Physical layer secure transmission method based on multipath selection independent transmission

Abstract

The invention provides a physical layer secure transmission method based on multipath selection independent transmission, which comprises the following steps of: firstly, acquiring multipath channel state information of legal users by using a large-scale MIMO (Multiple Input Multiple Output) channel estimation method; and secondly, performing multipath selection based on the multipath channel state information, matching an additive uniquely decomposable constellation group according to the multipath number, performing precoding design, and eliminating symbol interference among multiple paths, so that a legal user side receiving signal meets the sum constellation design of the additive uniquely decomposable constellation group, and further realizing accurate detection of a receiving symbol. In a single-user scene, the method only needs to perform multipath selection so as to improve the secrecy capacity. In a multi-user scene, a multi-path and user two-stage selection process needs to be carried out, that is, multi-path selection is carried out on multiple users to determine an optimal path combination, and then user selection is carried out based on the optimal path combination of each user, so that the secrecy capacity of the system is improved.

Description

Technical Field

[0001] This invention relates to the technical field of communication security, and in particular to a physical layer secure transmission method using a massive MIMO antenna and selection strategy. It utilizes a scenario-adaptive path or user selection mechanism to assist additively unique decomposable constellation groups, and leverages the multipath characteristics of the channel at the physical layer for independent secure transmission, aiming to maximize confidentiality in passive eavesdropping scenarios. Background Technology

[0002] Existing physical layer security technologies primarily leverage the overall characteristics of wireless channels, employing methods such as beamforming and artificial noise injection to establish security advantages. However, most current technologies model multi-antenna channels as a single, unified channel, failing to effectively distinguish and utilize the rich multipath components within the channel. This simplistic approach neglects the independence of each path and its unique channel characteristics, resulting in an inability to fully exploit the diversity gain and security potential offered by multipath channels. Furthermore, traditional large-scale antenna arrays rely on complex phased arrays or all-digital architectures, requiring each antenna element to have an independent RF link, leading to high hardware costs and enormous power consumption. Dynamic metasurface antennas (DMA), as an emerging technology, possess significant hardware advantages such as low cost and low power consumption; however, how to effectively apply their two-dimensional arrays to multipath physical layer secure transmission still requires in-depth research.

[0003] Furthermore, secure transmission schemes based on Additive Unique Decomposable Constellation Groups (UDCGs) have extremely high requirements for channel orthogonality. The transmitter typically needs to use precoding to forcibly eliminate symbol interference between multipath paths or users. In real-world, scatter-rich environments, while random selection of multipath paths or users can achieve basic independent transmission, if the selected channel combinations have high spatial correlation, the system will have to expend significant transmit power to "force" channel orthogonality. This suboptimal combination leads to a severe waste of transmit power, greatly limiting the power resources available for effective signals, thus becoming a bottleneck for improving system security capacity. Simultaneously, traditional physical layer security schemes, when facing passive, silent eavesdroppers, cannot obtain information about the eavesdropping channel state, making it difficult for traditional artificial noise techniques to accurately target and effectively ensure information security. Summary of the Invention

[0004] To address the technical problems of existing physical layer security technologies failing to fully utilize the hardware advantages of two-dimensional DMA and the independent transmission characteristics of channel multipath components when dealing with passive eavesdropping, and the fact that traditional random channel combination methods lead to a large amount of transmission power being wasted on forced orthogonality, thus limiting the improvement of confidentiality capacity, this invention proposes a physical layer secure transmission method based on multipath selection independent transmission.

[0005] The core of this invention lies in: based on obtaining legitimate user channel state information and matching additively uniquely decomposable constellation groups (UDCGs), it focuses on utilizing the hardware advantages of the two-dimensional DMA architecture, combined with scenario-adaptive multipath selection and user selection strategies, to optimize the power resource allocation of the system, thereby achieving efficient, multipath independent and secure transmission of the uniquely decomposable constellation group.

[0006] Specifically, in single-user scenarios, a greedy path selection strategy based on Gram determinant is implemented; in multi-user scenarios, a two-stage strategy of "path selection first, user selection later" is implemented, combining greedy path filtering with a greedy user selection algorithm based on multipath subspace projection. This strategy can accurately select high-gain paths or user combinations with excellent mutual orthogonality from the scattering-rich environment during the preprocessing stage. Its core function is to significantly improve the condition number of the equivalent channel matrix at the physical level, thereby greatly reducing the power cost incurred by the system to satisfy the strict orthogonality of additive UDCG. Through the pre-selection mechanism, this invention releases power resources that might otherwise be wasted on interference cancellation and refocuses them on improving the receiving gain of the effective signal.

[0007] Based on this, through scenario-adaptive precoding joint optimization, the legitimate receiver can accurately separate and detect coherently superimposed sub-constellation signals; while for the passive eavesdropping end, due to the inherent mismatch and uncorrelation between its channel spatial characteristics and the legitimate channel, signals specifically targeting legitimate users degenerate into strong inter-stream interference at its receiver, making correct decomposition impossible. This invention fundamentally and effectively suppresses passive eavesdropping without requiring access to the eavesdropper's channel state information, significantly improving the average confidentiality capacity and inherent security of the communication system.

[0008] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0009] A physical layer secure transmission method based on multipath selection independent transmission, comprising the following steps:

[0010] S1: Construct a communication system including a transmitter and a receiver. The transmitter is equipped with a massive MIMO antenna, and the receiver is a legitimate user with a passive eavesdropper present. Obtain the multipath channel state information of the legitimate user in the receiver.

[0011] S2: Based on multipath channel state information, an additively unique decomposable constellation group is matched for each legitimate user according to the number of multipaths. Each input message bit stream is mapped to a sub-constellation of the additively unique decomposable constellation group to obtain a symbol vector.

[0012] S3: Determine the current communication scenario. If it is a single-user scenario, execute a greedy path selection strategy based on multipath channel state information to select the optimal transmission path combination from the user's candidate paths. If it is a multi-user scenario, execute a two-level selection strategy: First, traverse all users in the user pool and execute a greedy path selection strategy for each user's candidate paths to select the optimal transmission path combination for that user. Second, based on the optimal transmission path combinations selected by each user, execute a greedy user selection strategy based on subspace projection to select the optimal user combination from the user pool.

[0013] S4: Based on the equivalent channel formed by the selected optimal transmission path combination or optimal user combination, for different scenarios, under the condition of satisfying orthogonality constraints, different optimization methods are used to jointly design the digital precoding matrix and the DMA simulated weight matrix.

[0014] S5: Multiply the symbol vector with the optimized digital precoding matrix and analog precoding matrix to obtain the transmitted signal vector;

[0015] S6: The transmitted signal vector reaches the receiving end after being radiated by a large-scale MIMO antenna and transmitted through a wireless channel, thus obtaining the received signal;

[0016] S7: The receiver detects the received signal and solves for the most likely sum constellation symbol based on the minimum distance criterion;

[0017] S8: Utilize the unique decomposability property of additively unique decomposable constellation groups to decompose the most likely sum constellation symbols and restore them to unique sub-constellation symbol vectors;

[0018] S9: Demodulate each symbol in the recovered sub-constellation symbol vector to obtain the final recovered message bitstream.

[0019] Preferably, the method for obtaining the multipath channel state information of legitimate users in step S1 is as follows:

[0020] The sender configuration includes Each microstrip contains A two-dimensional dynamic metasurface antenna with radiating elements, in In consecutive sampling time slots, the phase shift of the dynamic metasurface antenna is orthogonally reconstructed, at the th... In each sampling time slot, the first sample on each microstrip will be... The phase of each radiating element is set to Make its equivalent weight The phase of the remaining units is set to Set its equivalent weight to 0;

[0021] collect The received signals from each sampling time slot constitute a sampling matrix. The channel is estimated based on the minimum mean square error criterion combined with the pilot signal, using the following formula:

[0022] ,

[0023] in, , For the estimated full channel vector, Pilot signal, for conjugate, Indicates vectorization operation, Used to compensate for phase shift. This is the power correlation coefficient.

[0024] Preferably, the additively uniquely decomposable constellation set is defined as follows:

[0025] For any If and only if Only then will there be ,So It is called an additively unique factorization constellation group, that is ;in, Represents a constellation point within a sub-constellation. Indicates another constellation point within a sub-constellation. Indicates sub-constellations, Indicates the number of sub-constellations.

[0026] Preferably, in a single-user scenario, the method for executing the greedy path selection strategy is as follows:

[0027] Candidate path set for single user Bob ,Include Candidate paths; initialize the selected set to an empty set, and set the selected path set to an empty set. The candidate path set is ; using Gram determinant As a metric, among The set of selected paths The corresponding channel matrix;

[0028] The total number of iterations is ; in the In the next iteration, based on the set determined in the previous round... Iterate through the current remaining candidate set. Each path in ,in, ; calculation will The new metric generated after adding to the current set: Select the path that maximizes the metric. Add to collection: ;

[0029] The selected optimal path is added to the set of selected paths and removed from the set of candidate paths. , ;

[0030] When the maximum number of iterations is reached Stop iterating when the time is right, and output the final selected optimal path combination. and the corresponding channel matrix .

[0031] Preferably, in a multi-user scenario, the greedy user selection strategy based on subspace projection is as follows:

[0032] S31: Iterate through all users in the user pool For each user's candidate paths, a greedy path selection strategy is executed to filter out the optimal combination of transmission paths for that user, thus obtaining the user's optimal path combination. The optimal channel combination matrix is ;

[0033] S32: Initialize the set, setting the selected user set to an empty set. The orthogonal basis matrix is ​​empty. ;

[0034] Iterate through all candidate users and calculate the total multipath energy for each user. The user with the highest energy level is selected as the first user to join. Using Schmidt orthogonalization, the first selected user Orthogonalize the path vectors to serve as the initial orthogonal basis. ;

[0035] S33: For each unselected user remaining in the user pool Define the metric. For all of this user The path vectors in the current orthogonal basis The sum of the projected energies on the orthogonal complement of the spanned subspace: ,in For the first The user after the first level of screening Channel vectors of each path, Indicates user The The path vectors relative to the current orthogonal basis orthogonal components;

[0036] S34: Select the measure value Maximize users Add to the selected user set , the user of The path vectors are orthogonalized using the Schmitt method, and the resulting unit orthogonal vectors are extended to the current orthogonal basis. middle;

[0037] S35: Repeat steps S31 to S34 until the selected user set is reached. The number of users has reached the preset value.

[0038] Preferably, in step S4, the optimization method used in the single-user scenario is as follows:

[0039] Construct an objective function to maximize the confidentiality capacity of legitimate channels. By solving the problem of maximizing the security capacity while satisfying amplitude alignment constraints and interference cancellation requirements, the digital precoding matrix is ​​obtained. With DMA simulation weight matrix The objective function is:

[0040] ;

[0041] The constraints are:

[0042] ;

[0043] ;

[0044] when hour, ;

[0045] in, The average power of the constellation group. For the expected receive gain, The variance of additive white Gaussian noise, For DMA transfer response matrix, For the transmitted signal vector, Rated power, The optimal channel vector. A digital precoding matrix vector;

[0046] To decouple variables, the digital precoding matrix is... Represented as the pseudo-inverse form of the equivalent channel The equivalent channel matrix is Substitute into the total transmit power constraint Calculate the receiving gain ;

[0047] Among them, the DMA simulates the weight matrix Represented as a diagonal matrix, i.e. , , , For adjustable phase shift parameters Control vector, For the sake of vectors The relevant function represents the digital precoding matrix. For the sake of vectors The relevant function represents the expected received gain. For the sake of vectors The pseudo-inverse form of the equivalent channel represented by the relevant function. This represents the conjugate transpose of the optimal channel matrix. For the transmitted signal vector The covariance matrix, , , For the number of multipaths, Number of DMA elements;

[0048] The objective function The joint optimization is transformed into an unconstrained black-box optimization with respect to the DMA phase vector only. The constraints are The optimal DMA simulation weight matrix is ​​directly searched in the phase space using the Nelder-Mead algorithm. And based on this, the digital precoding matrix is ​​calculated. .

[0049] Preferably, in step S4, in a multi-user scenario, after obtaining the legally optimal multipath channel matrix for legal users, a step-by-step manifold optimization and orthogonal strategy are used to obtain the digital precoding matrix and the DMA simulated weight matrix:

[0050] First, analog domain tuning is performed to construct a directional channel matrix containing multipath components of all selected users. Define the equivalent channel and its Gram matrix To minimize the Gram matrix The off-diagonal element energy is the objective function, i.e. ; satisfying the constant mode constraint of the DMA radiating unit Under the given conditions, the optimal DMA simulation weight matrix is ​​solved using a manifold optimization algorithm. ;

[0051] Next, digital domain zero-forcing and power normalization are performed. Based on the established parameters, all user multipath channels are stacked to form the overall equivalent channel matrix. Based on the homogeneity and orthogonality constraints required for the transmission of additively uniquely decomposable constellation groups, an equivalent matrix equation is constructed. Using pseudo-inverse to compute unnormalized zero-forcing basis ;

[0052] Finally, the system's total transmit power boundary constraints are utilized. Calculate the optimal receive gain The optimal digital precoding matrix is ​​obtained by scaling the unnormalized basis proportionally. .

[0053] Preferably, the minimum distance criterion is:

[0054] ;

[0055] in, In order to receive signals, for The sum of the sent symbols, The equivalent channel gain introduced for precoding.

[0056] The beneficial effects of this invention are:

[0057] 1) This invention uses a two-dimensional DMA array to replace the traditional all-digital array, which greatly reduces the number of RF links, hardware costs and power consumption. At the same time, Lorentz constraint modeling ensures engineering feasibility.

[0058] 2) This invention proposes a scenario-adaptive multipath selection and independent transmission strategy. Compared to random channel selection, the greedy path selection (single-user) and two-level selection strategy (multi-user) of this invention accurately eliminate highly correlated components during the preprocessing stage, significantly improving the channel condition number. This measure greatly reduces the power cost incurred by the system to satisfy the strict orthogonality of additive UDCG, converting the saved valuable transmit power into higher effective signal gain, thereby maximizing the system's security capacity.

[0059] 3) The precoding optimization scheme of the present invention does not require obtaining any channel state information of the eavesdropping party. It utilizes the natural spatial mismatch between the legitimate channel and the eavesdropping channel to degrade the signal that is optimized for the legitimate channel into strong interference at the eavesdropping end, thereby achieving efficient defense in passive eavesdropping scenarios.

[0060] 4) This invention designs targeted optimization algorithms for different scenarios. In single-user scenarios, Nelder-Mead gradient-free search is used to handle strongly coupled variables, while in multi-user scenarios, manifold optimization and ZF step-by-step strategy are used to reduce the computational complexity of large-scale variables. Attached Figure Description

[0061] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0062] Figure 1 This is the overall flowchart of the present invention.

[0063] Figure 2 This invention addresses the different numbers of transmission paths in a single-user scenario. Simulation diagram comparing the average security capacity of greedy path selection strategy and random path selection strategy under certain conditions.

[0064] Figure 3 This is a simulation diagram comparing the system and security capacity of the greedy user selection strategy based on subspace projection and the random user selection strategy in a multi-user scenario according to the present invention. Detailed Implementation

[0065] 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.

[0066] like Figure 1 As shown, this embodiment of the invention provides a physical layer secure transmission method based on multipath selection independent transmission, the specific steps of which are as follows:

[0067] S1: Construct a communication system including a transmitter and a receiver. The transmitter is equipped with a massive MIMO antenna, and the receiver is a legitimate user, but a passive eavesdropper exists. Obtain the multipath channel state information of the legitimate user at the receiver. There are many types of massive MIMO antennas; this invention takes a transmitter equipped with a two-dimensional dynamic metasurface antenna array as an example.

[0068] The process of obtaining multipath channel state information of legitimate users in the receiver is as follows:

[0069] Due to the two-dimensional dynamic metasurface antenna array having Each microstrip contains The system employs an orthogonal time-slot sampling strategy with one radiating element. In consecutive sampling time slots, the array phase shift is orthogonally reconstructed. Specifically, in the first... Each sampling time slot The first microstrip on each microstrip The phase of each radiating element is set to Make its equivalent weight The phase of the remaining units is set to Make its equivalent weight 0.

[0070] collect The received signals from each sampling time slot constitute a sampling matrix. The channel is estimated based on the minimum mean square error criterion combined with the pilot signal, using the following formula: ,in, For the estimated full channel vector, Pilot signal, For their conjugate, Indicates vectorization operation, Used to compensate for phase shift. This is the power correlation coefficient.

[0071] S2: Based on channel state information, an additively uniquely decomposable constellation group (UDCG) is assigned to each legitimate user, and each input message bit stream is mapped to a sub-constellation of the additively uniquely decomposable constellation group to obtain a symbol vector;

[0072] The definition of an additively uniquely decomposable constellation set is: for any If and only if Only then will there be ,So It is called an additively unique factorization constellation group, that is ;in, Represents a constellation point within a sub-constellation. Indicates another constellation point within a sub-constellation. Indicates sub-constellations, Indicates the number of sub-constellations.

[0073] For example, for a unique decomposition of a cross-shaped 8-QAM constellation set: and constellation is It can be broken down into three sub-constellations. , , Therefore, it satisfies .

[0074] Will A legitimate user parallel information bit stream As input, each piece of information is mapped to a symbol vector. A symbol , where each symbol From a pre-defined, additively unique, decomposable constellation group corresponding to each legitimate user, the different sub-constellations. Selected from the options.

[0075] S3: Determine the current communication scenario and execute the selection strategy.

[0076] In a single-user scenario, a greedy path selection strategy is executed based on channel state information to select the optimal transmission path combination from the user's candidate paths; using the Gram determinant as a metric, the optimal path combination is selected from the user's candidate paths one by one. Choose from candidate paths Find the optimal path to maximize channel gain and orthogonality.

[0077] In a single-user scenario, the method for implementing a greedy path selection strategy is as follows:

[0078] Candidate path set for single user Bob ,Include Candidate paths; initialize the selected set to an empty set, and set the selected path set to an empty set. The candidate path set is ; using Gram determinant As a metric, among The set of selected paths The corresponding channel matrix;

[0079] The total number of iterations is ; in the In the next iteration, based on the set determined in the previous round... Iterate through the current remaining candidate set. Each path in ,in, ; calculation will The new metric generated after adding to the current set: Select the path that maximizes the metric. Add to collection: .

[0080] The selected optimal path is added to the set of selected paths and removed from the set of candidate paths. , .

[0081] When the maximum number of iterations is reached Stop iterating when the time is right, and output the final selected optimal path combination. and the corresponding channel matrix .

[0082] In multi-user scenarios, a two-level selection strategy is executed: First, all users in the user pool are traversed, and a greedy path selection strategy is applied to the candidate paths of each user, selecting the path from the available paths. Filtering from candidate paths The first stage selects the optimal path combination for each user, forming the optimal transmission path combination for that user. This ensures that each candidate user is in the optimal state under its own channel conditions. The second stage, based on the optimal transmission path combinations selected for each user, executes a greedy user selection strategy based on subspace projection, utilizing projection energy. As an evaluation function, users are selected successively from the user pool. The user with the least spatial interference.

[0083] In multi-user scenarios, the greedy user selection strategy based on subspace projection is as follows:

[0084] S31: Iterate through all users in the user pool For each user's candidate paths, a greedy path selection strategy is executed to filter out the optimal combination of transmission paths for that user, thus obtaining the user's optimal path combination. The optimal channel combination matrix is ;

[0085] S32: Initialize the set, setting the selected user set to an empty set. The orthogonal basis matrix is ​​empty. ;

[0086] Iterate through all candidate users and calculate the total multipath energy for each user. The user with the highest energy level is selected as the first user to join. Using Schmidt orthogonalization, the first selected user Orthogonalize the path vectors to serve as the initial orthogonal basis. ;

[0087] S33: For each unselected user remaining in the user pool Define the metric. For all of this user The path vectors in the current orthogonal basis The sum of the projected energies on the orthogonal complement of the spanned subspace: ,in For the first The user after the first level of screening Channel vectors of each path, Indicates user The The path vectors relative to the current orthogonal basis orthogonal components;

[0088] S34: Select the measure value Maximize users Add to the selected user set , the user of The path vectors are orthogonalized using the Schmitt method, and the resulting unit orthogonal vectors are extended to the current orthogonal basis. middle;

[0089] S35: Repeat steps S31 to S34 until the selected user set is reached. The number of users has reached the preset value.

[0090] S4: Based on the equivalent channel formed by the selected optimal transmission path combination or optimal user combination, for different scenarios, under the condition of satisfying orthogonality constraints, different optimization methods are used to jointly design the digital precoding matrix and the DMA simulated weight matrix.

[0091] The optimization method used in single-user scenarios is as follows:

[0092] Construct an objective function to maximize the confidentiality capacity of legitimate channels. By solving the problem of maximizing the security capacity while satisfying amplitude alignment constraints and interference cancellation requirements, the digital precoding matrix is ​​obtained. With DMA simulation weight matrix The objective function is:

[0093] ,

[0094] in, The average power of the constellation group. For the expected receive gain, The variance is the additive white Gaussian noise.

[0095] The constraints are:

[0096] ;

[0097] ;

[0098] when hour, ;

[0099] in, For DMA transfer response matrix, For the transmitted signal vector, Rated power, The optimal channel vector. It is a digital precoding matrix vector.

[0100] To decouple variables, the digital precoding matrix is... Represented as the pseudo-inverse form of the equivalent channel The equivalent channel matrix is Substitute into the total transmit power constraint Calculate the receiving gain .

[0101] Among them, the DMA simulates the weight matrix Represented as a diagonal matrix, i.e. , , , For adjustable phase shift parameters Control vector, For the sake of vectors The relevant function represents the digital precoding matrix. For the sake of vectors The relevant function represents the expected received gain. For the sake of vectors The pseudo-inverse form of the equivalent channel represented by the relevant function. This represents the conjugate transpose of the optimal channel matrix. For the transmitted signal vector The covariance matrix, , , For the number of multipaths, This represents the number of DMA elements.

[0102] The objective function The joint optimization is transformed into an unconstrained black-box optimization with respect to the DMA phase vector only. The constraints are The optimal DMA simulation weight matrix is ​​directly searched in the phase space using the Nelder-Mead algorithm. And based on this, the digital precoding matrix is ​​calculated. .

[0103] In multi-user scenarios, after obtaining the legal optimal multipath channel matrix for legitimate users, a step-by-step manifold optimization and orthogonal strategy are used to obtain the digital precoding matrix and the DMA simulated weight matrix.

[0104] The first step is to simulate domain DMA tuning and construct a directional channel matrix containing multipath components of all selected users. Define the equivalent channel and its Gram matrix The objective function is to minimize the energy of the off-diagonal elements of the Gram matrix. Under the condition of satisfying the constant mode constraint of DMA radiating unit Under the given conditions, the optimal DMA simulation weight matrix is ​​solved using a manifold optimization algorithm. .

[0105] Next, digital domain zero-forcing and power normalization are performed. Based on the established parameters, all user multipath channels are stacked to form the overall equivalent channel matrix. Based on the homogeneity and orthogonality constraints required for the transmission of additively uniquely decomposable constellation groups, an equivalent matrix equation is constructed. Using pseudo-inverse to compute unnormalized zero-forcing basis .

[0106] Finally, to maximize power utilization, the system's total transmit power boundary constraints are utilized. Calculate the optimal receive gain The optimal digital precoding matrix is ​​obtained by scaling the unnormalized basis proportionally. .

[0107] Get A legitimate user 3D legal optimal multipath channel matrix Among them, users Multipath channels are ,in For the number of DMA elements, For the number of multipaths, For the first The first user's Path 3D channel vector. The selected channel matrix... As input, the digital precoding matrix is ​​obtained through a scene-adaptive optimization method. With DMA simulation weight matrix .

[0108] S5: Multiply the symbol vector by the optimized digital precoding matrix and the DMA analog weight matrix to obtain the transmitted signal vector. .

[0109] S6: The transmitted signal vector is radiated by a two-dimensional DMA array and transmitted through a wireless channel to the receiving end, thus obtaining the received signal.

[0110] S7: The receiver detects the received signal and solves for the most likely sum constellation symbol based on the minimum distance criterion.

[0111] The minimum distance criterion is:

[0112] ;

[0113] in, In order to receive signals, for The sum of the sent symbols, The equivalent channel gain introduced for precoding.

[0114] S8: Utilizing the unique decomposability property of additively unique decomposable constellation groups, decompose the most likely sum constellation symbols and restore them to unique sub-constellation symbol vectors.

[0115] S9: Demodulate each symbol in the recovered sub-constellation symbol vector to obtain the final recovered message bitstream.

[0116] A specific example is as follows: Taking a single user as an example, the DMA microstrip number Nt=4, the number of elements per microstrip array Nr=4 (total number of elements M=16), the preset number of candidate paths N=8, the target transmission multipath number K=3, and the transmitted signal bit data m: [010110000110001;1010000011010010;1011011000011001]

[0118] The modulated transmitted symbol matrix s (3×16 dimensions) is obtained by using the uniquely decomposed constellation groups X1=[-2-i,-i], X2=[-1,1+2i], and X3=[i,2-i].

[0119] [-2-1i, -0-1i, -2-1i, -0-1i, -0-1i, -2-1i, -2-1i, -2-1i, -2-1i, -0-1i, -0-1i, -0-1i, -2-1i, -2-1i, -2-1i, -0-1i;1+2i, -1, 1+2i, -1, -1, -1, -1,-1, 1+2i, 1+2i, -1, 1+2i, -1, -1, 1+2i, -1;2-1i, 0+1i, 2-1i, 2-1i, 0+1i, 2-1i, 2-1i, 0+1i, 0+1i, 0+1i, 0+1i, 2-1i, 2-1i, 0+1i, [0+1i, 2-1i]

[0120] The receiver estimates eight candidate multipath channel matrices H_candidates (16×8 dimensions):

[0121] [0.027-0.057i,0.211+0.371i,-0.243-0.169i,-0.080-0.130i,-0.134+0.017i,-0.061+0.242i,0.142+0.173i,-0.091-0.352i;-0.063+0.006i, 0.359+0.231i,0.263-0.135i,-0.132+0.077i,-0.003-0.135i,0.217+0. 123i,0.205-0.091i,-0.338+0.134i;0.037+0.051i,0.425+0.038i,-0.0 04+0.296i,0.075+0.133i,0.135+0.012i,0.177-0.177i,-0.032-0.222i,0.175+0.318i;0.024-0.058i,0.395-0.163i,-0.259-0.142i,0.135-0. 072i, -0.027+0.133i, -0.124-0.217i, -0.222-0.029i, 0.294-0.214i; 0.035+0.053i, -0.400-0.150i, 0.287-0.072i, 0.131+0.079i, 0.083-0.107i -0.085, -0.235i, -0.224 + 0.003i, 0.260 + 0.253i; 0.027 - 0.057i, -0.424 + 0.052i, -0.070 + 0.287i, 0.081 - 0.129i, 0.097 + 0.094i, -0.249 + 0.020i, - 0.057+0.217i,0.219-0.290i;-0.063+0.006i,-0.351+0.242i,-0.221-0.197i,-0.128-0.084i,-0.104+0.086i,-0.046+0.246i,0.193+0.113i,-0 .315-0.181i;0.037+0.051i,-0.199+0.378i,0.277-0.103i,-0.086+0.1 26i,-0.074-0.113i,0.225+0.110i,0.161-0.156i,-0.140+0.335i;-0.0 63+0.003i,0.403-0.141i,-0.133+0.264i,-0.152-0.010i,0.016+0.134 i,0.203+0.146i,0.137-0.177i,-0.354-0.081i;0.035+0.053i,0.292-0.311i,-0.171-0.241i,-0.013+0.152i,-0.135+0.001i,0.195-0.157i,-0.134-0.179i,-0.036+0.361i;0.0 27-0.057i,0.115-0.411i,0.293-0.038i,0.152+0.016i,0.013-0.135i,-0.100-0.229i,-0.209+0.081i,0. 363-0.010i;-0.063+0.006i,-0.088-0.418i,-0.104+0.277i,0.019-0.152i,0.132+0.028i,-0.247+0.035i ,0.022+0.223i,-0.055-0.359i;0.030-0.055i,-0.220+0.366i,-0.112-0.274i,0.140-0.061i,-0.106-0.0 84i,-0.250-0.007i,0.053+0.217i,0.345-0.115i;-0.063+0.003i,-0.025+0.426i,0.294+0.029i,-0.059- 0.141i,0.095-0.096i,-0.073+0.239i,0.224+0.007i,-0.157-0.327i;0.035+0.053i,0.175+0.389i,-0.16 3+0.247i,-0.142+0.056i,0.085+0.105i,0.211+0.134i,0.067-0.214i,-0.305+0.197i;0.027-0.057i,0.3 35+0.264i,-0.141-0.260i,0.053+0.143i,-0.114+0.073i,0.185-0.168i,-0.188-0.122i,0.234+0.278i].

[0122] A greedy path selection strategy based on Gram determinant is implemented, and the optimal path combination index selected from the candidate set is: [2 8 3]. The optimal transmission legal multipath channel matrix H_B (16×3 dimensional) after filtering is:

[0123] [0.211+0.371i,-0.091-0.352i,-0.243-0.169i;0.359+0.231i,-0.338+0.134i,0.263-0.135i ;0.425+0.038i,0.175+0.318i,-0.004+0.296i;0.395-0.163i,0.294-0.214i,-0.259-0.142i;- 0.400-0.150i,0.260+0.253i,0.287-0.072i;-0.424+0.052i,0.219-0.290i,-0.070+0.287i;- 0.351+0.242i,-0.315-0.181i,-0.221-0.197i;-0.199+0.378i,-0.140+0.335i,0.277-0.103i; 0.403-0.141i,-0.354-0.081i,-0.133+0.264i;0.292-0.311i,-0.036+0.361i,-0.171-0.241i ;0.115-0.411i,0.363-0.010i,0.293-0.038i;-0.088-0.418i,-0.055-0.359i,-0.104+0.277i; -0.220+0.366i,0.345-0.115i,-0.112-0.274i;-0.025+0.426i,-0.157-0.327i,0.294+0.029i ;0.175+0.389i,-0.305+0.197i,-0.163+0.247i;0.335+0.264i,0.234+0.278i,-0.141-0.260i]

[0124] DMA transfer response matrix G (16×4-dimensional block diagonal matrix, full matrix display):

[0125] [1.000,0.000,0.000,0.000;0.998-0.003i,0.000,0.000,0.000;0. 995-0.006i,0.000,0.000,0.000;0.993-0.009i,0.000,0.000,0.000 ;0.000,1.000,0.000,0.000;0.000,0.998-0.003i,0.000,0.000;0. 000,0.995-0.006i,0.000,0.000;0.000,0.993-0.009i,0.000,0.000 ;0.000,0.000,1.000,0.000;0.000,0.000,0.998-0.003i,0.000;0. 000,0.000,0.995-0.006i,0.000;0.000,0.000,0.993-0.009i,0.000 ;0.000,0.000,0.000,1.000;0.000,0.000,0.000,0.998-0.003i;0.0 00,0.000,0.000,0.995-0.006i;0.000,0.000,0.000,0.993-0.009i]

[0126] The diagonal element diag(q) of the optimal DMA simulation weight matrix Q (16×1 dimension, satisfying Lorentz constraints) obtained by using the Nelder-Mead algorithm with multiple restarts:

[0127] [0.494+0.580i,0.389+0.814i,0.490+0.598i,-0.327+0.122i,-0.197+0.960i,-0.499+0.473i,0.478+0.354i,0.002+1.000i ,-0.423+0.767i,0.017+0.000i,0.066+0.996i,0.443+0.733i,-0.124+0.984i,0.265+0.924i,0.452+0.286i,0.179+0.033i]

[0128] The digital precoding matrix F (4×3 dimension) is calculated through zero-forcing in the digital domain and optimal power allocation:

[0129] [0.457-0.153i,-0.060+0.441i,0.835-0.548i;0.436-0.277i,0.510-0.511i,0.180-1.930i;- 0.313-0.778i,-1.436-0.915i,-0.052-1.379i;0.266+0.017i,-1.255-0.303i,0.332-0.049i]

[0130] The transmitted symbol vector s is concatenated with the precoding matrix F, the response matrix G, and the analog weight matrix Q to synthesize the transmitted signal vector x (16×16 dimensional, full matrix display):

[0131] [0.583-1.384i,0.262+0.233i,0.583-1.384i,2.148-0.800i,0.262+0.2] 33i,1.520-1.180i,1.520-1.180i,-0.367-0.147i,-1.304-0.352i,-0.6 75+0.028i,0.262+0.233i,1.212-1.005i,1.520-1.180i,-0.367-0.147i ,-1.304-0.352i,2.148-0.800i;1.081-1.409i,0.230+0.344i,1.081-1. 409i, 2.696-0.272i, 0.230+0.344i, 2.091-0.894i, 2.091-0.894i, -0.376-0.278i, -1.386-0.792i, -0.780-0.170i, 0.230+0.344i, 1.686-0.786i 2.091-0.894i,-0.376-0.278i,-1.386-0.792i,2.696-0.272i;0.607-1.392i,0.262+0.239i,0.607-1.392i,2.183-0.782i,0.262+0.239i,1.552 -1.174i, 1.552-1.174i, -0.369-0.153i, -1.314-0.372i, -0.683+0.020i, 0.262+0.239i, 1.238-1.001i, 1.552-1.174i, -0.369-0.153i, -1.314-0 .372i,2.183-0.782i;0.507+0.461i,-0.140+0.077i,0.507+0.461i,0.018+1.045i,-0.140+0.077i,0.277+0.832i,0.277+0.832i,0.119-0.135i, 0.349-0.507i, 0.090-0.294i, -0.140+0.077i, 0.248+0.673i, 0.277+0.832i, 0.119-0.135i, 0.349-0.507i, 0.018+1.045i; 3.509-0.467i, -0.470 +1.047i,3.509-0.467i,4.269-1.482i,-0.470+1.047i,3.909-2.427i,3 .909-2.427i,-0.830+0.102i,-1.230+2.062i,-0.870+3.007i,-0.470+1.047i, 3.869 + 0.478i, 3.909 - 2.427i, - 0.830 + 0.102i, - 1.230 + 2.062i, 4.269 - 1.482i; 2.206 + 1.133i, - 0.689 + 0.415i, 2.206 + 1.133i, 3.048 + 0.853i -0.689+0.415i,3.219+0.165i,3.219+0.165i,-0.518-0.273i,-1.532+0 .695i,-1.702+1.383i,-0.689+0.415i,2.035+1.821i,3.219+0.165i,-0. 518-0.273i,-1.532+0.695i,3.048+0.853i;0.626-2.047i,0.458+0.522i,0.626-2.047i,0.259-2.721i,0.458+0.522i,-0.351-2.761i,-0.351-2 .761i,-0.153+0.482i,0.824+1.195i,1.435+1.235i,0.458+0.522i,1.237-2.008i,-0.351-2.761i,-0.153+0.482i,0.824+1.195i,0.259-2.721i ;3.376-1.218i,-0.241+1.138i,3.376-1.218i,3.910-2.386i,-0.241+1.138i,3.350-3.245i,3.350-3.245i,-0.801+0.280i,-0.775+2.307i,-0. 215+3.166i,-0.241+1.138i,3.936-0.359i,3.350-3.245i,-0.801+0.280i,-0.775+2.307i,3.910-2.386i;4.071+1.003i,-1.763+1.065i,4.071+ 1.003i,1.483-0.008i,-1.763+1.065i,0.025-0.186i,0.025-0.186i,-3 .221+0.887i,0.825+2.076i,2.284+2.254i,-1.763+1.065i,5.530+1.182 i,0.025-0.186i,-3.221+0.887i,0.825+2.076i,1.483-0.008i;-0.020-0 .081i,0.035+0.021i,-0.020-0.081i,-0.014-0.026i,0.035+0.021i,-0.003+0.001i,-0.003+0.001i,0.046+0.048i,0.029-0.034i,0.018-0.061 i,0.035+0.021i,-0.031-0.108i,-0.003+0.001i,0.046+0.048i,0.029- 0.034i,-0.014-0.026i;4.491-1.564i,-1.018+2.103i,4.491-1.564i,1.405-0.924i,-1.018+2.103i,-0.092-0.192i,-0.092-0.192i,-2.514+2. 836i, ​​2.069+1.463i, 3.565+0.731i, -1.018+2.103i, 5.988-2.297i, -0.092-0.192i, -2.514+2.836i, ​​2.069+1.463i, 1.405-0.924i; 2.791-2.963i 0.059+1.999i,2.791-2.963i,0.701-1.257i,0.059+1.999i,-0.145-0.109i,-0.145-0.109i,-0.788+3.146i,2.149+0.293i,2.995-0.855i,0.059 +1.999i, 3.638-4.110i, -0.145-0.109i, -0.788+3.146i, 2.149+0.293i, 0.701-1.257i; 3.555-0.103i, -0.526+1.255i, 3.555-0.103i, 0.154+1.90 6i,-0.526+1.255i,0.254+1.386i,0.254+1.386i,-0.427+0.735i,2.874 -0.755i,2.775-0.235i,-0.526+1.255i,3.456+0.417i,0.254+1.386i,-0 0.427+0.735i,2.874-0.755i,0.154+1.906i;3.117-1.452i,0.013+1.315i,3.117-1.452i,0.866+1.633i,0.013+1.315i,0.756+1.134i,0.756+1.1 34i,-0.098+0.816i,2.263-1.770i,2.374-1.270i,0.013+1.315i,3.227-0.952i,0.756+1.134i,-0.098+0.816i,2.263-1.770i,0.866+1.633i;0.751-1.755i,0.493+0.539i,0.751-1.755i,0.963+0.354i,0.493+0.539i,0.733+0.189i,0.733+0.189i,0.262+0.374i,0. 0.0 12-0.646i,0.223+0.107i,0.012-0.646i,0.347-0.011i,0.223+0.107i,0.254-0.034i,0.254-0.034i,0.130+0.084i,-0. 112-0.528i,-0.018-0.506i,0.223+0.107i,0.106-0.624i,0.254-0.034i,0.130+0.084i,-0.112-0.528i,0.347-0.011i].

[0132] The scalar signal y received by the legitimate receiver after coherent superposition of the equivalent channel gain and the addition of noise is:

[0133] [1.313+0.001i,-1.323+0.004i,1.307-0.008i,1.295-2.620i,-1.308-0.013i,-1.310-2.626i,-1.309-2.634i,-3.928-0.003i ,-1.297+2.612i,1.306+2.616i,-1.301+0.010i,3.928+0.002i,-1.296-2.620i,-3.931-0.014i,-1.328+2.630i,1.324-2.619i]

[0134] Utilizing the unique decomposability property of UDCG, the sub-constellation symbol vector s_hat is correctly decomposed according to the minimum distance criterion:

[0135] [-2-1i,-0-1i,-2-1i,-0-1i,-0-1i,-2-1i,-2-1i,-2-1i,-2-1i,-0-1 i,-0-1i,-0-1i,-2-1i,-2-1i,-2-1i,-0-1i;1+2i,-1,1+2i,-1,-1,-1 ,-1,-1,1+2i,1+2i,-1,1+2i,-1,-1,1+2i,-1;2-1i,0+1i,2-1i,2-1i, 0+1i,2-1i,2-1i,0+1i,0+1i,0+1i,0+1i,2-1i,2-1i,0+1i,0+1i,2-1i]

[0136] Figure 2 This is a simulation graph comparing the performance of greedy path selection and random path selection in terms of average security capacity under single-user conditions. The horizontal axis represents the signal-to-noise ratio (SNR) of legitimate users, in dB; a gradually increasing value indicates better communication quality on the main channel. The vertical axis represents the average security capacity of the system, in bps / Hz; a higher value indicates better system security performance. The simulation compares different numbers of transmission paths. Below, the performance difference between the greedy path selection (GPS, solid line marker) and random path selection (Rand, dashed line marker) proposed in this invention is discussed.

[0137] Depend on Figure 2 It can be seen that the security capacity of all schemes increases with the increase of SNR. In any given... Under these conditions, the GPS strategy of this invention significantly outperforms the random selection strategy. This is because the GPS algorithm uses Gram determinant as a metric, effectively eliminating highly correlated multipath components during the iterative selection process, while retaining paths with high channel gain and mutual orthogonality. This reduces inter-flow interference at the physical level and greatly improves the equivalent quality of legitimate channels. Furthermore, compared with different... The value shows that as the number of parallel transmission paths increases... With the increase in [something], the confidentiality capacity has decreased (i.e.) (Optimal performance). This is because, with limited total transmit power, in order to meet the more stringent multipath orthogonality and alignment constraints of the Additive Uniquely Decomposable Constellation Group (UDCG), the system needs to consume more spatial degrees of freedom and transmit power to eliminate coupling interference between multiple paths. Nevertheless, in Under high constraints, the GPS algorithm still maintains a considerable safe transmission rate, proving its robustness in complex multipath environments.

[0138] Figure 3The figure shows the performance curves of the system's total security capacity as a function of the signal-to-noise ratio in a multi-user scenario. The solid line (Proposed) in the figure represents the greedy user selection strategy (SUS) based on subspace projection proposed in this invention, and the dashed line (Random) represents the traditional random user selection strategy.

[0139] Figure 3 It is evident that the SUS strategy of this invention exhibits an overwhelming advantage in both security capacity and overall security across the entire SNR range, and the performance gap between the two widens further as the signal-to-noise ratio increases. At an SNR of 30dB, the security capacity of this invention reaches approximately 36 bits / s / Hz, while the random selection scheme achieves only approximately 20 bits / s / Hz. This significant performance improvement is attributed to the two-stage selection mechanism of this invention: the SUS algorithm accurately selects the set of legitimate users with the best multipath spatial orthogonality during the preprocessing stage. Since the subspace spanned by all multipath components of the selected users is as orthogonal as possible to other users, the condition number of the total equivalent channel matrix is ​​greatly improved. This not only enables subsequent orthogonal precoding to eliminate multi-user interference and inter-stream interference at extremely low power cost, but also ensures that the transmitted signal energy is focused precisely on legitimate users, and degrades into strong endogenous interference at the eavesdropping end due to channel mismatch, thus perfectly achieving implicit suppression of passive eavesdroppers and maximizing the overall security capacity of the multi-user system.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A physical layer secure transmission method based on multipath selection independent transmission, characterized in that, The steps are as follows: S1: Construct a communication system including a transmitter and a receiver. The transmitter is equipped with a massive MIMO antenna, and the receiver is a legitimate user with a passive eavesdropper present. Obtain the multipath channel state information of the legitimate user in the receiver. S2: Based on multipath channel state information, an additively unique decomposable constellation group is matched for each legitimate user according to the number of multipaths. Each input message bit stream is mapped to a sub-constellation of the additively unique decomposable constellation group to obtain a symbol vector. S3: Determine the current communication scenario. If it is a single-user scenario, execute a greedy path selection strategy based on multipath channel state information to select the optimal transmission path combination from the user's candidate paths. If it is a multi-user scenario, execute a two-level selection strategy: First, traverse all users in the user pool and execute a greedy path selection strategy for each user's candidate paths to select the optimal transmission path combination for that user. Second, based on the optimal transmission path combinations selected by each user, execute a greedy user selection strategy based on subspace projection to select the optimal user combination from the user pool. S4: Based on the equivalent channel formed by the selected optimal transmission path combination or optimal user combination, for different scenarios, under the condition of satisfying orthogonality constraints, different optimization methods are used to jointly design the digital precoding matrix and the DMA simulated weight matrix. S5: Multiply the symbol vector with the optimized digital precoding matrix and analog precoding matrix to obtain the transmitted signal vector; S6: The transmitted signal vector reaches the receiving end after being radiated by a large-scale MIMO antenna and transmitted through a wireless channel, thus obtaining the received signal; S7: The receiver detects the received signal and solves for the most likely sum constellation symbol based on the minimum distance criterion; S8: Utilize the unique decomposability property of additively unique decomposable constellation groups to decompose the most likely sum constellation symbols and restore them to unique sub-constellation symbol vectors; S9: Demodulate each symbol in the recovered sub-constellation symbol vector to obtain the final recovered message bitstream.

2. The physical layer secure transmission method based on multipath selection independent transmission according to claim 1, characterized in that, The method for obtaining the multipath channel state information of legitimate users in step S1 is as follows: The sender configuration includes Each microstrip contains A two-dimensional dynamic metasurface antenna with radiating elements, in In consecutive sampling time slots, the phase shift of the dynamic metasurface antenna is orthogonally reconstructed, at the th... In each sampling time slot, the first sample on each microstrip will be... The phase of each radiating element is set to Make its equivalent weight The phase of the remaining units is set to Set its equivalent weight to 0; collect The received signals from each sampling time slot constitute a sampling matrix. The channel is estimated based on the minimum mean square error criterion combined with the pilot signal, using the following formula: ， in, , For the estimated full channel vector, Pilot signal, for conjugate, Indicates vectorization operation, Used to compensate for phase shift. This is the power correlation coefficient.

3. The physical layer secure transmission method based on multipath selection independent transmission according to claim 1, characterized in that, The definition of the additively uniquely decomposable constellation group is: For any If and only if Only then will there be ,So It is called an additively unique factorization constellation group, that is ;in, Represents a constellation point within a sub-constellation. Indicates another constellation point within a sub-constellation. Indicates sub-constellations, Indicates the number of sub-constellations.

4. The physical layer secure transmission method based on multipath selection independent transmission according to claim 1, characterized in that, In a single-user scenario, the method for implementing a greedy path selection strategy is as follows: Candidate path set for single user Bob ,Include Candidate paths; initialize the selected set to an empty set, and set the selected path set to an empty set. The candidate path set is ; using Gram determinant As a metric, among The set of selected paths The corresponding channel matrix; The total number of iterations is ; in the In the next iteration, based on the set determined in the previous round... Iterate through the current remaining candidate set. Each path in ,in, ; calculation will The new metric generated after adding to the current set: Select the path that maximizes the metric. Add to collection: ; The selected optimal path is added to the set of selected paths and removed from the set of candidate paths. , ; When the maximum number of iterations is reached Stop iterating when the time is right, and output the final selected optimal path combination. and the corresponding channel matrix .

5. The physical layer secure transmission method based on multipath selection independent transmission according to claim 1, characterized in that, In multi-user scenarios, the greedy user selection strategy based on subspace projection is as follows: S31: Iterate through all users in the user pool For each user's candidate paths, a greedy path selection strategy is executed to filter out the optimal combination of transmission paths for that user, thus obtaining the user's optimal path combination. The optimal channel combination matrix is ; S32: Initialize the set, setting the selected user set to an empty set. The orthogonal basis matrix is ​​empty. ; Iterate through all candidate users and calculate the total multipath energy for each user. The user with the highest energy level is selected as the first user to join. Using Schmidt orthogonalization, the first selected user Orthogonalize the path vectors to serve as the initial orthogonal basis. ; S33: For each unselected user remaining in the user pool Define the metric. For all of this user The path vectors in the current orthogonal basis The sum of the projected energies on the orthogonal complement of the spanned subspace: ,in For the first The user after the first level of screening Channel vectors of each path, Indicates user The The path vectors relative to the current orthogonal basis orthogonal components; S34: Select the measure value Maximize users Add to the selected user set , the user of The path vectors are orthogonalized using the Schmitt method, and the resulting unit orthogonal vectors are extended to the current orthogonal basis. middle; S35: Repeat steps S31 to S34 until the selected user set is reached. The number of users has reached the preset value.

6. The physical layer secure transmission method based on multipath selection independent transmission according to claim 4, characterized in that, In step S4, the optimization method used in the single-user scenario is as follows: Construct an objective function to maximize the confidentiality capacity of legitimate channels. By solving the problem of maximizing the security capacity while satisfying amplitude alignment constraints and interference cancellation requirements, the digital precoding matrix is ​​obtained. With DMA simulation weight matrix The objective function is: ； The constraints are: ； ； when hour, ; in, The average power of the constellation group. For the expected receive gain, The variance of additive white Gaussian noise, For DMA transfer response matrix, For the transmitted signal vector, Rated power, The optimal channel vector. A digital precoding matrix vector; To decouple variables, the digital precoding matrix is... Represented as the pseudo-inverse form of the equivalent channel The equivalent channel matrix is Substitute into the total transmit power constraint Calculate the receiving gain ; Among them, the DMA simulates the weight matrix Represented as a diagonal matrix, i.e. , , , For adjustable phase shift parameters Control vector, For the sake of vectors The relevant function represents the digital precoding matrix. For the sake of vectors The relevant function represents the expected received gain. For the sake of vectors The pseudo-inverse form of the equivalent channel represented by the relevant function. This represents the conjugate transpose of the optimal channel matrix. For the transmitted signal vector The covariance matrix, , , For the number of multipaths, Number of DMA elements; The objective function The joint optimization is transformed into an unconstrained black-box optimization with respect to the DMA phase vector only. The constraints are The optimal DMA simulation weight matrix is ​​directly searched in the phase space using the Nelder-Mead algorithm. And based on this, the digital precoding matrix is ​​calculated. .

7. The physical layer secure transmission method based on multipath selection independent transmission according to claim 6, characterized in that, In step S4, in a multi-user scenario, after obtaining the legally optimal multipath channel matrix for legitimate users, a step-by-step manifold optimization and orthogonal strategy are used to obtain the digital precoding matrix and the DMA simulated weight matrix: First, analog domain tuning is performed to construct a directional channel matrix containing multipath components of all selected users. Define the equivalent channel and its Gram matrix To minimize the Gram matrix The off-diagonal element energy is the objective function, i.e. ; satisfying the constant mode constraint of the DMA radiating unit Under the given conditions, the optimal DMA simulation weight matrix is ​​solved using a manifold optimization algorithm. ; Next, digital domain zero-forcing and power normalization are performed. Based on the established parameters, all user multipath channels are stacked to form the overall equivalent channel matrix. Based on the homogeneity and orthogonality constraints required for the transmission of additively uniquely decomposable constellation groups, an equivalent matrix equation is constructed. Using pseudo-inverse to compute unnormalized zero-forcing basis ; Finally, the system's total transmit power boundary constraints are utilized. Calculate the optimal receive gain The optimal digital precoding matrix is ​​obtained by scaling the unnormalized basis proportionally. .

8. The physical layer secure transmission method based on multipath selection independent transmission according to claim 1, characterized in that, The minimum distance criterion is: ； in, In order to receive signals, for The sum of the sent symbols, The equivalent channel gain introduced for precoding.

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