The Riemann expansion network is expanded in the iteration order to include... The neural network structure consists of cascaded layers, where each layer corresponds to one Riemann gradient descent iteration; each layer consists of an Euclidean gradient calculation module, a Riemann tangent space projection module, a parameter update module based on a learnable step size, and a manifold reverting mapping module.

[0013] Step S3: Iteratively solve the cost function using a Riemann expansion network, and obtain the normalized transmit beamforming matrix output from the previous layer. and reflection coefficient vector As the input to the current layer, after Euclidean gradient calculation, it is projected onto the tangent space of the corresponding manifold to obtain the Riemann gradient, and then the beam step size of the current layer is used. and reflection step size After completing the variable update, the temporary beamforming matrix and temporary reflection coefficient vector are obtained. Finally, the temporary beamforming matrix and temporary reflection coefficient vector are remapped back to the product Riemannian manifold by remapping, resulting in the next layer output normalized transmit beamforming matrix. and reflection coefficient vector ;

[0014] Step S4: Using the last layer of normalized transmit beamforming matrix and reflection coefficient vector output by the Riemann expansion network, update the phase shift of the reflection array elements of the base station transmit beamformer and the intelligent reflector controller, respectively, thereby achieving online communication transmission with maximum secure rate.

[0015] Further, step S3 includes the following steps:

[0016] Step S31: Input and Initialization of the Riemann Unfolded Network: The input of the Riemann unfolded network receives the channel state information dataset and fixed system configuration parameters; initialization is performed at layer 0 of the network, randomly generating an initial normalized transmit beamforming matrix. and initial reflection coefficient vector , as the initial feature input for network forward propagation;

[0017] Perform the following steps S32-S35 on each layer until the last layer:

[0018] Step S32: Calculate the Euclidean gradient of the cost function with respect to the normalized transmit beamforming matrix and reflection coefficient vector of the previous layer output;

[0019] Step S33: Project the Euclidean gradient of the cost function with respect to the normalized transmit beamforming matrix and reflection coefficient vector of the previous layer output onto the tangent space of the manifold to obtain the Riemann gradient of the cost function with respect to the normalized transmit beamforming matrix and reflection coefficient vector of the previous layer output.

[0020] Step S34: Use the current layer beam step size and reflection step size to perform gradient descent update on the tangent space of the normalized transmit beamforming matrix and reflection coefficient vector output from the previous layer, and obtain the temporary beamforming matrix and temporary reflection coefficient vector.

[0021] Step S35: Remap the temporary beamforming matrix and temporary reflection coefficient vector back to the product Riemannian manifold surface to generate the normalized transmit beamforming matrix and reflection coefficient vector output to the next layer;

[0022] Step S36: Output the final number. Layer normalized transmit beamforming matrix and the first Layer reflection coefficient vector;

[0023] Step S37: Perform backpropagation using the composite loss function to jointly update the set of all learnable step size parameters in the network. Training continues until the parameters converge, completing the training process.

[0024] Further, step S32 performs the following operations:

[0025]

[0026]

[0027] in, Indicates the first Layer cost function Regarding the first Layer-normalized transmit beamforming matrix The Euclidean gradient, This represents the intermediate feature matrix related to the eavesdropper. This represents the intermediate eavesdropping matrix regarding legitimate users. Indicates the first Layer cost function Regarding the first Layer reflection coefficient vector The Euclidean gradient, Represents the beamforming information matrix. Represents a diagonal matrix operator; This represents the channel matrix between the smart reflector and the eavesdropper; This represents the channel matrix between the smart reflector and the user.

[0028] Further, step S33 performs the following operations:

[0029]

[0030]

[0031] in, Indicates the first Layer cost function Regarding the first Layer-normalized transmit beamforming matrix The Riemann gradient, Indicates the first Layer cost function Regarding the first Layer reflection coefficient vector The Riemann gradient, This indicates extracting the real part. For trace operators, It represents the Hadamah accumulation. This indicates a conjugate operation.

[0032] Further, step S34 performs the following operations:

[0033]

[0034]

[0035] in, This represents the temporary beamforming matrix. Represents the temporary reflection coefficient vector. Indicates the first Layer beam step size, Indicates the first Layer reflection step size.

[0036] Further, step S35 performs the following operations:

[0037]

[0038]

[0039] in, Indicates the first Layer-normalized transmit beamforming matrix, Indicates the first Layer reflection coefficient vector, Represents the temporary beamforming matrix The Frobenius norm.

[0040] Furthermore, the composite loss function in step S37 is expressed as follows:

[0041]

[0042] in, Represents the composite loss function. For the first Layer weight allocation coefficients.

[0043] Compared to existing technologies, this invention offers the following advantages: This invention proposes a novel solution to the physical layer security beamforming problem in intelligent reflector-assisted multi-antenna systems. This method differs from existing methods in that traditional mathematical optimization algorithms (such as alternating optimization and block coordinate descent) typically have extremely high computational complexity and slow convergence, while conventional pure data-driven deep learning methods are like a "black box," lacking interpretability and failing to guarantee strict physical constraints. This invention innovatively unfolds the mathematical iterative process of the product Riemann gradient descent algorithm into a neural network, perfectly combining the advantages of traditional algorithms and deep learning. Specifically, this invention has the following significant advantages and technical effects:

[0044] 1) Extremely fast convergence speed and extremely low online computational complexity, meeting real-time requirements. Existing Riemannian manifold optimization algorithms typically rely on expensive line search or backtracking methods to find the descent step size for each iteration, which incurs unacceptable time overhead when the number of intelligent reflector elements is large. This invention cleverly extracts the iteration step size as a learnable scalar parameter of the neural network, utilizing the optimization capabilities of deep learning to complete step size tuning offline. During online deployment and testing, the system only needs to perform lightweight fixed-step forward propagation calculations, eliminating the need for time-consuming step size search, thereby greatly reducing computational complexity and significantly accelerating convergence speed.

[0045] 2) It possesses extremely strong model interpretability and can absolutely guarantee the strict physical constraints of the system. Unlike conventional "black box" neural networks that lack interpretability, each layer of the Riemann gradient descent network proposed in this invention strictly corresponds to the mathematical iterative physical process of the Riemann gradient descent algorithm, realizing the fusion of physical mechanism and data-driven approach. More importantly, by innovatively designing "Riemann tangent space projection" and "manifold feasible set recovery" processing modules within the network layers, this invention strictly preserves the intrinsic geometric structure of the constraints during the forward propagation of network features. This not only avoids the geometric deformation caused by conventional Euclidean space projection but also ensures that the solution output by the network absolutely satisfies the base station transmit power constraint and the constant mode constraint of the intelligent reflector array elements.

[0046] 3) This invention avoids local optima traps and significantly improves the system's security rate performance. Traditional algorithms that rely on manually setting or mathematically deriving step sizes are prone to getting trapped in local optima of non-convex problems. This invention utilizes an unsupervised loss function customized for maximizing security rate, and trains the network's step size parameters offline on massive channel datasets. This adaptive step size learning mechanism can automatically find the optimal descent trajectory based on channel characteristics, ensuring more accurate gradient descent in each iteration. Attached Figure Description

[0047] 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 some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a schematic diagram of the model-driven Riemann unrolling network of the present invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] Consider a multiple-input multiple-output downlink network assisted by a smart reflector. The network includes a device equipped with... The transmitter with the root antenna attempts to be equipped with In the case of an eavesdropper with a root antenna, for equipped The root antenna provides secure communication services to legitimate users and utilizes... Intelligent reflective surfaces of individual reflective units enhance physical layer security.

[0051] make This indicates a confidential information stream sent to legitimate users. Given the transmit beamforming matrix, the base station's transmit signal can be expressed as:

[0052] (1)

[0053] in, This indicates the transmitted signal from the base station; Indicates the maximum transmission power; Represents the set of complex numbers; Indicates the number of signal data streams; This indicates the number of base station antennas.

[0054] make This represents the reflection coefficient matrix of the intelligent reflective surface. Indicates the number of intelligent reflective surface units. Represents a diagonal matrix operator. Represents the reflection coefficient vector. Indicates the first The reflection coefficient of each reflecting unit. Indicates transpose. Definition , , , , Let represent the channel matrices between the base station and the user, the base station and the eavesdropper, the base station and the smart reflector, the smart reflector and the user, and the smart reflector and the eavesdropper, respectively. Assuming the channels are quasi-static flat fading channels, the received signals at the legitimate user and the eavesdropper are... and They can be represented as:

[0055] (2a)

[0056] (2b)

[0057] in, and These are Gaussian white noises from the legitimate user and the eavesdropper, respectively. and Dimensions and The identity matrix, This represents the average noise power at legitimate user locations. This represents the average noise power at the location of the eavesdropper.

[0058] In physical layer secure communication, the system's security rate is a core indicator for measuring information security transmission capabilities. Specifically, the system's security rate is defined as the difference between the reachable rate of the legitimate user's channel and the reachable rate of the eavesdropper's channel. The system can guarantee secure information transmission only if the reachable rate of the legitimate user's channel is strictly greater than the reachable rate of the eavesdropper's channel. Therefore, the system's security rate... The mathematical expression for it is defined as:

[0059] (3)

[0060] in, This indicates the operation of obtaining non-negative values, i.e. In the above formula, and These represent the reachable speeds of the link for legitimate users and eavesdroppers, respectively. Based on Shannon's formula, their specific expansion is as follows:

[0061] (4a)

[0062] (4b)

[0063] in, This represents the determinant operation of a matrix. Represents the conjugate transpose of a matrix. Representing dimensions The identity matrix, Representing dimensions The identity matrix, and These represent the equivalent channel for the legitimate user and the equivalent channel for the eavesdropper, respectively, referring to the effective noise floor values ​​including the reflection coefficients of the smart reflector and passing through the receivers of the legitimate user and the eavesdropper. and The equivalent channel after scaling and normalization is defined as follows:

[0064] (5a)

[0065] (5b)

[0066] The objective of this invention is to jointly optimize the transmit beamforming matrix while satisfying the maximum transmit power of the base station and the hardware constraints of the intelligent reflector. and the reflection coefficient matrix of the intelligent reflective surface To maximize the system's security rate, the problem of maximizing the system's security rate is modeled as follows:

[0067] (6a)

[0068] (6b)

[0069] (6c)

[0070] This indicates maximizing the system's security rate. This represents the transmit power at the base station side, and is the transmit beamforming matrix. The square of the Frobenius norm, and the constraint of formula (6b), limit the base station's transmit power to not exceed the maximum transmit power. The constraints of formula (6c) ensure that each reflective unit of the intelligent reflective surface meets the strict hardware-limited constant mode constraint.

[0071] Typically, in Equation 6(a), only when the base station uses its maximum transmit power, i.e. Only in this way can the system's maximum security rate be achieved; and only when Only then can secure communication be ensured. Based on this, by making an equivalent transformation of the system's security rate maximization problem in formula (6a), and utilizing... Channel scaling is achieved by introducing a normalized transmit beamforming matrix. To shape the transmitted beam matrix Frobenius norm Normalized to 1, the problem of maximizing the confidentiality rate of this system can be equivalently modeled as the following problem of minimizing relative information leakage:

[0072] (7a)

[0073] (7b)

[0074] (7c)

[0075] in, Represents the cost function; This means minimizing the cost function to maximize the rate of secrecy; Represents the normalized transmit power, and is the normalized transmit beamforming matrix. The square of the Frobenius norm.

[0076] The aforementioned problem of minimizing relative information leakage is extremely challenging: the cost function of formula (7a) is non-concave, and the normalized transmit beamforming matrix... With reflection coefficient vector The equations are highly coupled, and the constraints in equations (7b) and (7c) are both non-convex. To avoid the difficulty of solving the problem caused by non-convex constraints, this invention maps the constraints in equations (7b) and (7c) to a set of manifolds in Riemann space. Specifically, the normalized transmit power constraint in equation (7b) Equivalent to a complex spherical manifold ,Right now:

[0077] (8)

[0078] Simultaneously, the constant mode constraint of the intelligent reflective surface in formula (7c) Equivalent to a complex circular manifold ,Right now:

[0079] (9)

[0080] Furthermore, the complex spherical manifold and the complex circular manifold are combined into a product Riemannian manifold. ,Right now:

[0081] (10)

[0082] Based on this intrinsic geometric property, the original non-convex problem with complex physical constraints is successfully reconstructed by this invention into an unconstrained optimization problem on the product Riemannian manifold:

[0083] (11)

[0084] This represents the problem of maximizing the secret rate on a product Riemannian manifold.

[0085] Thus, the complex problem of security design for the physical layer of communication has been transformed into an optimization problem on a standard manifold space, laying a mathematical foundation for efficient solutions in subsequent applications of deep unfolded networks.

[0086] Overall Algorithm:

[0087] To efficiently solve the confidentiality rate maximization problem of the aforementioned reconstruction on the product Riemannian manifold, this invention proposes a model-driven Riemannian expansion network. Unlike traditional black-box models, this invention expands the iterative physical process of the product Riemann gradient descent algorithm into a network containing… The Riemann unfolded network is a cascaded neural network architecture, and the descent step size is extracted as a learnable weight parameter of the network. The overall Riemann unfolded network consists of two parts: offline unsupervised training and online inference.

[0088] The Riemann expansion network security waveform design method for intelligent reflector-assisted communication proposed in this invention includes the following steps:

[0089] Step 1: Riemann unfolding network construction.

[0090] Based on the aforementioned result of reconstructing the security rate maximization problem of the system in Equation (6a) into the security rate maximization problem on the product Riemann manifold of Equation (11), a model-driven Riemann expansion network is constructed. The Riemann expansion network is based on a single iteration of the product Riemann gradient descent algorithm, which is expanded sequentially into a network containing… The neural network structure consists of cascaded layers, with each layer corresponding to one Riemann gradient descent iteration.

[0091] like Figure 1 As shown, the first The layer network consists of an Euclidean gradient calculation module, a Riemannian tangent space projection module, a parameter update module based on a learnable step size, and a manifold recovery mapping module. The normalized transmit beamforming matrix output from the previous layer... and reflection coefficient vector As the input to the current layer, after Euclidean gradient calculation, it is projected onto the tangent space of the corresponding manifold to obtain the Riemann gradient, and then the learnable step size parameter specific to this layer is used. and After completing the variable update, the intermediate results are remapped back to the product Riemannian manifold by unmapping the mapping, thus obtaining the output of the next layer. and .

[0092] The trainable parameters of the network are the set of stride parameters corresponding to each unfolded layer. The remaining gradient calculations, tangent space projections, and manifold retraction processes are uniquely determined by the system model and physical constraints. Therefore, the constructed network retains the interpretability of traditional iterative algorithms while also possessing the ability to adaptively optimize the iteration step size through offline training. The network's final output is the... Normalized transmit beamforming matrix of the layer and reflection coefficient vector Used for online secure transmission control.

[0093] Step 2: Network input and initialization.

[0094] The input of the Riemann unrolled network receives a dataset of channel state information. and fixed system configuration parameters Initialization is performed at layer 0 of the network, randomly generating an initial normalized transmit beamforming matrix that satisfies the normalized transmit power constraint and the constant mode constraint of the smart reflector. and initial reflection coefficient vector , which serves as the initial feature input for network forward propagation.

[0095] Step 3: Calculate the Euclidean gradient.

[0096] In the network layer( ), based on the first one passed from the previous layer Layer-normalized transmit beamforming matrix and the Layer reflection coefficient vector Calculate the first Layer cost function Euclidean gradients of these two variables and :

[0097] (12a)

[0098] (12b)

[0099] in, Indicates the first Layer cost function Regarding the first Layer-normalized transmit beamforming matrix The Euclidean gradient, This represents the intermediate feature matrix related to the eavesdropper. This represents the intermediate eavesdropping matrix regarding legitimate users. Indicates the first Layer cost function Regarding the first Layer reflection coefficient vector The Euclidean gradient, This represents the beamforming information matrix.

[0100] The intermediate feature matrix of the eavesdropper, the intermediate eavesdropping matrix of the legitimate user, and the beamforming information matrix are defined as follows:

[0101] (13a)

[0102] (13b)

[0103] (13c)

[0104] Step 4: Calculate the Riemann chevron spatial gradient.

[0105] The Euclidean gradient obtained in step 3 is nonlinearly projected onto the tangent space of the manifold to extract the Riemann gradient, which preserves the geometric features of strict physical constraints. and :

[0106] (14a)

[0107] (14b)

[0108] in, Indicates the first Layer cost function Regarding the first Layer-normalized transmit beamforming matrix The Riemann gradient, This indicates the conjugate transpose. Representing the Euclidean gradient The conjugate transpose of . Indicates the first Layer cost function Regarding the first Layer reflection coefficient vector The Riemann gradient, This indicates extracting the real part. For trace operators, It represents the Hadamah accumulation. This indicates a conjugate operation.

[0109] Step 5: Update manifold parameters based on learnable step size.

[0110] Introduce learnable weight parameters specific to this network layer, namely the first... Layer beam step and the Layer reflection step size Using these two parameters that are dynamically optimized during the network training phase, the first... Layer-normalized transmit beamforming matrix and the Layer reflection coefficient vector Perform gradient descent updates on the tangent space to obtain the temporary beamforming matrix. and temporary reflection coefficient vector :

[0111] (15a)

[0112] (15b)

[0113] Step 6: Manifold revert to mapping.

[0114] Temporary beamforming matrix in tangent space and temporary reflection coefficient vector Remap back to the product Riemannian manifold surface to generate the state variables output to the next network layer, i.e., the th... Layer-normalized transmit beamforming matrix and the Layer reflection coefficient vector To strictly meet the physical constraints of normalized transmit power constraints and smart reflector constant mode constraints:

[0115] (16a)

[0116] (16b)

[0117] in, Represents the temporary beamforming matrix The Frobenius norm. Let ,if If so, return to step 3 for the next layer of network processing; Then the forward propagation process of the inner network ends.

[0118] Step 7: Calculate the network loss function.

[0119] During the offline unsupervised training phase, the network is computed using a dataset containing a large number of channel samples. Composite loss function of layer output :

[0120] (17)

[0121] in, For the first The layer weight allocation coefficients, by giving greater weight to the earlier layers, force the network to quickly approach the suboptimal solution in the shallow layers.

[0122] Step 8: Network parameter update and online secure transmission control.

[0123] Based on the composite loss function calculated in step 7, backpropagation is performed using an optimization algorithm to jointly update the set of all learnable step size parameters in the network. The training continues until the parameters converge, completing model training. In the online application phase, the Riemann unfolded network with fixed optimal step size parameters is deployed in the communication system. The system collects channel state information in real time and inputs it into the network, executing steps 3 to 6 sequentially in a single run. Layer forward propagation, using the final output of the first layer Layer-normalized transmit beamforming matrix and the Layer reflection coefficient vector The phase shift of the reflective array elements of the base station transmit beamformer and the intelligent reflector controller are updated respectively, thereby achieving online communication transmission with maximum secure rate.

[0124] Example 1

[0125] Network Configuration: Consider a smart reflector-assisted MIMO downlink secure communication system. The network topology is spatially laid out with the following distances configured: transmitter to legitimate user, transmitter to smart reflector, transmitter to eavesdropper, smart reflector to legitimate user, and smart reflector to eavesdropper, respectively, at 45 m, 51 m, 55 m, 6 m, and 6 m. The number of base station antennas is configured as follows: The number of intelligent reflective surface units is configured as follows: The number of receiving antennas and the number of data streams transmitted by both legitimate users and eavesdroppers are set to [specific values]. The maximum transmit power of the base station is set to... The average noise power at the legitimate user's location and the average noise power at the eavesdropper's location are set to... All communication links employ a channel model that includes both large-scale and small-scale fading, where the small-scale fading follows an independent and identically distributed Rayleigh distribution; the large-scale path loss is set to -30 dB at a 1 m reference distance, and the path loss exponent for all links is set to 3.

[0126] Define parameters: Number of layers in the Riemann unrolled network (equivalent number of iterations) Offline training epochs Number of training set samples The network optimizer was selected as Adam, and the learning rate was set to... The initial empirical value for the learnable step size is set to... The system variable to be optimized is the normalized transmit beamforming matrix. and reflection coefficient vector The set of learnable parameters of a network is defined as follows: .

[0127] Step 1: Dataset Generation and Network Initialization. Based on the channel model of the network configuration described above, randomly generate a dataset containing... Training dataset implemented using individual channels Each channel sample contains a dataset of channel state information. Initialization has A layered Riemannian unfolded network was constructed, and the learnable step size parameters of all layers were used. Initialize to 0.2; set the number of training rounds. .

[0128] Step 2: Start the outer loop of offline training. Begin iterating through the training set until the maximum number of training epochs is reached. .

[0129] Step 3: Generate initial guesses. Extract a channel sample from the training set and randomly initialize a pair of normalized transmit beamforming matrices on the feasible set of the product Riemannian manifold, satisfying both the normalized transmit power constraint and the constant mode constraint of the smart reflector. and reflection coefficient vector Set the current network layer number .

[0130] Step 4: Perform single-layer Euclidean calculation. Combine the channel samples and Input network, at the The Euclidean gradient is calculated using the formula for each layer.

[0131] Step 5: Tangent Space Projection and Parameter Descent. The Euclidean gradient is projected onto the Riemann tangent space to obtain the Riemann gradient. and Then, the currently stored step size parameter of the network is retrieved. and Gradient descent is performed to obtain a temporary beamforming matrix. and temporary reflection coefficient vector .

[0132] Step 6: Manifold Retraction Operation. Perform the retraction operation to generate the state variables output to the next network layer, i.e., the... Layer-normalized transmit beamforming matrix and the Layer reflection coefficient vector .make ,if If so, return to step 4 to continue the forward propagation of the next layer of the network.

[0133] Step 7: Calculate network loss. After 300 layers of forward propagation, extract the normalized transmit beamforming matrix of each layer's output. and reflection coefficient vector Using weighted coefficients Composite loss function Calculate the overall loss value for the current sample.

[0134] Step 8: Backpropagation and Weight Update. Based on the calculated overall loss value, use the Adam optimizer with a learning rate of 0.01 to calculate the composite loss function with respect to all layer step sizes. The gradient, and the step size for all layers. Perform a reverse update. If the training set has not been completely traversed, return to step 3 to extract the next sample; if the traversal is complete, let... Return to step 2.

[0135] Step 9: Online Deployment and Network Loading. After offline training, the learnable step size in the network... It is fixed at the optimal value. The Riemann unfolded network is then deployed to the edge computing controller of the actual base station system.

[0136] Step 10: Real-time Channel State Acquisition. In actual operation, the base station system acquires real-time channel state information datasets for legitimate links, eavesdropping links, and cascaded reflection links using channel estimation technology.

[0137] Step 11: Online Inference and Optimization. The acquired channel state information dataset and a set of randomly initialized... The input is fed into the deployed Riemann unroll network. The network directly utilizes fixed optimal step size parameters to execute at high speed. Forward propagation of the layer (i.e., repeating steps 4 to 6).

[0138] Step 12: Physical Execution and Secure Transmission. After completing 300 layers of calculation, the network outputs the extreme point results and the 300th layer normalized transmit beamforming matrix. and the reflection coefficient vector of the 300th layer Base station according to The base station directly updates the transmit beamformer of its radio frequency transmission front end; simultaneously, the base station uses the control link to... The data is sent to the intelligent reflective surface controller, which dynamically adjusts the phase shift of the 64 reflective array elements on the intelligent reflective surface panel, thereby establishing a secure transmission channel with maximum confidentiality rate in the physical environment.

[0139] This invention proposes a deep-expansion-based product Riemann gradient descent network architecture: the mathematical iterative process of the traditional Riemann manifold optimization algorithm is rigorously deconstructed and expanded into a neural network containing multiple cascaded hidden layers. This not only solves the problem of slow computation in traditional algorithms but also overcomes the "black box" defect of conventional deep neural networks, which lacks interpretability, thus achieving efficient beamforming design for intelligent reflector-assisted secure communication.

[0140] This invention proposes an unsupervised training mechanism with adaptive step size: it overcomes the bottleneck of traditional manifold algorithms that rely on high-complexity line search (such as backtracking) to find the step size, and extracts the iterative descent step size as a network-specific learnable weight parameter. Through offline automatic optimization using a loss function customized for the confidentiality rate, the optimal solution can be quickly output during the online inference stage with only lightweight forward propagation.

[0141] This invention constructs a physically constrained strict mapping method based on product Riemannian manifolds: "Tangent space gradient projection" and "manifold feasible set recovery" processing modules are specifically designed in the network hidden layer. This method perfectly preserves the intrinsic geometric structure of variables during network feature propagation, absolutely guaranteeing the transmit power constraints of the base station beams and the strict constant mode constraints of the IRS array elements.

[0142] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A Riemann expansion network security waveform design method for intelligent reflector-assisted communication, characterized in that, The method is applied to a multi-input multi-output downlink network assisted by a smart reflector, the downlink network comprising a device equipped with The transmitter with the root antenna attempts to be equipped with In the case of an eavesdropper with a root antenna, for equipped The root antenna provides secure communication services to legitimate users and utilizes... The method utilizes intelligent reflective surfaces of individual reflective units to enhance physical layer security; the method includes the following steps: Step S1: Construct a secret rate maximization problem on a product Riemannian manifold; represented as follows: in, This represents the secret rate maximization problem on a product Riemannian manifold. Represents the cost function; This represents the normalized transmit beamforming matrix; Represents the reflection coefficient vector; Represents a product Riemannian manifold; Represents the determinant operation of a matrix; Represents the conjugate transpose of a matrix; Representing dimensions The identity matrix; Representing dimensions The identity matrix; Indicates the maximum transmission power; and These represent the equivalent channel for a legitimate user and the equivalent channel for an eavesdropper, respectively. Step S2: Construct the Riemann expansion network. The Riemann expansion network is based on the single iteration process of the product Riemann gradient descent algorithm. The Riemann expansion network is expanded in the iteration order to include... The neural network structure consists of cascaded layers, where each layer corresponds to one Riemann gradient descent iteration; each layer consists of an Euclidean gradient calculation module, a Riemann tangent space projection module, a parameter update module based on a learnable step size, and a manifold reverting mapping module. Step S3: Iteratively solve the cost function using a Riemann expansion network, and obtain the normalized transmit beamforming matrix output from the previous layer. and reflection coefficient vector As the input to the current layer, after Euclidean gradient calculation, it is projected onto the tangent space of the corresponding manifold to obtain the Riemann gradient, and then the beam step size of the current layer is used. and reflection step size After completing the variable update, the temporary beamforming matrix and temporary reflection coefficient vector are obtained. Finally, the temporary beamforming matrix and temporary reflection coefficient vector are remapped back to the product Riemannian manifold by remapping, resulting in the next layer output normalized transmit beamforming matrix. and reflection coefficient vector ; Step S4: Using the last layer of normalized transmit beamforming matrix and reflection coefficient vector output by the Riemann expansion network, update the phase shift of the reflection array elements of the base station transmit beamformer and the intelligent reflector controller, respectively, thereby achieving online communication transmission with maximum secure rate.

2. The Riemann expansion network security waveform design method for intelligent reflector-assisted communication according to claim 1, characterized in that, Step S3 includes the following steps: Step S31: Input and Initialization of the Riemann Unfolded Network: The input of the Riemann unfolded network receives the channel state information dataset and fixed system configuration parameters; initialization is performed at layer 0 of the network, randomly generating an initial normalized transmit beamforming matrix. and initial reflection coefficient vector , as the initial feature input for network forward propagation; Perform the following steps S32-S35 on each layer until the last layer: Step S32: Calculate the Euclidean gradient of the cost function with respect to the normalized transmit beamforming matrix and reflection coefficient vector of the previous layer output; Step S33: Project the Euclidean gradient of the cost function with respect to the normalized transmit beamforming matrix and reflection coefficient vector of the previous layer output onto the tangent space of the manifold to obtain the Riemann gradient of the cost function with respect to the normalized transmit beamforming matrix and reflection coefficient vector of the previous layer output. Step S34: Use the current layer beam step size and reflection step size to perform gradient descent update on the tangent space of the normalized transmit beamforming matrix and reflection coefficient vector output from the previous layer, and obtain the temporary beamforming matrix and temporary reflection coefficient vector. Step S35: Remap the temporary beamforming matrix and temporary reflection coefficient vector back to the product Riemannian manifold surface to generate the normalized transmit beamforming matrix and reflection coefficient vector output to the next layer; Step S36: Output the final number. Layer normalized transmit beamforming matrix and the first Layer reflection coefficient vector; Step S37: Perform backpropagation using the composite loss function to jointly update the set of all learnable step size parameters in the network. Training continues until the parameters converge, completing the training process.

3. The Riemann expansion network security waveform design method for intelligent reflector-assisted communication according to claim 2, characterized in that, Step S32 performs the following operations: in, Indicates the first Layer cost function Regarding the first Layer-normalized transmit beamforming matrix The Euclidean gradient, This represents the intermediate feature matrix related to the eavesdropper. This represents the intermediate eavesdropping matrix regarding legitimate users. Indicates the first Layer cost function Regarding the first Layer reflection coefficient vector The Euclidean gradient, Represents the beamforming information matrix. Represents a diagonal matrix operator; This represents the channel matrix between the smart reflector and the eavesdropper; This represents the channel matrix between the smart reflector and the user.

4. The Riemann expansion network security waveform design method for intelligent reflector-assisted communication according to claim 3, characterized in that, Step S33 performs the following operations: in, Indicates the first Layer cost function Regarding the first Layer-normalized transmit beamforming matrix The Riemann gradient, Indicates the first Layer cost function Regarding the first Layer reflection coefficient vector The Riemann gradient, This indicates extracting the real part. For trace operators, It represents the Hadamah accumulation. This indicates a conjugate operation.

5. The Riemann expansion network security waveform design method for intelligent reflector-assisted communication according to claim 4, characterized in that, Step S34 performs the following operations: in, This represents the temporary beamforming matrix. Represents the temporary reflection coefficient vector. Indicates the first Layer beam step size, Indicates the first Layer reflection step size.

6. The Riemann expansion network security waveform design method for intelligent reflector-assisted communication according to claim 4, characterized in that, Step S35 performs the following operations: in, Indicates the first Layer-normalized transmit beamforming matrix, Indicates the first Layer reflection coefficient vector, Represents the temporary beamforming matrix The Frobenius norm.

7. The Riemann expansion network security waveform design method for intelligent reflector-assisted communication according to claim 4, characterized in that, The composite loss function in step S37 is expressed as follows: in, Represents the composite loss function. For the first Layer weight allocation coefficients.

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