Secure communication system and method for STAR-RIS assisted rate division multiple access system

Abstract

The invention discloses a secure communication system and a secure communication method for an STAR-RIS auxiliary rate division multiple access system. The system comprises a base station with M antennas; the STAR-RIS with N reflection units divides a communication area into a reflection area and a transmission area; the legal terminal devices serve as legal users, one part of the terminal devices are located in the reflection area, and the other part of the terminal devices are located in the transmission area; the illegal terminal equipment serves as an eavesdropper and is used for eavesdropping the confidential information transmitted by the base station to the legal terminal equipment in the reflection area or the transmission area; wherein the transmission beam forming vector of the base station and the phase shift matrix of the STAR-RIS are alternately optimized so as to maximize the lowest secrecy rate in the plurality of legal terminal devices. The invention provides a new solution for guaranteeing the security of a future wireless communication network, carries out research on the security performance optimization of the system, and can be widely applied to the technical field of wireless communication.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a secure communication system and method for a STAR-RIS assisted rate splitting multiple access system. Background Art

[0002] Industry and academia have conducted extensive research on STAR-RIS and RSMA technologies to enhance the security performance of communication systems.

[0003] The first prior art scheme studies a RIS-assisted secure communication system based on RSMA and proposes an iterative optimization algorithm. It maximizes the user's minimum confidentiality rate by jointly optimizing the active beamforming of the base station and the passive beamforming of the RIS. The second prior art scheme studies a STAR-RIS-assisted NOMA secure communication system, which interferes with eavesdroppers by transmitting additional artificial noise at the base station, and establishes an optimization problem for maximizing the confidentiality rate of legitimate users. The third prior art scheme derives the expression of the confidentiality interruption probability of the STAR-RIS-assisted NOMA network under the Nakagami-m fading channel. At the same time, the approximate expression of the confidentiality interruption probability under high signal-to-noise ratio is also studied.

[0004] However, current research in related fields mainly focuses on communication security issues in communication systems assisted by STAR-RIS or communication security issues in communication systems based on RSMA, and few studies explore the feasibility and potential advantages of combining STAR-RIS and RSMA in enhancing the security performance of communication systems. Considering the potential advantages of STAR-RIS in enhancing signal transmission quality and expanding service scope, as well as the outstanding performance of RSMA in ensuring communication security, studying the secure communication strategy combining STAR-RIS and RSMA is of great significance to ensuring the security of future wireless network environments.

[0005] In addition, current research in related fields usually assumes that the base station can obtain perfect channel state information (CSI) of legitimate users and eavesdroppers, and assumes the use of perfect serial interference cancellation (SIC) during user decoding, which is usually very difficult in practice. In order to make the proposed method more practical, it is necessary to consider imperfect CSI and imperfect SIC technology in the secure transmission scheme. Summary of the invention

[0006] In order to solve at least one of the technical problems existing in the prior art to a certain extent, the object of the present invention is to provide a secure communication system and method for a STAR-RIS assisted rate splitting multiple access system.

[0007] The first technical solution adopted by the present invention is:

[0008] A secure communication system for a STAR-RIS assisted rate splitting multiple access system, comprising:

[0009] A base station with M antennas;

[0010] STAR-RIS with N reflection units divides the communication area into reflection area and transmission area;

[0011] Multiple legal terminal devices, as legal users, some of which are located in the reflection area, and the other terminal devices are located in the transmission area;

[0012] Illegal terminal equipment, as an eavesdropper, is used to eavesdrop on confidential information transmitted from the base station to the legitimate terminal equipment in the reflection area or transmission area;

[0013] The base station's transmit beamforming vector and the STAR-RIS phase shift matrix are optimized alternately to maximize the lowest confidentiality rate among multiple legitimate terminal devices.

[0014] Furthermore, the steps of alternating optimization include:

[0015] Sub-problem 1: For the active beamforming vector at the base station, the SCA method and the penalty-based rank-one relaxation algorithm are used to calculate;

[0016] Sub-problem 2: For the phase shift matrix at STAR-RIS, the SCA method and the sequence rank-one constraint relaxation algorithm are used for calculation;

[0017] The two sub-problems are iterated alternately to obtain the final optimization parameters.

[0018] The second technical solution adopted by the present invention is:

[0019] A secure communication method for a STAR-RIS assisted rate splitting multiple access system comprises the following steps:

[0020] Construct a system model of STAR-RIS-assisted RSMA secure communication; the system model includes a base station, STAR-RIS, multiple legal terminal devices and illegal terminal devices;

[0021] Construct channel model, signal transmission and reception model, and confidentiality rate model based on the system model;

[0022] Determine the optimization problem based on the constructed model;

[0023] Based on the optimization problem, the base station's transmit beamforming vector and the STAR-RIS phase shift matrix are optimized alternately to maximize the lowest confidentiality rate among multiple legitimate terminal devices.

[0024] Furthermore, the channel model is constructed as follows:

[0025] Assume that all channels are quasi-static stationary fading channels, and the direct link from the base station to the terminal device obeys Rayleigh fading, while the cascaded links from the base station to STAR-RIS and from STAR-RIS to the terminal device obey Rice fading; the channels from the base station to STAR-RIS, STAR-RIS to the kth legal terminal device or illegal terminal device, and the base station to the kth legal terminal device or illegal terminal device are modeled as follows:

[0026]

[0027]

[0028] Where L0 represents the path loss when the reference distance is 1 meter; α1 and α2 represent the path loss exponents of the cascade link and the direct link respectively; d br d r,I and b,I They represent the distances from the base station to STAR-RIS, from STAR-RIS to the kth legal terminal device or illegal terminal device, and from the base station to the kth legal terminal device or illegal terminal device respectively; β1 and β2 represent the Rice fading coefficients of the corresponding channels; G L and h L is the line-of-sight component of the corresponding channel, G N and h N is the non-line-of-sight component of the corresponding channel;

[0029] is a set of legal users; {e} is an illegal user;

[0030] Taking into account the imperfect CSI estimation and delay-related errors, all channel matrices are remodeled according to the minimum mean square error as:

[0031]

[0032] Where δ∈[0,1] represents the accuracy of channel estimation, E br 、E b,I and E r,I represents the error matrix with mean 0 and unit variance for the corresponding channel.

[0033] Furthermore, the signal transmission and reception model is constructed as follows:

[0034] STAR-RIS uses an energy splitting protocol, that is, all units work in reflection and transmission modes at the same time. The reflection or transmission vector at STAR-RIS is expressed as:

[0035]

[0036] Where u1 represents the reflection vector and u2 represents the transmission vector, α k,n ∈[0,1] and θ k,n ∈(0,2π] represents the amplitude and phase shift of the nth element respectively. Each element of STAR-RIS is adjusted independently and satisfies the law of conservation of energy, i.e.

[0037] According to the principle of single-layer RSMA, the information sent by the base station to each legitimate user is divided into a public part and a private part; the public part is encoded into a public data stream s through a shared code book. c and decoded by both users, while the private part is independently encoded into a private data stream s k , which is decoded independently by the legitimate user k; at the base station, s c and k After linear precoding, the total transmitted signal of the base station is expressed as:

[0038]

[0039] In the formula, w c and w k They are c and k The precoding vector of

[0040] The base station sends confidential information to the user with the assistance of STAR-RIS. The received signal of the legitimate user k is expressed as:

[0041]

[0042] In the formula, v k =[u k 1], and represents the additive Gaussian white noise received by the legitimate user k;

[0043] Two situations are considered for the eavesdropper's location: 1) the eavesdropper is located in the reflection area; 2) the eavesdropper is located in the transmission area;

[0044] Therefore, the eavesdropper's received signal is expressed as:

[0045]

[0046] In the formula, E=1 and E=2 respectively indicate that the eavesdropper is located in the reflection area and the transmission area. Represents the additive white Gaussian noise received by the eavesdropper.

[0047] Furthermore, the confidentiality rate model is constructed as follows:

[0048] In the decoding phase, the legitimate user k will first use the private data stream as noise to decode the public data stream, so the legitimate user k decodes the public data stream s c The arrival rate is expressed as:

[0049]

[0050] In order to ensure that both legitimate users can successfully decode the public data stream s c , transmit public data streams c The achievable rate should not be greater than the user decoding s c The minimum achievable rate, i.e., the transmission rate s c The achievable rate should satisfy R c =min{R c,k}; After decoding c After that, the legitimate user k uses SIC technology to filter out the public part from the received signal and then decodes its own private data stream s k , considering the imperfect SIC in practical applications, legitimate users may be subject to residual interference from public information during decoding; therefore, legitimate user k decodes the private data stream s k The achievable rate is expressed as:

[0051]

[0052] Where β∈[0,1] represents the imperfect SIC factor;

[0053] An eavesdropper may also use SIC technology to decode the public and private information of legitimate users at the same time. c The achievable rate is expressed as:

[0054]

[0055] To prevent s c The eavesdropper successfully decodes the code, and the condition R should be met. c >R c,e ; At this time, when the eavesdropper decodes the user's private information, the public information can be used as noise to interfere with the eavesdropper; therefore, the eavesdropper decodes the legitimate user k's private data stream s k The achievable rate can be expressed as:

[0056]

[0057] After obtaining the achievable rates of public and private data streams decoded by the legitimate user and the achievable rates of public and private data streams decoded by the eavesdropper, the total confidentiality rate of the legitimate user k is expressed as:

[0058]

[0059] In the formula, represents the non-negative public secret rate assigned to the legitimate user k and satisfies represents the confidentiality rate of private information of legitimate user k.

[0060] Furthermore, determining the optimization problem according to the constructed model includes:

[0061] By jointly optimizing the base station's transmit beamforming vectors w1, w2 and w c , STAR-RIS reflection and transmission vectors v1 and v2 to maximize the minimum confidentiality rate among legitimate users; the mathematical expression of the optimization problem is P(1):

[0062]

[0063] C2:||w1|| 2 +||w2|| 2 +||w c || 2 ≤P max ,

[0064]

[0065] C4:|v 1,N+1 | 2 =|v 2,N+1 | 2 =1.

[0066] Constraint C1 The non-negative constraint ensures the condition R c >R c,e The constraint C2 indicates that the total transmission power of the base station is limited to P max Constraint C3 represents the coupling constraint between STAR-RIS reflection coefficient and transmission coefficient;

[0067] To facilitate the solution, define Satisfy W q ≥0, rank(W q )=1, and define Meet V k ≥0, rank(V k )=1; In addition, the slack variable t is introduced to deal with the non-concave objective function, so the problem P(1) is rewritten as P(2):

[0068]

[0069] C8:Tr(W1+W2+W c )≤P max ,

[0070]

[0071] C10:[V1] N+1,N+1 =[V2] N+1,N+1 =1,

[0072]

[0073] in:

[0074]

[0075] Since the variable {W q} and {V k}, P(2) is split into two sub-problems: active beamforming optimization and passive beamforming optimization, which are solved alternately.

[0076] Furthermore, the alternate optimization of the transmit beamforming vector of the base station and the phase shift matrix of STAR-RIS to maximize the lowest confidentiality rate among multiple legitimate terminal devices includes:

[0077] Sub-problem 1: For the active beamforming vector at the base station, the SCA method and the penalty-based rank-one relaxation algorithm are used to calculate;

[0078] Sub-problem 2: For the phase shift matrix at STAR-RIS, the SCA method and the sequence rank-one constraint relaxation algorithm are used for calculation;

[0079] The two sub-problems are iterated alternately to obtain the final optimization parameters.

[0080] Furthermore, the sub-question 1 specifically includes:

[0081] In the fixed variable {V k}, the active beamforming optimization subproblem is expressed as P(3):

[0082]

[0083] stC5-C8,C11.

[0084] Due to d p,k , g e and d c,k The concavity of may make constraints C6 and C7 non-convex. Use SCA technique to obtain their upper bounds. Let W, W and W denote the variable sets and Given a local feasible point W in the rth iteration r , W r and Wr , so d p,k , g e and d c,k The first-order Taylor expansion of is expressed as:

[0085]

[0086] D p,k , g e and d c,k Replacing them with upper bounds respectively, constraints C6 and C7 are transformed into convex form:

[0087]

[0088] Rank constraint rank(W q )=1 is rewritten into an equivalent form:

[0089] ||W q ||2-||W q || * ≥0

[0090] In the formula, ||W q || * and ||W q ||2 represents the matrix W q The nuclear norm and spectral norm of the variable W q Still non-convex, rewrite it into convex form using SCA technology:

[0091]

[0092] In the formula, express The eigenvector corresponding to the maximum eigenvalue of ; then, by introducing a non-negative penalty factor ρ, this formula is added as a penalty term to the objective function, and the problem P(3) is rewritten as P(3.1):

[0093]

[0094] In the formula, When ρ is small enough, the problem P(3.1) is solved to obtain a rank-one solution; at this time, the problem P(3.1) is a convex semidefinite programming problem; through singular value decomposition, the optimal {W q} to recover the optimal active beamforming vector {w q}.

[0095] Furthermore, the second sub-question specifically includes:

[0096] Given subproblem 1, we get {W q}, the passive beamforming optimization subproblem is expressed as P(4):

[0097]

[0098] stC5-C7,C9,C10,C12.

[0099] Given a local feasible point V in the rth iteration r After that, p,k , g e and d c,k The first-order Taylor expansion of is expressed as:

[0100]

[0101] Therefore, constraints C6 and C7 can be rewritten in convex form:

[0102]

[0103] The sequential rank-one constraint relaxation algorithm is used to replace the rank-one constraint in C12 with:

[0104]

[0105] In the formula, the parameters Used to control the matrix V k The ratio of the maximum eigenvalue and the trace of is the number of iterations according to the parameter The solution obtained; therefore, problem P(4) can be rewritten as the relaxed problem P(4.1):

[0106]

[0107] Solve problem P(4.1) and obtain the phase shift matrix at STAR-RIS.

[0108] The beneficial effects of the present invention are as follows: the present invention provides a new solution for ensuring the security of future wireless communication networks, and conducts research on optimizing the security performance of the system. In order to balance fairness and security, the present invention maximizes the minimum confidentiality rate among legitimate users by jointly optimizing the transmit beamforming of the base station and the reflection and transmission phase shift matrix of STAR-RIS. BRIEF DESCRIPTION OF THE DRAWINGS

[0109] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the embodiments of the present invention or the drawings of related technical solutions in the prior art are introduced below. It should be understood that the drawings introduced below are only for the convenience of clearly describing some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0110] Figure 1 A schematic diagram of a simulation position setting of a system in an embodiment of the present invention;

[0111] Figure 2 It is a schematic diagram of the average maximum and minimum confidentiality rates of the RSMA scheme assisted by STAR-RIS, the RSMA scheme assisted by traditional RIS, and the NOMA scheme assisted by STAR-RIS at different transmission powers in an embodiment of the present invention;

[0112] Figure 3 It is a schematic diagram of the average maximum and minimum confidentiality rates of the RSMA scheme assisted by STAR-RIS, the RSMA scheme assisted by STAR-RIS using the energy sharing protocol, the RSMA scheme assisted by the traditional RIS, and the NOMA scheme assisted by STAR-RIS under different numbers of reflection surface units in an embodiment of the present invention;

[0113] Figure 4 It is a schematic diagram of the average maximum and minimum confidentiality rates of the RSMA scheme assisted by STAR-RIS and the NOMA scheme assisted by STAR-RIS in an embodiment of the present invention under different numbers of base station transmitting antennas M and the vertical coordinates of the eavesdropper. DETAILED DESCRIPTION

[0114] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limitations of the present invention. For the step numbers in the following embodiments, they are only provided for the convenience of explanation, and the order between the steps is not limited in any way, and the execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0115] In the description of the present invention, it should be understood that descriptions involving orientations, such as up, down, front, back, left, right, etc., and orientations or positional relationships indicated are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0116] In the description of the present invention, "several" means one or more, "more" means more than two, "greater than", "less than", "exceed" etc. are understood as not including the number itself, and "above", "below", "within" etc. are understood as including the number itself. If there is a description of "first" or "second", it is only used for the purpose of distinguishing the technical features, and cannot be understood as indicating or implying the relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0117] In the description of the present invention, unless otherwise clearly defined, terms such as setting, installing, connecting, etc. should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in the present invention based on the specific content of the technical solution.

[0118] Terminology explanation:

[0119] STAR-RIS: A reconfigurable smart surface with dual functions of transmission and reflection.

[0120] RSMA: Rate Division Multiple Access.

[0121] RIS: Reconfigurable Intelligence Surface, intelligent supersurface, also called reconfigurable intelligent surface.

[0122] SROCR: A sequential rank-one constraint relaxation algorithm.

[0123] Reconfigurable smart surface (RIS) has become a revolutionary technology in the field of wireless communications, which can provide unprecedented control over the wireless propagation environment. With the development of metasurfaces, STAR-RIS has been proposed and widely studied in recent years. By supporting surface currents and magnetic currents at the same time, STAR-RIS can independently control the incident signal for reflection and transmission, thereby expanding its coverage to both sides of the surface and providing full spatial reconfigurability beyond traditional RIS. However, due to the broadcast characteristics of wireless channels, STAR-RIS-assisted systems are also exposed to the risk of omnidirectional eavesdropping. On the other hand, RSMA, as a robust and flexible multiple access technology, has significant advantages over space division multiple access (SDMA) technology and non-orthogonal multiple access (NOMA) technology in terms of spectrum efficiency, fairness and physical layer security (PLS). In terms of improving the security of communication systems, the main advantage of RSMA is that it can split user information into public and private parts, where public information can not only serve as useful data for legitimate users, but also interfere with potential eavesdroppers. Therefore, the present invention chooses to combine RSMA with STAR-RIS to ensure the communication security of users while expanding the coverage of the communication system.

[0124] In order to deal with the risk of eavesdropping in a STAR-RIS-assisted communication system, the present invention proposes a secure communication method for applying RSMA technology to a STAR-RIS-assisted transmission system. In order to balance fairness and security, this method maximizes the minimum confidentiality rate among legitimate users by jointly optimizing the transmit beamforming of the base station and the reflection and transmission phase shift matrices of STAR-RIS. Specifically, in order to solve the non-convex optimization problem of maximizing the minimum confidentiality rate among users, which contains multiple highly coupled variables, a two-stage joint optimization algorithm is designed, in which the active beamforming vector at the base station is obtained by adopting the continuous convex approximation (SCA) method and the penalty-based rank-one relaxation algorithm, and the phase shift matrix at the STAR-RIS is obtained by adopting the SCA method and the sequential rank-one constraint relaxation (SROCR) algorithm, and the final optimized parameters are obtained by an iterative algorithm.

[0125] The technical solution of the present invention is explained in detail below in conjunction with the accompanying drawings and specific embodiments.

[0126] (1) System model

[0127] The secure communication system of the STAR-RIS-assisted RSMA considered in the embodiment of the present invention includes a base station with M antennas, a STAR-RIS with N reflection units, and two single-antenna legitimate users, which are respectively located in the reflection area and the transmission area divided by the STAR-RIS. The legitimate user set is denoted as In addition, there is an untrusted single-antenna user, i.e., a potential eavesdropper, who will try to eavesdrop on the confidential information transmitted by the base station to the two legitimate users in the reflection area or the transmission area.

[0128] 1) Channel Modeling

[0129] Assume that all channels are quasi-static stationary fading channels, and the direct link from the base station to the user or eavesdropper obeys Rayleigh fading, while the cascaded links from the base station to STAR-RIS and from STAR-RIS to the user or eavesdropper obey Rician fading. The channels from the base station to STAR-RIS, STAR-RIS to the kth user or eavesdropper, and the base station to the kth user or eavesdropper are modeled as:

[0130]

[0131] Where L0 represents the path loss when the reference distance is 1 meter, α1 and α2 represent the path loss exponents of the cascade link and direct link, and their values ​​are set to 2.2 and 3.5, respectively. br d r,I and b,IThey represent the distances from the base station to STAR-RIS, STAR-RIS to the kth user or eavesdropper, and the base station to the kth user or eavesdropper, respectively. β1 and β2 represent the Rice fading coefficients of the corresponding channels, and their values ​​are both set to 3 dB. L and h L is the line-of-sight (Los) component of the corresponding channel, and G N and h N is the non-line-of-sight (NLoS) component of the corresponding channel.

[0132] Taking into account the imperfect CSI estimation and delay-related errors, all channel matrices are remodeled according to the minimum mean square error (MMSE) as:

[0133]

[0134] Among them, δ∈[0,1] represents the accuracy of channel estimation, E br 、E b,I and E r,I represents the error matrix with mean 0 and unit variance for the corresponding channel.

[0135] 2) Signal transmission and reception model

[0136] STAR-RIS uses an energy splitting protocol, that is, all units work in reflection and transmission modes at the same time. The reflection or transmission vector at STAR-RIS can be expressed as:

[0137]

[0138] Where u1 represents the reflection vector and u2 represents the transmission vector, α k,n ∈[0,1] and θ k,n ∈(0,2π] represents the amplitude and phase shift of the nth element respectively. Each element of STAR-RIS can be adjusted independently and satisfies the law of conservation of energy, i.e.

[0139] According to the principle of single-layer RSMA, the information sent by the base station to each user can be divided into a public part and a private part. The public part can be encoded into a public data stream s by a shared codebook. c The private part of each user is independently encoded into a private data stream s k , which is decoded independently by user k. c and k After linear precoding, the total transmitted signal of the base station can be expressed as:

[0140]

[0141] in and They are c and k The precoding vector of The base station sends confidential information to the user with the assistance of STAR-RIS. The received signal of user k can be expressed as:

[0142]

[0143] Among them, v k =[u k 1], and represents the additive white Gaussian noise (AWGN) received by user k. The location of the eavesdropper considers two situations: situation 1, the eavesdropper is located in the reflection area; situation 2, the eavesdropper is located in the transmission area. Therefore, the eavesdropper's received signal can be expressed as:

[0144]

[0145] Where E = 1 and E = 2 mean that the eavesdropper is located in the reflection area and the transmission area respectively. Indicates the AWGN received by the eavesdropper.

[0146] 3) Confidentiality Rate Model

[0147] In the decoding phase, user k will first use the private data stream as noise to decode the public data stream, so user k decodes the public data stream s c The achievable rate can be expressed as:

[0148]

[0149] In order to ensure that both legitimate users can successfully decode the public data stream s c , transmit public data streams c The achievable rate should not be greater than the user decoding s c The minimum achievable rate, i.e., the transmission rate s c The achievable rate should satisfy R c =min{R c,k}. After decoding c After that, user k uses SIC technology to filter out the public part from the received signal and then decodes its own private data stream s k , considering the imperfect SIC in practical applications, users may be subject to residual interference from public information during decoding. Therefore, user k decodes the private data stream s k The achievable rate can be expressed as:

[0150]

[0151] Here, β∈[0,1] represents the imperfect SIC factor.

[0152] An eavesdropper may also use SIC technology to decode the public and private information of legitimate users at the same time. c The achievable rate can be expressed as:

[0153]

[0154] To prevent s c The eavesdropper successfully decodes the code, and the condition R should be met. c >R c,e At this time, when the eavesdropper decodes the user's private information, the public information can act as noise to interfere with the eavesdropper. Therefore, the eavesdropper decodes the private data stream s of user k. k The achievable rate can be expressed as:

[0155]

[0156] After obtaining the achievable rates of the user decoding the public and private data streams and the achievable rates of the eavesdropper decoding the public and private data streams, the total confidentiality rate of user k can be expressed as:

[0157]

[0158] in, represents the non-negative public secret rate assigned to user k and satisfies represents the confidentiality rate of private information of user k.

[0159] (2) Optimization Problem

[0160] To complete the above definition, the present invention aims to optimize the base station's transmit beamforming vectors w1, w2 and w c , STAR-RIS reflection and transmission vectors v1 and v2 to maximize the minimum confidentiality rate among users. The mathematical expression of the optimization problem is P(1):

[0161]

[0162] Constraint C1 The non-negative constraint ensures the condition R c >R c,e Constraint C2 means that the total transmission power of the base station is limited to P max Constraint C3 represents the coupling constraint between the STAR-RIS reflection coefficient and transmission coefficient.

[0163] (3) Alternating Optimization Method

[0164] In the optimization problem P(1) under consideration, due to the non-concavity of the objective function, the non-convex unit module constraint in C3, and the high coupling between the optimization variables, the problem is difficult to solve directly. In order to effectively solve these parameters, the present invention first rephrases the problem P(1), and then designs a two-stage joint optimization algorithm, splits the problem into two sub-problems, and proposes an optimization method based on an alternating optimization framework. In sub-problem one, the continuous convex approximation (SCA) method is combined with a penalty-based rank-one relaxation algorithm to obtain the active transmit beamforming vector of the base station; in sub-problem two, the SCA method and the sequential rank-one constraint relaxation algorithm (SROCR) are used to obtain the passive beamforming vector of STAR-RIS. The last two sub-problems are iterated alternately to obtain the optimal solution. The specific process is:

[0165] 3.1) Reformulation of the optimization problem P(1)

[0166] To facilitate the solution, define Satisfy W q ≥0, rank(W q )=1, and define Meet V k ≥0, rank(V k )=1. In addition, the slack variable t is introduced to deal with non-concave objective functions, so the problem P(1) can be rewritten as P(2):

[0167]

[0168] in, Since the variable {W q} and {V k}, P(2) can be split into two sub-problems: active beamforming optimization and passive beamforming optimization, which are solved alternately.

[0169] 3.2) Sub-problem 1: Active beamforming optimization

[0170] In the fixed variable {V k}, the active beamforming optimization subproblem can be expressed as P(3):

[0171]

[0172] Due to d p,k , g e and d c,k The concavity of may make constraints C6 and C7 non-convex, and we can use SCA techniques to obtain their upper bounds. Let W, W, and W denote the variable sets and Given a local feasible point W in the rth iteration r , W r and W r , so d p,k , g e and d c,k The first-order Taylor expansion of can be expressed as:

[0173]

[0174] D p,k , g e and d c,k Substituting the upper bounds in (19)-(21) respectively, constraints C6 and C7 can be transformed into convex form:

[0175]

[0176] At this point, the only difficulty in solving P(3) is the rank-one constraint in constraint C11. Considering that C11 contains three variables, the present invention adopts a low-complexity penalty-based algorithm to obtain a rank-one solution. Specifically, the rank-one constraint rank(W q )=1 can be rewritten in an equivalent form:

[0177] ||W q ||2-||W q || * ≥0 (24)

[0178] Among them, ||W q |\ * and ||W q ||2 represents the matrix W q Since expression (24) is in the form of convex difference, with respect to the variable W q It is still non-convex, and we can use SCA technique to rewrite (24) into convex form:

[0179]

[0180] in express Then, by introducing a non-negative penalty factor ρ and adding expression (25) as a penalty term to the objective function, problem P(3) can be rewritten as P(3.1):

[0181]

[0182] in, When ρ is small enough, the problem P(3.1) can be solved to obtain a rank-one solution. In this case, the problem P(3.1) is a convex semidefinite programming problem (SDP), which can be solved using convex optimization tools such as CVX. By singular value decomposition, the optimal {W q} to recover the optimal active beamforming vector {w q}.

[0183] 3.3) Sub-problem 2: Passive beamforming optimization

[0184] Given subproblem 1, we get {W q}, the passive beamforming optimization subproblem can be expressed as P(4):

[0185]

[0186] Similar to the solution of subproblem 1, given the local feasible point V in the rth iteration r After that, p,k , g e and d c,k The first-order Taylor expansion of can be expressed as:

[0187]

[0188] Therefore, constraints C6 and C7 can be rewritten in convex form:

[0189]

[0190] At this time, the rank-one constraint in constraint condition C12 still makes the current problem non-convex. Considering that there are fewer variables in the constraint condition, the present invention adopts a SROCR algorithm with higher complexity but better performance to replace the rank-one constraint in C12 with:

[0191]

[0192] Among them, the parameters Used to control the matrix V k The ratio of the maximum eigenvalue and the trace of is the number of iterations according to the parameter The solution obtained. Therefore, problem P(4) can be rewritten as the relaxed problem P(4.1):

[0193]

[0194] Problem P(4.1) is convex and can be solved using CVX tools. The specific steps of the SROCR algorithm proposed in the embodiment of the present invention are:

[0195] Step 1: Initialization. Initialize the convergence threshold ξ1=ξ2=10-2 , and the feasible solution of problem P(4) and Set the number of iterations i = 0. Set parameters And solve the relaxation problem P(4.1) to obtain and Initialization step size δ (i) .

[0196] Step 2: Relax the problem and solve it. Given Use CVX to solve problem P(4.1). If the problem is solvable, the optimal solution at this time is recorded as And keep the step size δ (i) unchanged; if the problem is unsolvable, the solution of the previous iteration remains unchanged. And update the step size δ (i+1) =δ (i) / 2.

[0197] Step 3: Parameter update. Update parameters Update the number of iterations i=i+1.

[0198] Step 2 and step 3 are executed alternately until the condition is met and

[0199] By solving P(4.1) we can get the optimal {V k}, and recover the optimal passive beamforming vector {v k Considering the difficulty of realizing continuous phase shifting on STAR-RIS in practice, the obtained {v k}Quantize to the nearest feasible point of a discrete set:

[0200]

[0201] in, represents the set of discrete phase shifts and Z represents the number of discrete values ​​it can take.

[0202] 3.4) Alternating Optimization

[0203] The specific steps of the alternating optimization algorithm proposed in the embodiment of the present invention are as follows:

[0204] Step 1: Initialization. Initialize the convergence threshold ξ=10 -3 , and the maximum number of iterations ω, find a set of feasible solutions to problem P(2) and Set the number of iterations l=0.

[0205] Step 2: Solve subproblem 1. Given and Solve problem P(3.1) to get the optimal The optimal active beamforming vector is recovered by singular value decomposition

[0206] Step 3: Solve subproblem 2. Given Use the SROCR algorithm to solve problem P(4.1) and obtain the optimal The optimal passive beamforming vector is recovered by singular value decomposition The quantized Set the number of iterations l=l+1.

[0207] Step 2 and step 3 are performed alternately until the decrease in the score value of the objective function is lower than the threshold ξ or the number of iterations l ≥ ω.

[0208] (4) Simulation Experiment Results

[0209] In this embodiment, simulation analysis verifies the effectiveness of the proposed STAR-RIS-assisted RSMA scheme in improving the maximum and minimum confidentiality rates of users. It is also compared with the traditional RIS-assisted RSMA scheme, the STAR-RIS-assisted NOMA scheme, and the STAR-RIS-assisted RSMA scheme using the energy sharing protocol.

[0210] A comparison is made. In the traditional RIS-assisted RSMA scheme, STAR-RIS is replaced by two traditional RISs, one is a reflection RIS and the other is a transmission RIS, and both have N / 2 elements. In the STAR-RIS-assisted RSMA scheme using the energy-sharing protocol, the reflection and transmission coefficients of STAR-RIS use the same amplitude coefficient.

[0211] The locations of the base station, STAR-RIS, user 1, user 2, and the eavesdropper are set as follows: Figure 1 As shown in Figure 2, two cases are considered: the eavesdropper is located in the reflection area or the transmission area. The other simulation experiment related parameters are set as follows: The variance of AWGN at the user and the eavesdropper is The channel estimation accuracy δ is 0.99.

[0212] Figure 2The changes of the average maximum and minimum confidentiality rates of the RSMA scheme assisted by STAR-RIS in two cases with the increase of base station transmission power are shown, and compared with the RSMA scheme assisted by traditional RIS and the NOMA scheme assisted by STAR-RIS. The number of base station antennas M is set to 4, and the number of reflection surfaces N is set to 36. It can be seen that the maximum and minimum confidentiality rates that can be achieved by the RSMA scheme assisted by STAR-RIS proposed in the present invention are better than the other two schemes. It can be seen that in terms of improving the security performance of the RSMA communication system, STAR-RIS is better than the traditional RIS, and the RSMA strategy provides better security performance gains than the NOMA strategy.

[0213] Figure 3 The changes of the average maximum and minimum confidentiality rates of the RSMA scheme assisted by STAR-RIS proposed in the present invention with the increase of the number of reflector units N in two cases are shown, and compared with the RSMA scheme assisted by STAR-RIS using the energy sharing protocol, the RSMA scheme assisted by the traditional RIS, and the NOMA scheme assisted by STAR-RIS. The number of base station antennas M is set to 4, and the base station transmission power is set to 15 dBm. It can be seen from the simulation diagram that the maximum and minimum confidentiality rates that can be achieved by the RSMA scheme assisted by STAR-RIS proposed in the present invention are better than those of the other three schemes. It can be seen that the combination of STAR-RIS and RSMA can more effectively ensure the communication security of the system.

[0214] Figure 4 The simulation results show that the average maximum and minimum confidentiality rates of the RSMA scheme assisted by STAR-RIS proposed in the present invention change with the increase of the vertical coordinates of the eavesdropper under different base station transmitting antenna numbers M, and are compared with the NOMA scheme assisted by STAR-RIS. It can be seen from the simulation diagram that the maximum and minimum confidentiality rates that can be achieved by the RSMA scheme assisted by STAR-RIS proposed in the present invention are significantly better than those of the comparison scheme, which shows that the RSMA strategy can provide better security performance gains than the NOMA strategy.

[0215] (5) Advantages and beneficial effects

[0216] At present, the research in related fields mainly focuses on the communication security issues in the communication system assisted by STAR-RIS or the communication security issues in the communication system based on RSMA, but there are few studies on the feasibility and potential advantages of combining STAR-RIS and RSMA in enhancing the security performance of the communication system. At the same time, the current research in related fields usually assumes that the base station can obtain the perfect CSI of the legitimate user and the eavesdropper, and assumes the use of perfect SIC when decoding the user, which is usually very difficult in practice. Taking into account the research status of the prior art, the present invention proposes a secure communication method based on RSMA assisted by STAR-RIS. The present invention mainly has the following advantages:

[0217] 1) The present invention proposes a secure communication system based on RSMA assisted by STAR-RIS, which provides a new solution for ensuring the security of future wireless communication networks, and conducts research on the security performance optimization of the system.

[0218] 2) Considering the difficulty of obtaining perfect CSI and realizing perfect SIC in practice, the present invention further considers the cases of imperfect CSI and imperfect SIC in the secure transmission scheme.

[0219] 3) Based on the proposed system, in order to maximize the user's minimum confidentiality rate, the present invention proposes a method for jointly optimizing the active beamforming vector of the base station and the passive beamforming vector of STAR-RIS, which can effectively improve the security performance of the system.

[0220] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0221] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable ordinary technicians in the field to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. A secure communication system for a STAR-RIS assisted rate splitting multiple access system, characterized in that: include: A base station with M antennas; STAR-RIS with N reflection units divides the communication area into reflection area and transmission area; Multiple legitimate terminal devices, as legitimate users; Illegal terminal equipment, as an eavesdropper, is used to eavesdrop on confidential information transmitted from the base station to the legitimate terminal equipment in the reflection area or transmission area; The base station's transmit beamforming vector and the STAR-RIS phase shift matrix are optimized alternately to maximize the lowest confidentiality rate among multiple legitimate terminal devices.

2. A secure communication system for a STAR-RIS assisted rate splitting multiple access system according to claim 1, characterized in that: The steps of alternating optimization include: Sub-problem 1: For the active beamforming vector at the base station, the SCA method and the penalty-based rank-one relaxation algorithm are used to calculate; Sub-problem 2: For the phase shift matrix at STAR-RIS, the SCA method and the sequence rank-one constraint relaxation algorithm are used for calculation; The two sub-problems are iterated alternately to obtain the final optimization parameters.

3. A secure communication method for a STAR-RIS assisted rate splitting multiple access system, characterized in that: The following steps are involved: Construct a system model for STAR-RIS-assisted RSMA secure communication; The system model includes base stations, STAR-RIS, multiple legal terminal devices and illegal terminal devices; Construct channel model, signal transmission and reception model, and confidentiality rate model based on the system model; Determine the optimization problem based on the constructed model; Based on the optimization problem, the base station's transmit beamforming vector and the STAR-RIS phase shift matrix are optimized alternately to maximize the lowest confidentiality rate among multiple legitimate terminal devices.

4. A secure communication method for a STAR-RIS assisted rate splitting multiple access system according to claim 3, characterized in that: The channel model is constructed as follows: Assume that all channels are quasi-static stationary fading channels, and the direct link from the base station to the terminal device obeys Rayleigh fading, while the cascaded links from the base station to STAR-RIS and from STAR-RIS to the terminal device obey Ricean fading; The channels from the base station to STAR-RIS, from STAR-RIS to the kth legal terminal device or illegal terminal device, and from the base station to the kth legal terminal device or illegal terminal device are modeled as follows: Where L0 represents the path loss when the reference distance is 1 meter; α1 and α2 represent the path loss exponents of the cascade link and the direct link respectively; d br d r,I and b,I They represent the distances from the base station to STAR-RIS, from STAR-RIS to the kth legal terminal device or illegal terminal device, and from the base station to the kth legal terminal device or illegal terminal device respectively; β1 and β2 represent the Rice fading coefficients of the corresponding channels; G L and h L is the line-of-sight component of the corresponding channel, G N and h N is the non-line-of-sight component of the corresponding channel; is a set of legal users; {e} is an illegal user; Taking into account the imperfect CSI estimation and delay-related errors, all channel matrices are remodeled according to the minimum mean square error as: Where δ∈[0,1] represents the accuracy of channel estimation, E br 、E b,I and E r,I represents the error matrix with mean 0 and unit variance for the corresponding channel.

5. A secure communication method for a STAR-RIS assisted rate splitting multiple access system according to claim 3, characterized in that: The signal transmission and reception model is constructed as follows: STAR-RIS uses an energy splitting protocol, that is, all units work in reflection and transmission modes at the same time. The reflection or transmission vector at STAR-RIS is expressed as: Where u1 represents the reflection vector, u2 represents the transmission vector, and α k,n ∈[0,1] and θ k,n ∈(0,2π] represents the amplitude and phase shift of the nth element respectively; According to the principle of single-layer RSMA, the information sent by the base station to each legitimate user is split into a public part and a private part; The public part is encoded into a public data stream s through a shared codebook c and decoded by both users, while the private part is independently encoded into a private data stream s k , which is decoded independently by the legitimate user k; at the base station, s c and k After linear precoding, the total transmitted signal of the base station is expressed as: In the formula, w c and w k They are c and k The precoding vector of The base station sends confidential information to the user with the assistance of STAR-RIS. The received signal of the legitimate user k is expressed as: In the formula, v k =[u k 1], and represents the additive Gaussian white noise received by the legitimate user k; Two situations are considered for the eavesdropper's location: 1) the eavesdropper is located in the reflection area; 2) the eavesdropper is located in the transmission area; Therefore, the eavesdropper's received signal is expressed as: In the formula, E=1 and E=2 respectively indicate that the eavesdropper is located in the reflection area and the transmission area. Represents the additive white Gaussian noise received by the eavesdropper.

6. A secure communication method for a STAR-RIS assisted rate splitting multiple access system according to claim 3, characterized in that: The confidentiality rate model is constructed as follows: In the decoding phase, the legitimate user k will first use the private data stream as noise to decode the public data stream, so the legitimate user k decodes the public data stream s c The arrival rate is expressed as: In order to ensure that both legitimate users can successfully decode the public data stream s c , transmit public data streams c The achievable rate should not be greater than the user decoding s c The minimum achievable rate, i.e., the transmission rate s c The achievable rate should satisfy R c =min{R c,k }; After decoding c After that, the legitimate user k uses SIC technology to filter out the public part from the received signal and then decodes its own private data stream s k , considering the imperfect SIC in practical applications, legitimate users may be subject to residual interference from public information during decoding; therefore, legitimate user k decodes the private data stream s k The achievable rate is expressed as: Where β∈[0,1] represents the imperfect SIC factor; An eavesdropper may also use SIC technology to decode the public and private information of legitimate users at the same time. c The achievable rate is expressed as: To prevent s c The eavesdropper successfully decodes the code, and the condition R should be met. c >R c,e ; At this time, when the eavesdropper decodes the user's private information, the public information can be used as noise to interfere with the eavesdropper; therefore, the eavesdropper decodes the legitimate user k's private data stream s k The achievable rate can be expressed as: After obtaining the achievable rates of public and private data streams decoded by the legitimate user and the achievable rates of public and private data streams decoded by the eavesdropper, the total confidentiality rate of the legitimate user k is expressed as: In the formula, represents the non-negative public secret rate assigned to the legitimate user k and satisfies represents the confidentiality rate of private information of legitimate user k.

7. A secure communication method for a STAR-RIS assisted rate splitting multiple access system according to claim 3, characterized in that: Determining the optimization problem according to the constructed model includes: By jointly optimizing the base station's transmit beamforming vectors w1, w2 and w c , STAR-RIS reflection and transmission vectors v1 and v2 to maximize the minimum confidentiality rate among legitimate users; the mathematical expression of the optimization problem is P(1): Constraint C1 The non-negative constraint ensures the condition R c >R c,e The constraint C2 indicates that the total transmission power of the base station is limited to P max Constraint C3 represents the coupling constraint between STAR-RIS reflection coefficient and transmission coefficient; To facilitate the solution, define Satisfy W q ≥0, rank(W q )=1, and define Meet V k ≥0, rank(V k )=1; In addition, the slack variable t is introduced to deal with the non-concave objective function, so the problem P(1) is rewritten as P(2): in: k,j∈{1,2},k≠j; Since the variable {W q } and {V k }, P(2) is split into two sub-problems: active beamforming optimization and passive beamforming optimization, which are solved alternately.

8. A secure communication method for a STAR-RIS assisted rate splitting multiple access system according to claim 7, characterized in that: The alternate optimization of the base station's transmit beamforming vector and the STAR-RIS phase shift matrix to maximize the lowest confidentiality rate among multiple legal terminal devices includes: Sub-problem 1: For the active beamforming vector at the base station, the SCA method and the penalty-based rank-one relaxation algorithm are used to calculate; Sub-problem 2: For the phase shift matrix at STAR-RIS, the SCA method and the sequence rank-one constraint relaxation algorithm are used for calculation; The two sub-problems are iterated alternately to obtain the final optimization parameters.

9. A secure communication method for a STAR-RIS assisted rate splitting multiple access system according to claim 8, characterized in that: The sub-question 1 specifically includes: In the fixed variable {V k }, the active beamforming optimization subproblem is expressed as P(3): Due to d p,k , g e and d c,k The concavity of may make constraints C6 and C7 non-convex. Use SCA technique to obtain their upper bounds. Let W, W and W denote the variable sets and Given a local feasible point W in the rth iteration r , W r and W r , so d p,k , g e and d c,k The first-order Taylor expansion of is expressed as: D p,k , g e and d c,k Replacing them with upper bounds respectively, constraints C6 and C7 are transformed into convex form: Rank constraint rank(W q )=1 is rewritten into an equivalent form: ||In q ||2-||In q || * ≥0 In the formula, ||W q || * and ||W q ||2 represents the matrix W q The nuclear norm and spectral norm of the variable W q Still non-convex, rewrite it into convex form using SCA technology: In the formula, express The eigenvector corresponding to the maximum eigenvalue of ; then, by introducing a non-negative penalty factor ρ, this formula is added as a penalty term to the objective function, and the problem P(3) is rewritten as P(3.1): In the formula, When ρ is small enough, the problem P(3.1) is solved to obtain a rank-one solution; at this time, the problem P(3.1) is a convex semidefinite programming problem; through singular value decomposition, the optimal {W q } to recover the optimal active beamforming vector {w q }.

10. A secure communication method for a STAR-RIS assisted rate splitting multiple access system according to claim 9, characterized in that: The second sub-question specifically includes: Given subproblem 1, we get {W q }, the passive beamforming optimization subproblem is expressed as P(4): Given a local feasible point V in the rth iteration r After that, p,k , g e and d c,k The first-order Taylor expansion of is expressed as: Therefore, constraints C6 and C7 can be rewritten in convex form: The sequential rank-one constraint relaxation algorithm is used to replace the rank-one constraint in C12 with: In the formula, the parameters Used to control the matrix V k The ratio of the maximum eigenvalue and the trace of is the number of iterations according to the parameter The solution obtained; therefore, problem P(4) can be rewritten as the relaxed problem P(4.1): Solve problem P(4.1) and obtain the phase shift matrix at STAR-RIS.

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