A secure transmission system and method for a symbiotic radio system based on STAR-RIS assistance

Abstract

The application discloses a kind of symbiotic radio safety transmission systems and methods based on STAR-RIS auxiliary, including the channel data between acquisition transmitting base station, primary user PU, secondary user Sur and eavesdropping user Eve, design base station beamforming vector and STAR-RIS transmission and transmission coefficient matrix;By introducing simultaneous transmission and reflection reconfigurable intelligent surface, the space is fully covered by the reflection and transmission of signal, which greatly improves the flexibility of equipment deployment.The application proposes a method of alternately optimizing base station beamforming vector and STAR-RIS transmission and transmission coefficient matrix, which can greatly improve the minimum communication secrecy rate of secondary user under the condition of meeting the normal communication requirements and power constraints of the system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wireless communication, and particularly relates to a security transmission system and method of a symbiotic radio system based on STAR-RIS assistance. BACKGROUND

[0002] In the sixth generation mobile communication (6G), large-scale coverage of Internet of Things devices puts higher requirements on energy-spectrum resources. As a high energy efficiency, high spectrum utilization and low cost technology, symbiotic radio (SR) is a promising technology in the future Internet of Things (IoD) field. The SR communication network aims to establish a mutual symbiosis relationship between the main system transmission and the secondary system transmission, so that the main system transmission and the secondary system transmission can simultaneously meet the requirements of energy efficiency and spectrum efficiency. Since the backscattering information transmission experiences double fading channels, the performance of the main system is limited on the one hand, and the performance of the secondary system is limited on the other hand. The symbiotic communication system assisted by the intelligent reflecting surface (RIS) not only can improve the channel environment and enhance the system performance, but also can be used as a secondary user transmitter to realize the transmission of the secondary user information by passively adjusting the incident signal of each element. Since the traditional RIS can only realize the reflection of the signal, it is required that the user and the base station are deployed on the same side of the RIS, which limits the application scenarios of the RIS and the deployment flexibility of the device. SUMMARY

[0003] The application aims at the defects and deficiencies of the prior art, and proposes a symbiotic radio transmission system and method based on STAR-RIS assistance. Under the constraints of meeting 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 eavesdropper Eve, the minimum communication secrecy rate of the secondary user SUr is maximized, the transmission power outside the base station is minimized under the constraint of STAR-RIS coupling similarity, and the spatial full coverage characteristic of the STAR-RIS makes the device deployment more flexible.

[0004] The present application adopts the technical scheme for solving its technical problems: a symbiotic radio transmission system based on STAR-RIS assistance, the system comprises: the STAR-RIS is a simultaneous transmission and reflection reconfigurable intelligent reflecting surface, STAR-RIS has a plurality of elements, each element includes a reflecting element and a transmission element, STAR-RIS divides the target area into R area and T area, the R area is a reflection area, and the T area is a transmission area, 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, a STAR-RIS is arranged 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 area 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 area of the STAR-RIS, and the minimum communication secrecy rate of the secondary user SUr is maximized.

[0005] The present application also provides an implementation method of a symbiotic radio transmission system based on STAR-RIS assistance, the method comprises the following steps:

[0006] Step 1: under the condition of considering the existence of an eavesdropper and the non-perfect CSI of an eavesdropping channel, a minimum communication secrecy rate maximization model of a secondary user in a symbiotic radio system assisted by STAR-RIS under non-perfect CSI is established;

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

[0008] Step 3: based on the channel data obtained in step 1, the base station beam forming vector, the STAR-RIS reflection and transmission coefficient matrix, a minimum communication secrecy rate expression of the secondary user SUr is constructed;

[0009] Step 4: based on the minimum communication secrecy rate expression of the secondary user SUr, a minimum communication secrecy rate maximization problem of the secondary user SUr is constructed, the STAR-RIS reflection and transmission coefficient matrix is given, and the base station beam forming vector that maximizes the minimum communication secrecy rate of the secondary user SUr is calculated;

[0010] Step 5: given the base station beam forming vector, the STAR-RIS reflection and transmission coefficient matrix that maximizes the minimum communication secrecy rate of the secondary user SUr is calculated;

[0011] Step 6: Repeat the above steps 4, 5 until convergence, and the obtained solution is a suboptimal solution of the secondary user SUr's secure transmission rate maximization problem ω in the suboptimal solution * , is the base station beamforming vector that maximizes the secure transmission rate of the secondary user SUr, and the reflection transmission coefficient matrix of the STAR-RIS.

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

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

[0014]

[0015] where C 1×M is a 1×M complex matrix, and || || represents the two-norm;

[0016] Then the signal-to-interference-and-noise ratios (SINRs) of the PU, SUr, SUt and Eve are respectively:

[0017]

[0018]

[0019] where γ p (c) is the signal-to-interference-and-noise ratio at the primary user PU, Φ r is the reflection coefficient matrix of the STAR-RIS, and 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 the STAR-RIS to the primary user PU, G is the channel data from the base station to the STAR-RIS, and γ r (c), γ t (c) are the signal-to-interference-and-noise ratios of the secondary users SUr and SUt, respectively, R sur , R sut are the transmission rates of the secondary users SUr and SUt, respectively, Φ t is the transmission coefficient matrix of the STAR-RIS, are the noise powers at the secondary users SUr and SUt, respectively; respectively, where N denotes that the symbol period of the secondary users SU is a multiple of the symbol period of the primary user PU, γ e (c) is the signal-to-noise ratio of the eavesdropper Eve, e is the transmission rate of the eavesdropper Eve, is the noise power at the eavesdropper Eve; is the channel data from the STAR-RIS to the eavesdropper Eve;

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

[0021]

[0022] where,

[0023]

[0024] Since there is a channel estimation error in the channel of Eve, the minimum secure communication rate is:

[0025]

[0026] Optimizing the base station active beamforming parameters and the STAR-RIS passive beamforming parameters to maximize the minimum secure communication rate forms the following optimization problem model:

[0027]

[0028]

[0029] where M = {1, 2, …, m, …, M} is the STAR-RIS element set, denotes the reflection coefficient amplitude of the mth element of the STAR-RIS, denotes the reflection coefficient phase of the mth element of the STAR-RIS, denotes the transmission coefficient amplitude of the mth element of the STAR-RIS, denotes the transmission coefficient phase of the mth element of the STAR-RIS, R s,min denotes the minimum achievable rate of decoding the primary user signal required for the normal operation of the primary user PU, γ min denotes the minimum signal-to-noise ratio required for the secondary users SUr and SUt to decode the secondary user signal for normal operation, C E denotes the maximum achievable eavesdropping rate of the eavesdropper Eve.

[0030] Further, the steps 4 and 5 in the alternating optimization solve the beamforming vector of the base station and the reflection transmission coefficient matrix of the STAR-RIS, respectively, and specifically include:

[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 r and t Optimize ω, at this time, the objective function and the constraint condition are defined by the parameter ω, and W = ωω is defined H , F t = f t f t H , E p = H p +F p , And introduce the slack variable τ, R' sur , μ, and use the S-procedure theorem to convert the secondary user Sur's safe 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. In order to solve the optimization problem, the upper limit of log2(1+τ) in the objective function is obtained by using the CVX tool, and the non-convex constraint condition is rewritten as a standard convex optimization constraint. The specific operation is as follows:

[0035]

[0036] Where τ (n) represents the Taylor expansion point of the nth iteration, and the non-convex constraint condition is converted into a convex constraint condition. Then the secondary user Sur's safe transmission rate maximization problem can be rewritten as problem P2.

[0037]

[0038] But because of the existence of the constraint condition Rank(W) = 1, the problem is still non-convex. By using the semi-definite relaxation method to relax the rank-one constraint condition, the problem P2 is converted into a convex optimization problem. The CVX tool is used to solve the convex optimization problem, and it is proved that the solution of the problem after relaxing the rank-one still satisfies Where represents the value obtained by solving the convex optimization problem, and τ (n)= τ, the updated value is substituted into the convex optimization problem iteration until convergence, and the suboptimal solution W of W is finally obtained * The suboptimal solution ω of ω is obtained from W by using eigenvalue decomposition * ; * ;

[0039] wherein 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 matrix of the STAR-RIS is optimized, that is, ω is fixed to optimize Φ r and Φ t , that is, (v r and v t ), at this time, the objective function and the constraint condition are defined by the parameter ω, and ω is defined and the relaxation variable τ, R' sur , μ are introduced;

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

[0042]

[0043] In the same way as above, the objective function is rewritten as:

[0044]

[0045] However, due to the existence of the constraint condition Rank(V l ) = 1, l ∈ {t, r}, the problem is still non-convex. By using the semi-definite relaxation method to relax the rank-one constraint condition, the problem P3 is converted into a convex optimization problem. The CVX tool is used to solve the convex optimization problem, and it is proved that the solution of the problem after relaxing the rank-one still satisfies wherein the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and V represents the value obtained by solving the convex optimization problem, and τ (n) = τ, the updated value is substituted into the convex optimization problem iteration until convergence, and the suboptimal solution V l of V l * The suboptimal solution v l of v * is obtained from v l ; l wherein the function Tr() represents the matrix trace operation, the function Rank() represents the rank of the matrix, and V l represents the reflection and transmission coefficient matrix of the STAR-RIS;

[0046] Alternately solve P2 and P3 until convergence, and the obtained solution is a suboptimal solution of the security transmission rate maximization problem of the secondary user SUr ω in the 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 the STAR-RIS.

[0047] Advantages:

[0048] 1. The present application designs a symbiotic radio security transmission method based on STAR-RIS assistance, wherein the STAR-RIS can assist in transmitting the primary user signal, effectively improving the performance of the primary system.

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

[0050] 3. The present application introduces a simultaneously transmitting and reflecting reconfigurable intelligent surface, which realizes full coverage of space through signal reflection and transmission, greatly improving the flexibility of device deployment. DETAILED DESCRIPTION

[0051] Figure 1 The present application is a STAR-RIS assisted symbiotic radio system model diagram.

[0052] Figure 2 The present application is a graph showing the influence of the number of STAR-RIS units on the minimum secrecy rate of the secondary user SUr.

[0053] Figure 3 The present application is a graph showing the change of the minimum communication secrecy rate of the secondary user with the base station transmission power threshold.

[0054] Figure 4 The present application is a method flowchart. DETAILED DESCRIPTION

[0055] The embodiments of the present application will be described in detail below in conjunction with the accompanying drawings of the specification, and the embodiments are implemented on the premise of the technical solutions of the present application, and detailed implementation manners and specific operation processes are given.

[0056] As Figure 1 described, the present application embodiment proposes a symbiotic radio security transmission system based on STAR-RIS assistance, which exists in a target area and includes a base station, secondary users SUr and SUt, a primary user PU, and an eavesdropping user Eve, Figure 1The base station BS represents a base station, sets a STAR-RIS between the secondary users SUr and SUt, the STAR-RIS is a simultaneously transmitting and reflecting reconfigurable intelligent reflecting surface, the STAR-RIS has a plurality of elements, each element includes a reflecting element and a transmitting element, divides a target area into an R area and a T area, the R area is a reflecting area, and the T area is a transmitting area, the base station, a primary user PU, the secondary user SUr and an eavesdropping user Eve are located in the R area of the STAR-RIS, the secondary user SUt is located in the T area of the STAR-RIS, the minimum communication secrecy rate of the secondary user SUr is maximized, and radio transmission is completed.

[0057] As shown in Figure 4 , the present application further provides an implementation method of a symbiotic radio transmission system assisted by a STAR-RIS, the method comprises:

[0058] Step 1: under the condition of considering the existence of an eavesdropper and non-perfect CSI of an eavesdropping channel, a minimum communication secrecy rate maximization model of a secondary user in a symbiotic radio system assisted by a STAR-RIS under non-perfect CSI is established;

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

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

[0061] The channel data from the base station to the STAR-RIS is , which represents a complex matrix of MxN t , the channel data from the base station to the primary user PU is represented as , which represents a complex matrix of 1xN t , the channel data from the STAR-RIS to the primary user PU, from the STAR-RIS to the secondary users SUr and SUt, and from the STAR-RIS to the eavesdropping user Eve are respectively represented as C 1×M , which represents a complex matrix of 1xM.

[0062] Considering the symbiotic scenario of coexisting radio, the symbol period of the secondary user (SU) is N times the symbol period of the primary user (PU). Within one secondary user (SU) symbol period, the base station simultaneously sends independent signals to all primary users (PU), and its expression is: u(n)=ωs(n), n∈N.

[0063] u(n) represents the signal sent by the base station to the primary user PU, ω represents the beamforming vector of the base station, N=={1,...,N} represents the set of primary signals within the duration of a secondary signal symbol, and s(n) represents the information sent by the base station to the primary user PU, satisfying E{|s(n)| 2}=1,E represents the desired operation,|| represents the modulo 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. Consider 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's direct link and STAR-RIS reflected link is represented as follows:

[0065]

[0066] y p (n) represents the mixed information received by the primary user PU from the base station direct link and the STAR-RIS reflected link within the duration of a secondary user SU symbol period, z p (n) represents the noise at the main user PU, z p (n) is a subset of n that has a mean of zero and a variance of 0. The complex Gaussian signal, Φ r Φ represents the reflection coefficient matrix of STAR-RIS. r ∈C M×M .

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

[0068]

[0069] y sur (n) represents the information received by the secondary user SUr from the STAR-RIS reflection link, z r (n) represents the noise at the secondary user's SUR, z r (n) is a subset of n that has a mean of zero and a variance of 0. The complex Gaussian signal, y sut(n) represents the information received by the secondary user SUt from the STAR-RIS reflection link, z t (n) represents the noise at the secondary user's SUt, z t (n) is a subset of n that has a mean of zero and a variance of 0. The complex Gaussian signal, y e (n) represents the information received by the eavesdropping user Eve from the STAR-RIS reflection link, z e (n) represents the noise at the location of the eavesdropping user Eve, z e (n) is a subset of n that has a mean of zero and a variance of 0. The complex Gaussian signal, Φ t Φ represents the reflection coefficient matrix of STAR-RIS. t ∈C M×M .

[0070] Φ r =diag(v r ),

[0071] Φ t =diag(v t ),

[0072] In the formula, M represents the number of STAR-RIS components, v r Let v be the reflection coefficient vector. 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 This represents the amplitude of the reflection coefficient of the m-th element in STAR-RIS. This represents the phase of the reflection coefficient of the m-th element in STAR-RIS. This represents the amplitude of the transmission coefficient of the m-th element in STAR-RIS. Let represent the phase of the transmission coefficient of the m-th element in STAR-RIS, 1≤m≤M, the function diag() represents the diagonal matrix of the vector, e represents the natural constant, the superscript , and j represents the imaginary unit.

[0073] In step 2 of the present invention, the legitimate primary user, secondary user, and illegal eavesdropper are referred to as PU, SUr, SUt, and Eve, respectively. The mathematical modeling method for the physical layer security problem of the downlink co-existing 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 represented as:

[0075]

[0076] where C 1×M denotes a complex matrix of 1 x M, || || denotes the two-norm;

[0077] Then the signal-to-interference-and-noise ratios (SINRs) of PU, SUr, SUt and Eve are respectively:

[0078]

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

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

[0081]

[0082] where,

[0083]

[0084] Due to the channel estimation error of the channel of Eve, the minimum secure communication rate is:

[0085]

[0086] Optimizing the base station active beamforming parameters and the STAR-RIS passive beamforming parameters to maximize the minimum secure communication rate forms the following optimization problem model:

[0087]

[0088] where M = {1, 2, …, m, …, M} is the STAR-RIS element set, denotes the reflection coefficient amplitude of the mth element of the STAR-RIS, denotes the reflection coefficient phase of the mth element of the STAR-RIS, denotes the transmission coefficient amplitude of the mth element of the STAR-RIS, denotes the transmission coefficient phase of the mth element of the STAR-RIS, R s,min denotes the minimum achievable rate of decoding the primary user signal required for the normal operation of the primary user PU, γ min denotes the minimum signal-to-noise ratio required for decoding the secondary user signal for the normal operation of the secondary users SUr and SUt, C E denotes the maximum achievable eavesdropping rate of the eavesdropper Eve.

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

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

[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 can be written as:

[0096]

[0097] In the formula γ p (c) Signal-to-interference-plus-noise ratio (SIR) at the main user's PU, R p The transmission rate of the primary user PU, Φ r Let ω be the reflection coefficient matrix of STAR-RIS, and ω be the beamforming vector of the base station. Noise power at the main user's PU; This refers to the channel data from the base station to the primary user unit (PU). G represents the channel data from STAR-RIS to the primary user PU, and G represents the channel data from the base station to STAR-RIS.

[0098] The transmission rates of the decoded secondary signal c at secondary users SUR and SUT in the co-existing radio transmission system are calculated as follows:

[0099]

[0100] In the formula γ r (c), γ t (c) R represents the signal-to-interference-plus-noise ratio (SIR) of sub-users SUR and SUt, respectively. sur R sut The transmission rates of secondary users SUr and SUt are Φ, respectively. r Here is the reflection coefficient matrix of STAR-RIS, Φ t Let ω be the transmission coefficient matrix of STAR-RIS, and ω be the beamforming vector of the base station. These are the noise power at the secondary user's SUR and SUT, respectively; G represents the channel data from STAR-RIS to secondary users SUr and SUt, respectively; G represents the channel data from the base station to STAR-RIS; and N represents the multiple of the symbol period of the secondary user SU to the symbol period of the primary user PU.

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

[0102]

[0103] In the formula γ e (c) R is the signal-to-interference-plus-noise ratio for the user Eve being eavesdropped on. e To eavesdrop on user Eve's transmission rate, Φ r Let ω be the reflection coefficient matrix of STAR-RIS, and ω be the beamforming vector of the base station. To eavesdrop on the noise power at user Eve; G represents the channel data from STAR-RIS to the eavesdropping user Eve, and N represents the channel data from the base station to STAR-RIS. N indicates that the symbol period of the secondary user SU is a multiple of the symbol period of the primary user PU.

[0104] Due to the channel estimation error of Eve's channel, the secure transmission rate of the secondary user SUr in the coexisting radio transmission system is calculated as follows:

[0105]

[0106] Step 4: Based on the minimum communication secrecy rate expression of the secondary user SUr, a minimum communication secrecy rate maximization problem of the secondary user SUr is constructed, given the STAR-RIS reflection and transmission coefficient matrix, and the base station beamforming vector that maximizes the minimum communication secrecy rate of the secondary user SUr is calculated.

[0107] The constructed minimum communication secrecy rate maximization problem P1 of the secondary user SUr is as follows:

[0108]

[0109] s.t: 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] In the formula, M == {1, 2, …, m, …, M} is a STAR-RIS element set, denotes the reflection coefficient amplitude of the mth element of the STAR-RIS, denotes the reflection coefficient phase of the mth element of the STAR-RIS, denotes the transmission coefficient amplitude of the mth element of the STAR-RIS, denotes the transmission coefficient phase of the mth element of the STAR-RIS, R s,min denotes the minimum achievable rate required for the primary user PU to normally work to decode the primary user signal, γ min denotes the minimum signal-to-noise ratio required for the secondary user SUr and SUt to normally work to decode the secondary user signal, C E denotes the maximum achievable eavesdropping rate of the eavesdropper Eve.

[0117] Analysis of the objective function and constraints reveals that, given Φ r and Φ t In this case, a suboptimal solution to ω can be obtained by solving the problem using the Successive Convex Approximation (SCA) method and the Semi-Definite Relaxation (SDR) method. * Let Φ be a given value. r and Φ t In this case, the suboptimal solution obtained is W. * The suboptimal solution ω is obtained using the eigenvalue decomposition method. * Then, given the suboptimal solution ω * In the case of solving Φ 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 and R' sur The suboptimal solution ω is obtained by solving the secure transmission rate maximization problem P1 of the secondary user SUr using the continuous convex approximation method and the semidefinite relaxation method. * .

[0119] Step 4-1 specifically includes:

[0120] Optimize the base station transmit beamforming vector given the STAR-RIS reflection coefficient matrix and transmission coefficient matrix, i.e., fix Φ r and Φ t Optimize ω. At this point, the objective function and constraints are defined by the parameter ω, and we define W = ωω. H , F t =f t f t H , E p =H p +F p , Furthermore, slack variables τ and R' are introduced. sur Meanwhile, using the S-procedure theorem, the problem P1, which maximizes the secure transmission rate of the secondary user SUR, is transformed 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 upper bound of log2(1+τ) in the objective function is obtained using the CVX tool, and the non-convex constraint is rewritten as a standard convex optimization constraint. The specific operation is as follows:

[0123]

[0124] where τ (n) represents the Taylor expansion point of the nth iteration. At this time, the non-convex constraint is converted to a convex constraint, and the maximum safety transmission rate problem of the secondary user Sur can be rewritten as problem P2.

[0125]

[0126]

[0127] However, due to the existence of the constraint condition Rank(W) = 1, the problem is still non-convex. By using the semi-definite relaxation method to relax the rank-one constraint, the problem P2 is converted into a convex optimization problem. The CVX tool is used to solve the convex optimization problem, and it is proved that the solution of the relaxed rank-one problem still satisfies where represents the value obtained by solving the convex optimization problem. Let τ (n) = τ, and substitute the updated value into the convex optimization problem. Iterate until convergence to obtain the suboptimal solution W * of W. * The suboptimal solution ω * of ω is obtained from W * by using eigenvalue decomposition.

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

[0129] Step 4-2: According to the obtained suboptimal solution ω * of ω, introduce relaxation variables τ, R s ' ur , μ, and solve Φ r and Φ t by using the successive convex approximation method and the semi-definite relaxation method, respectively, to obtain the suboptimal solutions r and t of Φ r and Φ t , respectively. and

[0130] Step 4-2 specifically includes:

[0131] Under the condition of obtaining the base station beamforming vector ω, the reflection and transmission coefficient matrix of STAR-RIS is optimized, i.e., fixing ω to optimize Φ r and Φ t , i.e., (vr and v t ), where the objective function and constraints are defined by the parameter ω, defined as and introduce the slack variable τ, R' sur , μ;

[0132] The problem P1 of maximizing the secure transmission rate of the secondary user SUr is converted to P3:

[0133]

[0134] In the same way as above, the objective function is rewritten as:

[0135]

[0136] But due to the existence of the constraint Rank(V l ) = 1, l ∈ {t, r}, the problem is still non-convex. By using the semi-definite relaxation method to relax the rank-one constraint, the problem P3 is converted to a convex optimization problem. The CVX tool is used to solve the convex optimization problem, and it is proved that the solution of the relaxed rank-one problem still satisfies where denotes the value obtained by solving the convex optimization problem. Let τ (n) = τ, and substitute the updated value into the convex optimization problem to iterate until convergence. Finally, the suboptimal solution V l , l ∈ {t, r} is obtained. l * , l ∈ {t, r}, the suboptimal solution v l , l ∈ {t, r} is obtained from v * , l ∈ {t, r} by using eigenvalue decomposition. l , l ∈ {t, r}, where the function Tr() represents the trace operation of a matrix, the function Rank() represents the rank of a matrix, and V l , l ∈ {t, r} represents the reflection and transmission coefficient matrix of the STAR-RIS.

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

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

[0139] Step 6: Repeat Step 4, Step 5 until convergence, the obtained solution is a suboptimal solution of the secondary user SUr's secure transmission rate maximization problem ω in suboptimal solution * , is the base station beamforming vector that maximizes the secure transmission rate of the secondary user SUr, the reflection transmission coefficient matrix of STAR-RIS. Two schemes are adopted for performance comparison:

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

[0141]

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

[0143] G NLoS is modeled as Rician 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 Rician fading, and the variable satisfies the complex Gaussian distribution with a mean of 0 and a variance of 1. The path loss factors of the base station to the primary user PU, the STAR-RIS to the primary user PU, the secondary users SUr and SUt and the eavesdropping user Eve, and the base station to the STAR-RIS are set to 3.8, 2 and 2.4 respectively, and the Rician 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 symbol period of the secondary user SU to the symbol period of the primary user PU N = 50, R s,min = 3 bit / s / Hz, γ min = 20 dB, ζ = 750 MHz.

[0144] As Figure 2 shown, the change of 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 elements of STAR-RIS is shown. The parameters are set as the number of elements of STAR-RIS M = 20, M = 60. In the case of M = 20, the performance of the algorithm proposed in this paper is improved by 20.6%. In the case of M = 60, the performance of the algorithm proposed in this paper is improved by 23.2%. It can also be seen from the figure that when the number of elements of STAR-RIS increases, the secure transmission rate of the secondary user SUr also increases.

[0145] As Figure 3 shown, the influence of different base station transmitting power thresholds on the minimum communication secrecy rate of the secondary user is shown. With the increase of the transmitting power, the minimum communication secrecy rate of the secondary user also gradually increases, and the performance of the proposed scheme is always better than that of the fixed power allocation scheme.

[0146] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered in the protection scope of the present application.

Claims

1. An implementation method of a symbiotic radio transmission system based on STAR-RIS assistance, characterized in that, The method comprises the following steps: Step 1: Under the condition of considering the existence of an eavesdropper and the non-perfect CSI of the eavesdropping channel, a minimum communication secrecy rate maximization model of a secondary user in a symbiotic radio system assisted by STAR-RIS under non-perfect CSI is established; Step 2: The related parameters of the target problem are initialized, including channel data from the base station to the primary user PU, channel data from the base station to the STAR-RIS, channel data from the STAR-RIS to the primary user PU, channel data from the STAR-RIS to the secondary users SUr and SUt, channel estimation data and real channel data from the STAR-RIS to the eavesdropper Eve, a beamforming vector, a STAR-RIS reflection and transmission phase shift matrix, quality of service threshold requirements and a base station power threshold; Step 3: Based on the channel data obtained in step 2, the base station beamforming vector and the STAR-RIS reflection and transmission coefficient matrix, a minimum communication secrecy rate expression of the secondary user SUr is constructed; Step 4: Based on the minimum communication secrecy rate expression of the secondary user SUr, a minimum communication secrecy rate maximization problem of the secondary user SUr is constructed, the STAR-RIS reflection and transmission coefficient matrix is given, and the base station beamforming vector that maximizes the minimum communication secrecy rate of the secondary user SUr is calculated; Step 5: Given the base station beamforming vector, the STAR-RIS reflection and transmission coefficient matrix that maximizes the minimum communication secrecy rate of the secondary user SUr is calculated; Step 6: Repeat the above steps 4, 5 until convergence, and the obtained solution is a suboptimal solution of the secondary user SUr's secure transmission rate maximization problem In the suboptimal solution That is, the base station beamforming vector that maximizes the secure transmission rate of the secondary user SUr, the reflection transmission coefficient matrix of the STAR-RIS; The STAR-RIS is a simultaneous transmission and reflection reconfigurable intelligent reflecting surface, each element of the STAR-RIS includes a reflection element and a transmission element, the STAR-RIS divides a target area into an R region and a T region, the R region is a reflection region, and the T region is a transmission region, the symbiotic radio transmission system exists in the target area and includes a base station, two secondary users SUr and SUt, a primary user PU and an eavesdropper Eve, the STAR-RIS is arranged between the secondary user SUr and the secondary user SUt, the base station, the primary user PU, the secondary user SUr and the eavesdropper Eve are located in the R region of the STAR-RIS, the eavesdropper Eve has the ability to eavesdrop on the secondary user SUr, and the secondary user SUt is located in the T region of the STAR-RIS.

2. The implementation method of a symbiotic radio transmission system based on STAR-RIS assistance according to claim 1, characterized in that, In step 2, the legal primary user, secondary user and illegal eavesdropper are referred to as PU, SUr, SUt and Eve, and the mathematical modeling method of the downlink symbiotic radio system physical layer security problem based on the STAR-RIS under the condition of non-perfect eavesdropper CSI specifically comprises: The channel data from the STAR-RIS to the eavesdropper Eve is expressed as: wherein denotes a complex matrix of 1 x M, denotes the two-norm; Then the signal-to-interference-and-noise ratios (SINRs) of the PU, SUr, SUt and Eve are: where γ p (c) is the signal-to-interference-plus-noise ratio (SINR) at the primary user PU, Φ r is the reflection coefficient matrix of the STAR-RIS, and 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 the STAR-RIS to the primary user PU, G is the channel data from the base station to the STAR-RIS, and γ r (c), γ t (c) are the signal-to-interference-plus-noise ratios (SINRs) of the secondary users SUr and SUt, respectively, are the transmission rates of the secondary users SUr and SUt, respectively, Φ t is the transmission coefficient matrix of the STAR-RIS, are the noise powers at the secondary users SUr and SUt, respectively; are the channel data from the STAR-RIS to the secondary users SUr and SUt, respectively, N indicates that the symbol period of the secondary users SU is a multiple of the symbol period of the primary user PU, and γ e (c) is the signal-to-interference-plus-noise ratio (SINR) of the eavesdropper Eve, is the transmission rate of the eavesdropper Eve, is the noise power at the eavesdropper Eve; is the channel data from the STAR-RIS to the eavesdropper Eve; The achievable communication rates of the PU, SUr, SUt and Eve are: wherein Since there is a channel estimation error in the channel of the Eve, the minimum secrecy communication rate is: The active beamforming parameters of the base station and the passive beamforming parameters of the STAR-RIS are optimized to maximize the minimum secrecy communication rate, and the following optimization problem model is formed: wherein, is a set of STAR-RIS elements, denotes the reflection coefficient amplitude of the mth element of STAR-RIS, denotes the reflection coefficient phase of the mth element of STAR-RIS, denotes the transmission coefficient amplitude of the mth element of STAR-RIS, denotes the transmission coefficient phase of the mth element of STAR-RIS, denotes the minimum achievable rate for decoding the primary user signal required for the primary user PU to operate properly, γ min denotes the minimum achievable signal-to-noise ratio for decoding the secondary user signal required for the secondary users SUr and SUt to operate properly, C E denotes the maximum achievable eavesdropping rate for the eavesdropper Eve.

3. The implementation method of a symbiotic radio transmission system based on STAR-RIS assistance according to claim 1, characterized in that, The step 4 and step 5 in the alternating optimization solve the beamforming vector of the base station and the reflection transmission coefficient matrix of the STAR-RIS respectively, and specifically include: Optimize the base station transmit beamforming vector under the given STAR-RIS reflection coefficient matrix and transmission coefficient matrix, that is, fix Φr and Φt to optimize ω, at this time, the objective function and the constraint condition are defined by the parameter ω, and W = ωω H , E p = H p + F p , And introduce the relaxation variable τ, μ, while using the S-procedure theorem to maximize the safe transmission rate of the secondary user SuR P1 into the following form: The upper limit of log2(1+tau) in the objective function is obtained using the CVX tool, and the non-convex constraint condition is rewritten as a standard convex optimization constraint, and the specific operation is as follows: where τ (n) denotes the Taylor expansion point at the n-th iteration, at which the non-convex constraint is approximated by a convex one. Then, the problem of maximizing the safe transmission rate of the secondary user, Sr, can be reformulated as problem P2. By using the semi-definite relaxation method to relax the rank-one constraint, the problem P2 is transformed into a convex optimization problem, which is solved by using the CVX tool. It is proved that the solution of the relaxed problem still satisfies where is the value obtained by solving the convex optimization problem, and let τ (n) = τ. The updated value is substituted into the convex optimization problem, and the iteration is performed until convergence. Finally, the sub-optimal solution of W is obtained as W * ; the sub-optimal solution of ω is obtained from W * as ω * . Wherein, 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 matrix of STAR-RIS is optimized, that is, ω is fixed and Φ is optimized r and Φ t , that is, (v r and v t ), at this time, the objective function and the constraint condition are defined by the parameter ω, and the definition And introduce the slack variable τ, μ; The problem of maximizing the security transmission rate of the secondary user Sur P1 is converted into P3: In the same way as above, the objective function is rewritten as: By using the semi-definite relaxation method to relax the rank-one constraint, the problem P3 is converted into a convex optimization problem, which is solved by using the CVX tool. It is proved that the solution of the relaxed problem still satisfies where denotes the value obtained by solving the convex optimization problem, and let τ (n) = τ. The updated value is substituted into the convex optimization problem until convergence is achieved, and the final value of V l , l ∈ {t, r} is obtained. The eigenvector decomposition is used to obtain the suboptimal solution of v , l ∈ {t, r} from V l , l ∈ {t, r}, where the function Tr() represents the trace operation of a matrix, the function Rank() represents the rank of a matrix, and V l , l ∈ {t, r} represents the reflection transmission coefficient matrix of the STAR-RIS. Alternately solve P2 and P3 until convergence, the obtained solution is the suboptimal solution of the maximum security transmission rate of the secondary user SUr In the suboptimal solution That is, the base station beamforming vector that maximizes the security transmission rate of the secondary user SUr, the reflection transmission coefficient matrix of the STAR-RIS.

Images