Secure transmission system and method of symbiotic radio system based on STAR-RIS assistance

Abstract

The invention discloses a symbiotic radio secure transmission system and method based on STAR-RIS assistance, and the method comprises the steps: collecting channel data among a transmitting base station, a primary user PU, a secondary user SUr and an eavesdropping user Eve, and designing a base station beam forming vector and a transmitting and transmission coefficient matrix of STAR-RIS; by introducing a reconfigurable intelligent surface capable of transmitting and reflecting at the same time, full coverage of space is realized through reflection and transmission of signals, and the flexibility of equipment deployment is greatly improved. According to the method for alternately optimizing the beam forming vector of the base station and the transmitting and transmitting coefficient matrix of the STAR-RIS, the bottommost communication secrecy rate of the secondary user can be greatly improved under the condition that the normal communication requirement and the power constraint of the system are met.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a secure transmission system and method based on a STAR-RIS-assisted symbiotic radio system. Background Art

[0002] In the sixth generation of mobile communications (6G), the large-scale coverage of IoT devices has put forward higher requirements for resources such as energy and spectrum. As a high-energy-efficiency, high-spectrum-utilization-low-cost technology, symbiotic radio (SR) is a promising technology in the future field of Internet-of-Things (IoD). The SR communication network aims to establish a mutually beneficial symbiotic relationship between the primary system transmission and the secondary system transmission, so that the primary system transmission and the secondary system transmission can simultaneously achieve energy efficiency and spectrum efficiency requirements. Since the backscattered information transmission experiences a double fading channel, on the one hand, the performance enhancement of the primary system is limited, and on the other hand, the performance of the secondary system is also limited. The symbiotic communication system assisted by the reconfigurable intelligent surface (RIS) can not only improve the channel environment and enhance the system performance, but also can be used as a secondary user transmitter to realize the transmission of secondary user information by passively adjusting the incident signal of each element. Since the traditional RIS can only realize the reflection of the signal, this requires the user and the base station to be deployed on the same side of the RIS, which limits the application scenarios of RTS and the deployment flexibility of the equipment. . Summary of the invention

[0003] The purpose of the present invention is to address the defects and shortcomings of the above-mentioned prior art and propose a symbiotic radio transmission system and method based on STAR-RIS assistance, which maximizes the minimum communication confidentiality rate of the secondary user SUr under the constraints of satisfying the minimum transmission rate of decoding the primary user PU signal and the minimum signal-to-noise ratio of decoding the secondary user SUr and SUt signals and the maximum threshold requirement of the eavesdropping rate of the eavesdropping user Eve, and minimizes the external transmission power of the base station under the constraints of STAR-RIS coupling. At the same time, the spatial full coverage characteristics of STAR-RIS make the equipment deployment more flexible.

[0004] The technical solution adopted by the present invention to solve its technical problems is: a symbiotic radio transmission system based on STAR-RIS assistance, the system comprising: the STAR-RIS is a reconfigurable intelligent reflection surface for simultaneous transmission and reflection, the STAR-RIS has a plurality of elements, each element comprises a reflection element and a transmission element, the STAR-RIS divides the target area into an R zone and a T zone, the R zone is a reflection zone, the T zone is a transmission zone, the symbiotic radio transmission system exists in the target area, comprises a base station, two secondary users SUr and SUt, a primary user PU and an eavesdropping user Eve, a STAR-RIS is set between the secondary user SUr and the secondary user SUt, the base station, the primary user PU, the secondary user SUr and the eavesdropping user Eve are located in the R zone of the STAR-RIS, wherein the eavesdropping user Eve only has the ability to eavesdrop on the secondary user SUr, the secondary user SUt is located in the T zone of the STAR-RIS, and the minimum communication confidentiality rate of the maximized secondary user SUr is obtained.

[0005] The present invention also proposes a method for implementing a symbiotic radio transmission system based on STAR-RIS assistance, the method comprising the following steps:

[0006] Step 1: Considering the existence of eavesdroppers and the imperfect CSI of the eavesdropping channel, a model for maximizing the minimum communication confidentiality rate of secondary users in the STAR-RIS-assisted symbiotic radio system under imperfect CSI is established;

[0007] Step 2: Initialize the relevant parameters of the target problem, including the channel data from the base station to the primary user PU, the channel data from the base station to STAR-RIS, the channel data from STAR-RIS to the primary user PU, the channel data from STAR-RIS to the secondary users SUr and SUt, the beamforming vector, the STAR-RIS reflection and transmission phase shift matrix, the quality of service threshold requirement, and the base station power threshold;

[0008] Step 3: Based on the channel data, base station beamforming vector, STAR-RIS reflection and transmission coefficient matrix obtained in step 1 above, construct the expression of the minimum communication confidentiality rate of the secondary user SUr;

[0009] Step 4: Based on the expression of the minimum communication confidentiality rate of the secondary user SUr, construct the problem of maximizing the minimum communication confidentiality rate of the secondary user SUr, give the STAR-RIS reflection and transmission coefficient matrix and calculate the base station beamforming vector that maximizes the minimum communication confidentiality rate of the secondary user SUr;

[0010] Step 5: Given the base station beamforming vector, calculate the STAR-RIS reflection and transmission coefficient matrix that maximizes the minimum communication confidentiality rate of the secondary user SUr;

[0011] Step 6: Repeat steps 4 and 5 until convergence. The solution obtained is the suboptimal solution to the problem of maximizing the security transmission rate of the secondary user SUr. ω in suboptimal solution * , That is, the base station beamforming vector that maximizes the security transmission rate of the secondary user SUr and the reflection transmission coefficient matrix of STAR-RIS.

[0012] Furthermore, in step 2, the legal primary user, the secondary user and the illegal eavesdropper are referred to as PU, SUr, SUt and Eve. The mathematical modeling method for the physical layer security problem of the downlink symbiotic radio system based on STAR-RIS under the condition of imperfect eavesdropper CSI specifically includes:

[0013] The channel data from STAR-RIS to the eavesdropping user Eve can be expressed as:

[0014]

[0015] Among them, C 1×M represents a 1×M complex matrix, || || represents the binary norm;

[0016] Then the SINR of PU, SUr, SUt and Eve are:

[0017]

[0018]

[0019] Among them, γ p (c) Signal-to-interference-noise ratio at the primary user PU, Φ r is the reflection coefficient matrix of STAR-RIS, ω is the beamforming vector of the base station, is the noise power at the primary user PU; is the channel data from the base station to the primary user PU, is the channel data from STAR-RIS to the primary user PU, G is the channel data from the base station to STAR-RIS, γ r (c), γ t (c) are the signal-to-interference-noise ratios of the secondary users SUr and SUt, R sur , R sut are the transmission rates of the secondary users SUr and SUt, Φ t is the transmission coefficient matrix of STAR-RIS, are the noise power at the secondary users SUr and SUt respectively; are the channel data from STAR-RIS to the secondary users SUr and SUt, respectively. N indicates that the symbol period of the secondary user SU is a multiple of the symbol period of the primary user PU. e (c) is the signal-to-interference-noise ratio of the eavesdropping user Eve, R e To eavesdrop on the transmission rate of user Eve, is the noise power at the eavesdropping user Eve; is the channel data from STAR-RIS to the eavesdropping user Eve;

[0020] The achievable communication rates of PU, SUr, SUt and Eve are:

[0021]

[0022] in,

[0023]

[0024] Since Eve's channel has channel estimation error, the minimum secure communication rate is:

[0025]

[0026] Optimize the base station active beamforming parameters and STAR-RIS passive beamforming parameters to maximize the minimum confidential communication rate, forming the following optimization problem model:

[0027]

[0028]

[0029] Where, M=={1, 2, ..., m, ..., M} is the set of STAR-RIS components, represents the reflection coefficient amplitude of the mth element of STAR-RIS, represents the reflection coefficient phase of the mth element of STAR-RIS, represents the transmission coefficient amplitude of the mth element of STAR-RIS, represents the transmission coefficient phase of the mth element of STAR-RIS, R s,min The minimum achievable rate of decoding the primary user signal required for the normal operation of the primary user PU, γ min The minimum signal-to-noise ratio of the decoded secondary user signal required for the normal operation of the secondary users SUr and SUt, C E Indicates the maximum eavesdropping rate that can be achieved by the eavesdropping user Eve.

[0030] Further, the alternate optimization in step 4 and step 5 respectively solves the beamforming vector of the base station and the reflection transmission coefficient matrix of STAR-RIS, specifically including:

[0031] Optimize the base station transmit beamforming vector under the condition of given STAR-RIS reflection coefficient matrix and transmission coefficient matrix, that is, fix Φ r and Φ t Optimize ω. At this time, the objective function and constraints are defined by the parameter ω. Define W = ωω H , F t =f t f t H , E p =H p +F p , And introduce slack variables τ, R' sur , μ, and use the S-procedure theorem to transform the secondary user SUr's secure transmission rate maximization problem P1 into the following form:

[0032]

[0033]

[0034] At this time, the problem is still non-convex, and the optimal solution of W cannot be directly obtained. To solve the optimization problem, the CVX tool is used to obtain the upper limit of log2(1+τ) in the objective function, and the non-convex restriction conditions are rewritten as standard convex optimization restrictions. The specific operation is as follows:

[0035]

[0036] Among them, τ (n) represents the Taylor expansion point of the nth iteration. At this time, the non-convex constraint condition is transformed into a convex constraint, and the problem of maximizing the secure transmission rate of the secondary user SUr can be rewritten as problem P2;

[0037]

[0038] However, due to the constraint condition Rank(W) = 1, the problem is still non-convex. By using the semi-positive definite relaxation method to relax the rank-one constraint, problem P2 is transformed into a convex optimization problem. The convex optimization problem is solved using the CVX tool, and it is proved that the solution to the problem after relaxing the rank to one still satisfies in Denotes the value obtained by solving the convex optimization problem, let τ (n)=τ, substitute the updated value into the convex optimization problem and iterate until convergence, and finally get the suboptimal solution W * , using eigenvalue decomposition from W * The suboptimal solution ω is obtained from * ;

[0039] Among them, the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and W represents the base station beamforming matrix;

[0040] Under the condition of obtaining the base station beamforming vector ω, the reflection and transmission coefficient matrices of STAR-RIS are optimized, that is, ω is fixed to optimize Φ r and Φ t That is (v r and v t ), in this case, the objective function and the constraints are defined by the parameter ω, defined as And introduce slack variables τ, R' sur , μ;

[0041] The problem P1 of maximizing the security transmission rate of the secondary user SUr is transformed into P3:

[0042]

[0043] In the same way as above, rewrite the objective function as follows:

[0044]

[0045] However, due to the constraint Rank(V l )=1,l∈{t,r} exists, the problem is still non-convex. By using the semi-positive definite relaxation method to relax the rank-one constraint, problem P3 is transformed into a convex optimization problem. The convex optimization problem is solved using the CVX tool, and it is proved that the solution of the problem after relaxing the rank to one still satisfies in Denotes the value obtained by solving the convex optimization problem, let τ (n) =τ, substitute the updated value into the convex optimization problem and iterate until convergence, and finally get V l ,l∈{t,r}, the suboptimal solution V l * ,l∈{t,r}, using eigenvalue decomposition from v l * ,l∈{t,r} to get v l ,l∈{t,r}, where the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and V l ,l∈{t,r} represents the reflection transmission coefficient matrix of STAR-RIS;

[0046] Solve P2 and P3 alternately until convergence. The solution obtained is the suboptimal solution to the problem of maximizing the secure transmission rate of the secondary user SUr. ω in suboptimal solution * , That is, the base station beamforming vector that maximizes the security transmission rate of the secondary user SUr and the reflection transmission coefficient matrix of STAR-RIS.

[0047] Beneficial effects:

[0048] 1. The present invention designs a symbiotic radio security transmission method based on STAR-RIS assistance, in which STAR-RIS can assist in transmitting the main user signal and effectively improve the performance of the main system.

[0049] 2. The STAR-RIS of the present invention can be used as a secondary user signal transmitter to transmit secondary user information and realize symbiotic communication.

[0050] 3. The present invention introduces a simultaneously transmitting and reflecting reconfigurable smart surface, which achieves full spatial coverage through signal reflection and transmission, greatly improving the flexibility of equipment deployment. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a model diagram of the STAR-RIS-assisted symbiotic radio system of the present invention.

[0052] Figure 2 This is a diagram showing the effect of the number of STAR-RIS units of the present invention on the minimum confidentiality rate of the secondary user SUr.

[0053] Figure 3 This is a curve diagram showing the variation of the minimum communication confidentiality rate of the secondary user with the base station transmission power threshold of the present invention.

[0054] Figure 4 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0055] The following is a detailed description of an embodiment of the present invention in conjunction with the accompanying drawings. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and specific operation process are given.

[0056] like Figure 1 The embodiment of the present invention proposes a symbiotic radio security transmission system based on STAR-RIS assistance. The symbiotic radio transmission system exists in the target area and includes a base station, secondary users SUr and SUt, a primary user PU, and an eavesdropping user Eve. Figure 1BS stands for base station. STAR-RIS is set between the secondary users SUr and SUt. STAR-RIS is a reconfigurable intelligent reflection surface that can transmit and reflect simultaneously. STAR-RIS has several elements, each of which includes a reflection element and a transmission element. The target area is divided into R zone and T zone. The R zone is the reflection zone, and the T zone is the transmission zone. The base station, the primary user PU, the secondary user SUr and the eavesdropping user Eve are located in the R zone of STAR-RIS, and the secondary user SUt is located in the T zone of STAR-RIS. The minimum communication confidentiality rate of the secondary user SUr is maximized to complete the radio transmission.

[0057] like Figure 4 As shown, the present invention also proposes a method for implementing a symbiotic radio transmission system based on STAR-RIS assistance, the method comprising:

[0058] Step 1: Considering the existence of eavesdroppers and the imperfect CSI of the eavesdropping channel, a model for maximizing the minimum communication confidentiality rate of secondary users in the STAR-RIS-assisted symbiotic radio system under imperfect CSI is established;

[0059] Step 2: Initialize the relevant parameters of the target problem, including the channel data from the base station to the primary user PU, the channel data from the base station to STAR-RIS, the channel data from STAR-RIS to the primary user PU, the channel data from STAR-RIS to the secondary users SUr and SUt, the beamforming vector, the STAR-RIS reflection and transmission phase shift matrix, the quality of service threshold requirement, and the base station power threshold;

[0060] The base station includes N t The STAR-RIS is a base station with M transmitting antennas, and includes M reflecting elements. The primary user PU, secondary users SUr and SUt, and eavesdropping user Eve are all single-antenna users.

[0061] The channel data from the base station to STAR-RIS is Represents M×N t The complex matrix of the channel data from the base station to the primary user PU is expressed as Represents 1×N t The complex matrix of the channel data from STAR-RIS to the primary user PU, from STAR-RIS to the secondary users SUr and SUt, and from STAR-RIS to the eavesdropping user Eve are expressed as: C 1×M Represents a 1×M complex matrix.

[0062] Considering the symbiotic scenario of symbiotic radio, the symbol period of the secondary user SU is N times that of the primary user PU. Within one secondary user SU symbol period, the base station sends independent signals to all primary users PU at the same time, which is expressed as: u(n)=ωs(n),n∈N.

[0063] u(n) indicates that the base station sends a signal to the primary user PU, ω indicates the beamforming vector of the base station, N == {1,...,N} indicates the set of primary signals within the duration of a secondary signal symbol, s(n) indicates the information sent by the base station to the primary user PU, and satisfies E{|s(n)| 2}=1, E represents the expected operation, | | represents the modular operation of complex numbers; STAR-RIS assists in transmitting the primary user PU signal and passively modulates the primary user PU signal to realize the transmission of the secondary user SU signal c. Considering that the secondary user SU signal adopts Binary Phase Shift Keying (BPSK) modulation and satisfies c∈{-1,1}.

[0064] The mixed information received by the primary user PU from the base station direct link and the STAR-RIS reflection link is expressed as:

[0065]

[0066] y p (n) indicates that during the duration of a secondary user SU symbol period, the primary user PU receives mixed information from the base station direct link and the STAR-RIS reflected link, z p (n) represents the noise at the primary user PU, z p (n) satisfies the mean of zero and the variance of The complex Gaussian signal, Φ r represents the reflection coefficient matrix of STAR-RIS, Φ r ∈C M×M .

[0067] The mixed information received by the secondary users SUr, SUt and the eavesdropping user Eve from the STAR-RIS reflection link is expressed as:

[0068]

[0069] y sur (n) indicates that the secondary user SUr receives information from the STAR-RIS reflection link, z r (n) represents the noise at the secondary user SUr, z r (n) satisfies the mean of zero and the variance of The complex Gaussian signal, y sut(n) indicates that the secondary user SUt receives information from the STAR-RIS reflection link, z t (n) represents the noise at the secondary user SUt, z t (n) satisfies the mean of zero and the variance of The complex Gaussian signal, y e (n) indicates that the eavesdropping user Eve receives information from the STAR-RIS reflection link, z e (n) represents the noise at the eavesdropping user Eve, z e (n) satisfies the mean of zero and the variance of The complex Gaussian signal, Φ t represents the reflection coefficient matrix of STAR-RIS, Φ t ∈C M×M .

[0070] Φ r =diag(v r ),

[0071] Φ t =diag(v t ),

[0072] Where M represents the number of STAR-RIS components, v r is the reflection coefficient vector, v r ∈C M×1 , which contains the following elements: v t represents the transmission coefficient vector, v t ∈C M×1 , which contains the following elements: represents the reflection coefficient amplitude of the mth element of STAR-RIS, represents the reflection coefficient phase of the mth element of STAR-RIS, represents the transmission coefficient amplitude of the mth element of STAR-RIS, It represents the transmission coefficient phase of the mth element of STAR-RIS, 1≤m≤M, the function diag() represents the diagonal matrix of the vector, e represents the natural constant, the superscript,j represents the imaginary unit.

[0073] In the above step 2 of the present invention, the legal primary user, the secondary user and the illegal eavesdropper are referred to as PU, SUr, SUt and Eve. The mathematical modeling method for the physical layer security problem of the downlink symbiotic radio system based on STAR-RIS under the condition of imperfect eavesdropper CSI specifically includes:

[0074] The channel data from STAR-RIS to the eavesdropping user Eve can be expressed as:

[0075]

[0076] Among them, C 1×M represents a 1×M complex matrix, || || represents the binary norm;

[0077] Then the SINR of PU, SUr, SUt and Eve are:

[0078]

[0079] Among them, γ p (c) Signal-to-interference-noise ratio at the primary user PU, Φ r is the reflection coefficient matrix of STAR-RIS, ω is the beamforming vector of the base station, is the noise power at the primary user PU; is the channel data from the base station to the primary user PU, is the channel data from STAR-RIS to the primary user PU, G is the channel data from the base station to STAR-RIS, γ r (c), γ t (c) are the signal-to-interference-noise ratios of the secondary users SUr and SUt, R sur , R sut are the transmission rates of the secondary users SUr and SUt, Φ t is the transmission coefficient matrix of STAR-RIS, are the noise power at the secondary users SUr and SUt respectively; are the channel data from STAR-RIS to the secondary users SUr and SUt, respectively. N indicates that the symbol period of the secondary user SU is a multiple of the symbol period of the primary user PU. e (c) is the signal-to-interference-noise ratio of the eavesdropping user Eve, R e To eavesdrop on the transmission rate of user Eve, is the noise power at the eavesdropping user Eve; is the channel data from STAR-RIS to the eavesdropping user Eve;

[0080] The achievable communication rates of PU, SUr, SUt and Eve are:

[0081]

[0082] in,

[0083]

[0084] Since there is a channel estimation error in Eve's channel, the minimum secure communication rate is:

[0085]

[0086] Optimize the base station active beamforming parameters and STAR-RIS passive beamforming parameters to maximize the minimum confidential communication rate, forming the following optimization problem model:

[0087]

[0088] Where, M=={1, 2, ..., m, ..., M} is the set of STAR-RIS components, represents the reflection coefficient amplitude of the mth element of STAR-RIS, represents the reflection coefficient phase of the mth element of STAR-RIS, represents the transmission coefficient amplitude of the mth element of STAR-RIS, represents the transmission coefficient phase of the mth element of STAR-RIS, R s,min The minimum achievable rate of decoding the primary user signal required for the normal operation of the primary user PU, γ min The minimum signal-to-noise ratio of the decoded secondary user signal required for the normal operation of the secondary users SUr and SUt, C E Indicates the maximum eavesdropping rate that can be achieved by the eavesdropping user Eve.

[0089] Step 3: Based on the channel data, base station beamforming vector, STAR-RIS reflection and transmission coefficient matrix obtained in step 1, construct the expression of the minimum communication confidentiality rate of the secondary user SUr.

[0090] Due to the requirement of energy conservation, the reflection and transmission coefficients of STAR-RIS need to meet certain restrictions, that is, the sum of the reflected signal and the transmitted signal power should be equal to the incident signal. Therefore, the amplitude and phase coefficients of STAR-RIS need to meet:

[0091]

[0092] The transmission rate of the primary user PU in the symbiotic radio transmission system is calculated as follows:

[0093] R p =E c [log2(1+γ p (c))]

[0094]

[0095] according to R p It can be written as:

[0096]

[0097] Where γ p (c) Signal-to-interference-noise ratio at the primary user PU, R p is the transmission rate of the primary user PU, Φ r is the reflection coefficient matrix of STAR-RIS, ω is the beamforming vector of the base station, is the noise power at the primary user PU; is the channel data from the base station to the primary user PU, is the channel data from STAR-RIS to the primary user PU, and G is the channel data from the base station to STAR-RIS.

[0098] The transmission rates of the decoded secondary signal c at the secondary users SUr and SUt in the symbiotic radio transmission system are calculated as follows:

[0099]

[0100] Where γ r (c), γ t (c) are the signal-to-interference-noise ratios of the secondary users SUr and SUt, R sur , R sut are the transmission rates of the secondary users SUr and SUt, Φ r is the reflection coefficient matrix of STAR-RIS, Φ t is the transmission coefficient matrix of STAR-RIS, ω is the beamforming vector of the base station, are the noise power at the secondary users SUr and SUt respectively; They are the channel data from STAR-RIS to the secondary users SUr and SUt respectively, G is the channel data from the base station to STAR-RIS, and N indicates that the symbol period of the secondary user SU is a multiple of the symbol period of the primary user PU.

[0101] The transmission rate of the eavesdropping user Eve in the symbiotic radio transmission system is calculated as follows:

[0102]

[0103] Where γ e (c) is the signal-to-interference-noise ratio of the eavesdropping user Eve, R e is the transmission rate of the eavesdropping user Eve, Φ r is the reflection coefficient matrix of STAR-RIS, ω is the beamforming vector of the base station, is the noise power at the eavesdropping user Eve; is the channel data from STAR-RIS to the eavesdropping user Eve, G is the channel data from the base station to STAR-RIS, and N indicates that the symbol period of the secondary user SU is a multiple of the symbol period of the primary user PU.

[0104] Since there is a channel estimation error in Eve's channel, the safe transmission rate of the secondary user SUr in the symbiotic radio transmission system is calculated as follows:

[0105]

[0106] Step 4: Based on the expression of the minimum communication confidentiality rate of the secondary user SUr, construct the problem of maximizing the minimum communication confidentiality rate of the secondary user SUr, give the STAR-RIS reflection and transmission coefficient matrix and calculate the base station beamforming vector that maximizes the minimum communication confidentiality rate of the secondary user SUr.

[0107] The constructed security transmission rate maximization problem P1 of the secondary user SUr is as follows:

[0108]

[0109] st:C1:R p ≥R s,min

[0110] C2:γ l (c)≥γ min ,l∈{t,r}

[0111] C3:||ω|| 2 ≤P max

[0112] C4:

[0113] C5:

[0114] C6:

[0115] C7:

[0116] Where, M=={1, 2, …, m, …, M} is the set of STAR-RIS components, represents the reflection coefficient amplitude of the mth element of STAR-RIS, represents the reflection coefficient phase of the mth element of STAR-RIS, represents the transmission coefficient amplitude of the mth element of STAR-RIS, represents the transmission coefficient phase of the mth element of STAR-RIS, R s,min The minimum achievable rate of decoding the primary user signal required for the normal operation of the primary user PU, γ min The minimum signal-to-noise ratio of the decoded secondary user signal required for the normal operation of the secondary users SUr and SUt, C E Indicates the maximum eavesdropping rate that can be achieved by the eavesdropping user Eve.

[0117] Analyzing the objective function and constraints, we find that given Φ r and Φ t In the case of , the problem can be solved by the Successive Convex Approximation (SCA) and the Semi-Definite Relaxation (SDR) method to obtain the suboptimal solution ω * , given Φ r and Φ t In the case of * . Using the eigenvalue decomposition method to obtain the suboptimal solution ω * , then given the suboptimal solution ω * In the case of r and Φ t Suboptimal solution and The specific steps are as follows:

[0118] Step 4-1: Given Φ r and Φ t , introduce slack variables τ, R' sur , μ, solve the security transmission rate maximization problem P1 of the secondary user SUr by continuous convex approximation method and semi-positive relaxation method, and obtain the suboptimal solution ω * .

[0119] Step 4-1 specifically includes:

[0120] Optimize the base station transmit beamforming vector under the condition of given STAR-RIS reflection coefficient matrix and transmission coefficient matrix, that is, fix Φ r and Φ t Optimize ω. At this time, the objective function and constraints are defined by the parameter ω. Define W = ωω H , F t =f t f t H , E p =H p +F p , And introduce slack variables τ, R' sur , μ, and use the S-procedure theorem to transform the secondary user SUr's secure transmission rate maximization problem P1 into the following form:

[0121]

[0122] At this time, the problem is still non-convex, and the optimal solution of W cannot be directly obtained. To solve the optimization problem, the CVX tool is used to obtain the upper limit of log2(1+τ) in the objective function, and the non-convex restriction conditions are rewritten as standard convex optimization restrictions. The specific operation is as follows:

[0123]

[0124] Among them, τ (n) represents the Taylor expansion point of the nth iteration. At this time, the non-convex constraint condition is transformed into a convex constraint, and the problem of maximizing the secure transmission rate of the secondary user SUr can be rewritten as problem P2;

[0125]

[0126]

[0127] However, due to the constraint condition Rank(W) = 1, the problem is still non-convex. By using the semi-positive definite relaxation method to relax the rank-one constraint, problem P2 is transformed into a convex optimization problem. The convex optimization problem is solved using the CVX tool, and it is proved that the solution to the problem after relaxing the rank to one still satisfies in Denotes the value obtained by solving the convex optimization problem, let τ (n) =τ, substitute the updated value into the convex optimization problem and iterate until convergence, and finally get the suboptimal solution W * , using eigenvalue decomposition from W * The suboptimal solution ω is obtained from * ;

[0128] Among them, the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and W represents the base station beamforming matrix.

[0129] Step 4-2: Based on the obtained suboptimal solution ω * , introduce slack variables τ, R s ' ur , μ, and solve Φ by continuous convex approximation method and semi-positive definite relaxation method r and Φ t , respectively get Φ r and Φ t Suboptimal solution and

[0130] Step 4-2 specifically includes:

[0131] Under the condition of obtaining the base station beamforming vector ω, the reflection and transmission coefficient matrices of STAR-RIS are optimized, that is, ω is fixed to optimize Φ r and Φ t That is (vr and v t ), in this case, the objective function and the constraints are defined by the parameter ω, defined as And introduce slack variables τ, R' sur , μ;

[0132] The problem P1 of maximizing the security transmission rate of the secondary user SUr is transformed into P3:

[0133]

[0134] In the same way as above, rewrite the objective function as follows:

[0135]

[0136] However, due to the constraint Rank(V l )=1,l∈{t,r} exists, the problem is still non-convex. By using the semi-positive definite relaxation method to relax the rank-one constraint, problem P3 is transformed into a convex optimization problem. The convex optimization problem is solved using the CVX tool, and it is proved that the solution of the problem after relaxing the rank to one still satisfies in Denotes the value obtained by solving the convex optimization problem, let τ (n) =τ, substitute the updated value into the convex optimization problem and iterate until convergence, and finally get V l ,l∈{t,r}, the suboptimal solution V l * ,l∈{t,r}, using eigenvalue decomposition from v l * ,l∈{t,r} to get v l ,l∈{t,r}, where the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and V l ,l∈{t,r} represents the reflection transmission coefficient matrix of STAR-RIS;

[0137] Step 4-3: Alternately solve P2 and P3 until convergence. The solution obtained is the suboptimal solution to the problem of maximizing the security transmission rate of the secondary user SUr. ω in suboptimal solution * , That is, the base station beamforming vector that maximizes the security transmission rate of the secondary user SUr and the reflection transmission coefficient matrix of STAR-RIS.

[0138] Step 5: Given the base station beamforming vector, calculate the STAR-RIS reflection and transmission coefficient matrix that maximizes the minimum communication confidentiality rate of the secondary user SUr;

[0139] Step 6: Repeat steps 4 and 5 until convergence. The solution obtained is the suboptimal solution to the problem of maximizing the security transmission rate of the secondary user SUr. ω in suboptimal solution * , That is, the base station beamforming vector that maximizes the security transmission rate of the secondary user SUr, and the reflection transmission coefficient matrix of STAR-RIS. Two schemes are used for performance comparison:

[0140] 1.STAR-RIS fixed energy allocation scheme; 2. Traditional RIS scheme. The simulated network topology is described as a 2D coordinate system, where the base station, primary user PU and STAR-RIS are located at (0,0), (100,20) and (100,0) respectively; secondary users SUr, SUt and eavesdropping user Eve are randomly distributed in a circle with a center of (100,20) and a radius of 20, in meters. The channel data consists of large-scale fading and small-scale fading. The large-scale fading is modeled as Where ζ represents the wavelength, d represents the distance between nodes, represents the path attenuation factor. The small-scale fading of the STAR-RIS related channel is modeled as Rician fading. Taking the channel G between the base station and STAR-RIS as an example, G can be expressed as:

[0141]

[0142] Among them G LoS , G NLoS , κ G , d BS,RIS G represents the line-of-sight component, non-line-of-sight component, Rice factor and the distance between the base station and STAR-RIS. LoS satisfy where β X (υ)=[1,e jπsin(υ) ,…,e jπ(X-1)sin(υ) ] T ,X∈{M,N t}. AoA is the angle of arrival, υ AoD is the departure angle.

[0143] G NLoS The model is Rayleigh fading, and each element in the matrix is ​​a complex Gaussian variable with a mean of 0 and a variance of 1. The channel unrelated to STAR-RIS is modeled as Rayleigh fading, and the variable satisfies a complex Gaussian distribution with a value of 0 and a variance of 1. The path loss factors from the base station to the primary user PU, from STAR-RIS to the primary user PU, from the secondary user SUr and SUt, and from the eavesdropping user Eve, from the base station to STAR-RIS are set to 3.8, 2, and 2.4, respectively, and the Rice factor is set to 3. Unless otherwise specified, the noise power The number of base station transmitting antennas is N t =4, the number of STAR-RIS elements M = 20, the ratio of the secondary user SU symbol period to the primary user PU symbol period N = 50, R s,min =3bit / s / Hz, γ min =20dB,ζ=750MHz.

[0144] like Figure 2 As shown in the figure, the change in the convergence value of the secure transmission rate of the secondary user SUr in the scheme proposed in this paper and the fixed power allocation scheme under different numbers of STAR-RIS units is shown. The number of STAR-RIS units is set to M=20, M=60. When M=20, the algorithm proposed in this invention improves the performance by 20.6%. When M=60, the algorithm proposed in this invention improves the performance by 23.2%. It can also be seen from the figure that when the number of STAR-RIS units increases, the secure transmission rate of the secondary user SUr also increases.

[0145] like Figure 3 As shown in Figure 2, it shows the impact of different base station transmit power thresholds on the minimum communication confidentiality rate of secondary users. As the transmit power increases, the minimum communication confidentiality rate of secondary users also gradually increases, and the performance of the proposed scheme is always better than that of the fixed power allocation scheme.

[0146] The above description is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a technician familiar with the technical field within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A symbiotic radio transmission system based on STAR-RIS assistance, characterized in that: The STAR-RIS is a reconfigurable intelligent reflection surface that can transmit and reflect simultaneously. Each element of the STAR-RIS includes a reflection element and a transmission element. The STAR-RIS divides the target area into an R zone and a T zone. The R zone is a reflection zone, and the T zone is a transmission zone. The symbiotic radio transmission system exists in the target area, including a base station, two secondary users SUr and SUt, a primary user PU and an eavesdropping user Eve. The STAR-RIS is set between the secondary user SUr and the secondary user SUt. The base station, the primary user PU, the secondary user SUr and the eavesdropping user Eve are located in the R zone of the STAR-RIS. The eavesdropping user Eve has the ability to eavesdrop on the secondary user SUr. The secondary user SUt is located in the T zone of the STAR-RIS.

2. A method for implementing a symbiotic radio transmission system based on STAR-RIS assistance, characterized in that: The method comprises the following steps: Step 1: Considering the existence of eavesdroppers and the imperfect CSI of the eavesdropping channel, a model for maximizing the minimum communication confidentiality rate of secondary users in the STAR-RIS-assisted symbiotic radio system under imperfect CSI is established; Step 2: Initialize the relevant parameters of the target problem, including the channel data from the base station to the primary user PU, the channel data from the base station to STAR-RIS, the channel data from STAR-RIS to the primary user PU, the channel data from STAR-RIS to the secondary users SUr and SUt, the channel estimation data and the real channel data from STAR-RIS to the eavesdropping user Eve, the beamforming vector, the STAR-RIS reflection and transmission phase shift matrix, the quality of service threshold requirement, and the base station power threshold; Step 3: Based on the channel data, base station beamforming vector, STAR-RIS reflection and transmission coefficient matrix obtained in step 1 above, construct the expression of the minimum communication confidentiality rate of the secondary user SUr; Step 4: Based on the expression of the minimum communication confidentiality rate of the secondary user SUr, construct the problem of maximizing the minimum communication confidentiality rate of the secondary user SUr, give the STAR-RIS reflection and transmission coefficient matrix and calculate the base station beamforming vector that maximizes the minimum communication confidentiality rate of the secondary user SUr; Step 5: Given the base station beamforming vector, calculate the STAR-RIS reflection and transmission coefficient matrix that maximizes the minimum communication confidentiality rate of the secondary user SUr; Step 6: Repeat steps 4 and 5 until convergence. The solution obtained is the suboptimal solution to the problem of maximizing the security transmission rate of the secondary user SUr {ω * ,Φ r * ,Φ t * }, ω in the suboptimal solution * ,Φ r * ,Φ t * That is, the base station beamforming vector that maximizes the security transmission rate of the secondary user SUr and the reflection transmission coefficient matrix of STAR-RIS.

3. The method for implementing a symbiotic radio transmission system based on STAR-RIS assistance according to claim 2, characterized in that: In step 2, the legal primary user, the secondary user and the illegal eavesdropper are referred to as PU, SUr, SUt and Eve. The mathematical modeling method for the physical layer security problem of the downlink symbiotic radio system based on STAR-RIS under the condition of imperfect eavesdropper CSI specifically includes: The channel data from STAR-RIS to the eavesdropping user Eve is expressed as: Among them, C 1×M represents a 1×M complex matrix, || || represents the binary norm; Then the SINR of PU, SUr, SUt and Eve are: Among them, γ p (c) Signal-to-interference-noise ratio at the primary user PU, Φ r is the reflection coefficient matrix of STAR-RIS, ω is the beamforming vector of the base station, is the noise power at the primary user PU; is the channel data from the base station to the primary user PU, is the channel data from STAR-RIS to the primary user PU, G is the channel data from the base station to STAR-RIS, γ r (c), γ t (c) are the signal-to-interference-noise ratios of the secondary users SUr and SUt, R sur , R sut are the transmission rates of the secondary users SUr and SUt, Φ t is the transmission coefficient matrix of STAR-RIS, are the noise power at the secondary users SUr and SUt respectively; are the channel data from STAR-RIS to the secondary users SUr and SUt, respectively. N indicates that the symbol period of the secondary user SU is a multiple of the symbol period of the primary user PU. e (c) is the signal-to-interference-noise ratio of the eavesdropping user Eve, R e To eavesdrop on the transmission rate of user Eve, is the noise power at the eavesdropping user Eve; is the channel data from STAR-RIS to the eavesdropping user Eve; The achievable communication rates of PU, SUr, SUt and Eve are: in, Since Eve's channel has channel estimation error, the minimum secure communication rate is: Optimize the base station active beamforming parameters and STAR-RIS passive beamforming parameters to maximize the minimum confidential communication rate, forming the following optimization problem model: Where, M=={1, 2, ..., m, ..., M} is the set of STAR-RIS components, represents the reflection coefficient amplitude of the mth element of STAR-RIS, represents the reflection coefficient phase of the mth element of STAR-RIS, represents the transmission coefficient amplitude of the mth element of STAR-RIS, represents the transmission coefficient phase of the mth element of STAR-RIS, R s,min The minimum achievable rate of decoding the primary user signal required for the normal operation of the primary user PU, γ min The minimum signal-to-noise ratio of the decoded secondary user signal required for the normal operation of the secondary users SUr and SUt, C E Indicates the maximum eavesdropping rate that can be achieved by the eavesdropping user Eve.

4. The method for implementing a symbiotic radio transmission system based on STAR-RIS assistance according to claim 2, characterized in that: The alternate optimization in step 4 and step 5 respectively solves the beamforming vector of the base station and the reflection transmission coefficient matrix of STAR-RIS, specifically including: Optimize the base station transmit beamforming vector under the condition of given STAR-RIS reflection coefficient matrix and transmission coefficient matrix, that is, fix Φ r and Φ t Optimize ω. At this time, the objective function and constraints are defined by the parameter ω. Define W = ωω H , E p =H p +F p , And introduce slack variables τ, R′ sur , μ, and use the S-procedure theorem to transform the secondary user SUr's secure transmission rate maximization problem P1 into the following form: Use the CVX tool to obtain the upper limit of log2(1+τ) in the objective function and rewrite the non-convex constraints into standard convex optimization constraints. The specific operation is as follows: Among them, τ (n) represents the Taylor expansion point of the nth iteration. At this time, the non-convex constraint condition is transformed into a convex constraint, and the problem of maximizing the secure transmission rate of the secondary user SUr can be rewritten as problem P2; Using the semi-positive definite relaxation method to relax the rank-one constraint, problem P2 is transformed into a convex optimization problem. The convex optimization problem is solved using the CVX tool, and it is proved that the solution to the problem after relaxing the rank-one still satisfies in Denotes the value obtained by solving the convex optimization problem, let τ (n) =τ, substitute the updated value into the convex optimization problem and iterate until convergence, and finally get the suboptimal solution W * , using eigenvalue decomposition from W * The suboptimal solution ω is obtained from * ; Among them, the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and W represents the base station beamforming matrix; Under the condition of obtaining the base station beamforming vector ω, the reflection and transmission coefficient matrices of STAR-RIS are optimized, that is, ω is fixed to optimize Φ r and Φ t That is (v r and v t ), in this case, the objective function and the constraints are defined by the parameter ω, defined as And introduce slack variables τ, R′ sur , μ; The problem P1 of maximizing the secure transmission rate of the secondary user SUr is transformed into P3: In the same way as above, rewrite the objective function as follows: Using the semi-positive definite relaxation method to relax the rank-one constraint, problem P3 is transformed into a convex optimization problem. The convex optimization problem is solved using the CVX tool, and it is proved that the solution to the problem after relaxing the rank-one still satisfies in Denotes the value obtained by solving the convex optimization problem, let τ (n) =τ, substitute the updated value into the convex optimization problem and iterate until convergence, and finally get V l , the suboptimal solution of l∈{t,r} Using eigenvalue decomposition from Get v l ,l∈{t,r}, where the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and V l ,l∈{t,r} represents the reflection transmission coefficient matrix of STAR-RIS; Solve P2 and P3 alternately until convergence. The solution obtained is the suboptimal solution to the problem of maximizing the secure transmission rate of the secondary user SUr. Suboptimal solution That is, the base station beamforming vector that maximizes the security transmission rate of the secondary user SUr and the reflection transmission coefficient matrix of STAR-RIS.

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