A STAR-RIS-assisted NOMA system uplink low-power transmission method

Abstract

The present invention discloses a low-power uplink transmission method for a STAR-RIS-assisted NOMA system, comprising: establishing channel models required by the system between a central user and a base station, between a STAR-RIS and the base station, and between a transmission zone user / a reflection zone user and the STAR-RIS, and then calculating a mathematical expression for a total received signal at a base station receiving end; sorting different users based on a demodulation order of the NOMA system and a mathematical expression for the total received signal, and obtaining expressions for signal-to-interference-and-noise ratios and achievable rates for different users; establishing an original optimization problem for user transmit power, a transmission / reflection beamformer, and time allocation, alternately optimizing user transmit power, a transmission / reflection coefficient matrix, and a time allocation coefficient variable, and solving the original optimization problem after convergence to obtain the minimized total transmit power of the NOMA system.

Description

Technical Field

[0001] The present invention relates to a STAR-RIS-assisted NOMA system uplink low-power transmission method, and in particular to a reconfigurable intelligent surface-assisted non-orthogonal multiple access system uplink low-power transmission method for simultaneous projection and reflection, belonging to the technical field of non-orthogonal multiple access in wireless communications. Background Art

[0002] Reconfigurable smart surfaces (RIS) are a new technology for sixth-generation wireless communication systems, aiming to improve spectral and energy efficiency. RIS is a planar surface composed of a large number of low-cost passive components that consumes virtually no energy. By adjusting the amplitude and phase of the incident signal, RIS can improve communication system performance. However, these advantages are primarily limited to situations where the RIS can only reflect the incident signal, requiring the base station and users to be located on the same side of the RIS, which lacks deployment flexibility. Because traditional RIS-assisted NOMA systems can only serve users on one side, STAR-RIS-assisted NOMA systems, a reconfigurable smart surface that simultaneously projects and reflects, have emerged to provide omnidirectional wireless coverage.

[0003] Current transmission methods for STAR-RIS-assisted NOMA systems do not fully jointly optimize user transmit power, projection and reflection beamformers, and time allocation. STAR-RIS-assisted OMA schemes fail to leverage the system's advantages in superimposed coding and continuous interference cancellation. Traditional RIS-assisted NOMA schemes fail to maximize STAR-RIS deployment flexibility. Non-RIS-assisted NOMA schemes fail to leverage the advantages of RIS in both enhancing useful signals and canceling interfering signals. Therefore, in STAR-RIS-assisted NOMA systems, the power allocation and phase offset schemes designed for traditional RIS systems fail to fully leverage the advantages of STAR-RIS for bilateral user channel configuration, fail to fully unleash the potential advantages of STAR-RIS-assisted NOMA technology in reducing transmit power consumption, and fail to achieve efficient utilization of system power resources. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a STAR-RIS-assisted NOMA system uplink low-power transmission method to achieve efficient utilization of the system's power resources.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0006] The present invention provides a STAR-RIS-assisted NOMA system uplink low-power transmission method, characterized by comprising the following steps:

[0007] Establish the channel models required by the system between the central user and the base station, between STAR-RIS and the base station, and between the transmission area user / reflection area user and STAR-RIS;

[0008] According to the channel model, calculate the mathematical expression of the total received signal at the base station receiving end;

[0009] Based on the demodulation order of the NOMA system and the mathematical expression of the total received signal, different users are sorted to obtain the signal-to-interference-noise ratio and achievable rate expressions of different users;

[0010] Establish the original optimization problem of user transmit power, transmission / reflection beamformer and time allocation, and alternately optimize the user transmit power, transmission / reflection coefficient matrix and time allocation coefficient variables;

[0011] The original optimization problem is solved after convergence, and the minimized total transmit power of the NOMA system is obtained.

[0012] Furthermore, the mathematical expression of the total received signal at the base station receiving end is:

[0013]

[0014] in, represents the transmission data of the kth central user, represents the transmission data of the kth edge user; represents the transmission power of the kth central user, represents the transmission power of the kth edge user; represents the reflection / projection coefficient matrix of STAR-RIS; The mean is 0 and the variance is Complex Gaussian noise; represents the channel link between the kth transmission / reflection area user and STAR-RIS, represents the communication link between BS and STAR-RIS, represents the channel link between the BS and the kth central user.

[0015] Furthermore, the achievable rate expression is as follows:

[0016]

[0017]

[0018] in, represents the achievable rate of the central user, represents the achievable rate of edge users, represents the time allocation coefficient for projected user or reflected user transmission; represents the signal-to-interference-and-noise ratio of the kth central user, It represents the signal-to-interference-and-noise ratio of the user in the kth transmission area / reflection area.

[0019] Furthermore, the original optimization problem is expressed as follows:

[0020]

[0021] in, and Indicates the minimum transmission rate required by the user, where Constraint Q1 indicates that STAR-RIS adopts an orthogonal time slot protocol; constraints Q2 and Q3 indicate that the user's transmission rate is higher than the minimum rate requirement; constraint Q4 indicates that each reflection element only changes the phase shift of the incident signal; constraints Q5 and Q6 indicate the strength order of the user channels in the NOMA system.

[0022] Furthermore, the specific steps for converging the original optimization problem are as follows:

[0023] When the reflection / projection coefficient matrix and time allocation coefficient are fixed, the original optimization problem is transformed into the first sub-optimization problem and solved using the contradiction method to obtain the optimal user transmit power.

[0024] When the user transmission power and time allocation coefficient are fixed, the original optimization problem is transformed into a second sub-optimization problem to obtain the optimal solution of the reflection / projection coefficient matrix;

[0025] When the user transmit power and reflection / projection coefficient matrix are fixed, the original optimization problem is transformed into a third sub-optimization problem by using the Lagrange multiplier method, and the optimal solution of the time allocation coefficient is obtained by a one-dimensional search method;

[0026] Furthermore, the steps for obtaining the optimal transmit power of a user are as follows:

[0027] The first sub-optimization problem is solved using the contradiction method. The first sub-optimization problem is expressed as follows:

[0028] ;

[0029] When the optimal solution of the first sub-optimization problem is obtained, the constraint condition takes the equal sign, and the closed-form expression of the optimal transmission power of users in the transmission area / reflection area is obtained, which is expressed as follows:

[0030] ,

[0031] in, ,when , ;when , ;

[0032] Substituting the optimal transmit power of users in the transmission / reflection areas into the minimum rate requirement of users in the central area, the closed-form expression for the optimal transmit power of users in the central area is obtained as follows:

[0033] ,

[0034] in, ,when , ;when , , .

[0035] Furthermore, the specific steps for obtaining the optimal solution of the reflection / projection coefficient matrix are as follows:

[0036] The original optimization problem is constrained to a semi-definite programming problem, and the convex optimization solving tool is used to solve the semi-definite programming problem.

[0037] By performing eigenvalue decomposition on the optimal solution of the semidefinite programming problem, the eigenvector corresponding to the maximum eigenvalue is taken as the approximate solution to satisfy the rank-one constraint;

[0038] Each element after decomposition is normalized to meet the unit modulus constraint and obtain the optimal solution of the reflection / projection coefficient matrix.

[0039] Furthermore, the second sub-optimization problem is expressed as follows:

[0040] ;

[0041] definition and ,in , represents the Hadamard product operation, and the second sub-optimization problem is simplified to the optimization problem P4, which is expressed as follows:

[0042]

[0043] On the basis of satisfying the rank-one constraint, the auxiliary matrix is ​​introduced to transform the objective function in the optimization problem P4;

[0044] According to the objective function, the optimization problem P4 is transformed into the optimization problem P5, which is expressed as follows:

[0045] ,

[0046] Ignoring the rank-one constraint, the CVX toolkit is used to obtain the optimal solution to the semidefinite programming problem.

[0047] Furthermore, the steps for obtaining the optimal solution of the time allocation coefficient are as follows:

[0048] The Lagrange multiplier method is used to transform the original optimization problem into a third sub-optimization problem. The third sub-optimization problem is an unconstrained nonlinear optimization problem, which is specifically expressed as follows:

[0049]

[0050] The one-dimensional search method is used to solve the third sub-optimization problem and obtain the optimal solution of the time allocation coefficient.

[0051] Furthermore, solving the optimization problem includes iterating the above steps in sequence, repeatedly converging the optimization problem until the optimization objective function value converges, and obtaining the optimal user transmission power, transmission / reflection coefficient matrix and time allocation coefficient of the system.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] This paper studies a low-power uplink transmission method for a STAR-RIS-assisted NOMA system. By jointly designing the phase shift, power control, and time allocation of RIS, the total power consumption of the STAR-RIS-assisted NOMA uplink is minimized.

[0054] Based on BCA, SDP and one-dimensional search techniques, a new algorithm is developed to solve the time allocation optimization problem and significantly reduce the total transmission power consumption of the STAR-RIS-assisted uplink NOMA system. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a STAR-RIS-assisted NOMA system uplink transmission model diagram provided by an embodiment of the present invention;

[0056] Figure 2 This is a curve diagram of the total transmit power consumption of the NOMA system under different minimum signal-to-noise ratio conditions provided by an embodiment of the present invention;

[0057] Figure 3 This is a curve diagram of the total transmission power consumption of the NOMA system under different numbers of STAR-RIS reconstruction units provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0059] The present invention considers the uplink transmission of the non-orthogonal multiple access system NOMA, in which the base station BS is deployed in the center of the cell and its coverage radius is .have The reconfigurable smart surface STAR-RIS with simultaneous projection and reflection of reconfigurable units is deployed at the edge of the cell to assist the data transmission of users at the cell edge. Its coverage radius is .

[0060] According to the deployment of BS and STAR-RIS, the entire cell space is divided into three parts, namely the cell center area, the cell edge reflection area and the cell edge transmission area. In addition, the number of users in the cell center area, the cell edge reflection area and the cell edge transmission area are 、 and , the BS and the reflection area users are on the same side of STAR-RIS, while the transmission area users are on the other side. The user sets in the cell center, cell edge reflection area and cell edge transmission area are expressed as 、 and Both users and base stations are equipped with a single antenna. Users in the central area are located near the base station BS and can communicate directly with the base station BS. Users in the reflection area and the transmission area transmit messages to the BS through direct signals and STAR-RIS reflection / transmission channels.

[0061] The present invention provides a STAR-RIS assisted NOMA system uplink transmission method, the system model diagram is as follows Figure 1 As shown, the specific transmission method includes the following steps:

[0062] S1: Establish channel models between users in the system center area and the base station, between STAR-RIS and the base station, and between users in the transmission / reflection area and STAR-RIS.

[0063] The central user is located in the central area of ​​the cell, and the channel link between the BS and the kth central user is expressed as:

[0064] , ,

[0065] in, represents the path loss index between BS and central user, represents the propagation distance between the BS and the kth central user, represents the small-scale fading between the BS and the k-th central user.

[0066] The small-scale fading of the channel between the BS and the cell center user is independent of each other and obeys Rayleigh fading, following a complex Gaussian distribution with a mean of 0 and a variance of 1, that is, .

[0067] Similarly, the direct channel between the BS and the kth reflection / projection user is expressed as , , ,in, Represents the path loss index between BS and reflection / projection user, represents the propagation distance between the BS and the kth reflection / projection user, represents the small-scale fading between the BS and the kth reflecting / projecting user.

[0068] The small-scale fading of the direct channel between the BS and the reflection / projection user is independent of each other and obeys Rayleigh fading, which follows a complex Gaussian distribution with a mean of 0 and a variance of 1, that is, .

[0069] set up As the channel link between the BS and STAR-RIS, STAR-RIS can be pre-deployed at a pre-selected location to ensure a line-of-sight link between STAR-RIS and its service users. The channel link between the BS and STAR-RIS is modeled using Rician fading. The channel modeling is as follows:

[0070]

[0071] in, is the communication link between BS and STAR-RIS, represents the Ricean factor of the channel, represents the line-of-sight link component, represents the non-line-of-sight link component of the channel, Indicates the propagation distance between BS and STAR-RIS, Represents the path loss exponent.

[0072] The channel link between the kth transmission / reflection area user and STAR-RIS is expressed as , deploy STAR-RIS near users in the transmission / reflection area to improve channel quality. The modeling is as follows:

[0073]

[0074] in, , express The Rice factor, represents the line-of-sight link component, represents the non-line-of-sight link component of the channel, represents the propagation distance between the kth transmission / reflection area user and STAR-RIS, Represents the path loss exponent.

[0075] S2: Based on the channel model and the transceiver mode, obtain the mathematical expression of the total received signal at the base station receiving end.

[0076] Taking into account the path loss and ignoring the user signals reflected or transmitted more than twice by STAR-RIS, the received signal at the BS during the transmission / reflection period can be obtained as The expression is:

[0077]

[0078] in, represents the transmission data of the kth central user, represents the transmission data of the kth edge user; represents the transmission power of the kth central user, represents the transmission power of the kth edge user; represents the reflection / projection coefficient matrix of STAR-RIS; The mean is 0 and the variance is complex Gaussian noise.

[0079] S3: According to the demodulation principle of the uplink NOMA system, users in the central area, reflection area, and transmission area are sorted separately. Users with good channel conditions are demodulated first, and then the signals of the demodulated users are deleted from the mathematical expression of the total received signal in sequence. Then, based on the mathematical expression of the received signal after deleting the demodulated signal, the expressions of the signal-to-interference-and-noise ratio of different users are obtained respectively, and the achievable rate expression of each user is further obtained.

[0080] The specific process is as follows: Central users have better channel conditions than users in the reflection and transmission zones due to lower path loss. According to the uplink NOMA system's decoding order, the BS first decodes the central user's signal by treating the transmission / reflection zone signals as interference. During the transmission / reflection period, the BS uses Successive Interference Cancellation (SIC) to remove the central user's signal. Then, without interference from the central user, the BS decodes the transmission / reflection zone signals.

[0081] Assumptions The channel order of the central users is as follows:

[0082]

[0083] Similarly, The ranking of users in the transmission area / reflection area is as follows:

[0084]

[0085] Therefore, during the transmission / reflection period, the signal-to-interference-plus-noise ratio (SINR) of the kth central user is expressed as:

[0086] ,

[0087] The SINR of the kth transmission / reflection area user can be expressed as:

[0088] ,

[0089] In summary, the achievable rates corresponding to the kth central area user and the transmission area / reflection area user are expressed as:

[0090]

[0091]

[0092] in, Indicates the time allocation coefficient used for projected user or reflected user transmission.

[0093] S4, under the premise of meeting the minimum transmission rate requirements of each user, establish a joint optimization problem P1 of user transmission power, transmission / reflection beamformer and time allocation coefficient. The optimization goal is to minimize the total transmission power of the system, and the optimization variables are the transmission power of each user, the reflection / projection coefficient matrix and the time allocation coefficient.

[0094] In order to reduce the total system transmission power while ensuring the quality of service for each user, the original optimization problem P1 is established as follows:

[0095]

[0096] in, and is the minimum transmission rate required by the user, where Constraint Q1 indicates that STAR-RIS adopts an orthogonal time slot protocol; constraints Q2 and Q3 indicate that the user's transmission rate is higher than the minimum rate requirement; constraint Q4 ensures that each reflection element only changes the phase shift of the incident signal; constraints Q5 and Q6 represent the strength order of the user channels in the NOMA system.

[0097] S5: Optimized variables in the objective function of the original optimization problem P1 、 and There is a high degree of coupling between them, and the constraints Q2-Q4 are nonlinear and non-convex, so the original optimization problem P1 is a complex non-convex optimization problem. Since each optimization variable is under different constraints, specifically, constraint Q1 is The constraints, Q2 and Q3 are Constraint, Q4 is constraints.

[0098] In order to further solve the original optimization problem, the original optimization problem P1 is decomposed into three sub-optimization problems, and the alternating optimization method is further used to obtain the optimal solution of each sub-optimization problem. The specific operations are as follows:

[0099] (1) When the reflection / projection coefficient matrix and time allocation coefficient Fixed, when the optimal value of the simplified optimization problem is obtained by the contradiction method, the constraint condition should be equal, so as to use the equality relationship to first obtain the optimal transmission power of the user in the transmission area / reflection area The closed expression of the transmission area / reflection area user is substituted into the constraint condition of the minimum rate requirement of the central area user to further obtain the optimal transmission power of the central area user. The closed expression of .

[0100] According to the given reflection / projection coefficient matrix and time allocation coefficient , transform the original optimization problem P1 into problem P2 as follows:

[0101]

[0102] By contradiction, it is proved that when the optimization problem P2 obtains the optimal solution, the constraint condition takes the equal sign, so the first The closed-form expression for the minimum transmission power of a user in the transmission area / reflection area is as follows:

[0103]

[0104] Then, the closed-form expression of the minimum transmission power of the kth transmission / reflection area user is as follows:

[0105]

[0106] Simplifying the above formula, the closed-form expression for the optimal transmission power of users in the transmission area / reflection area is as follows:

[0107]

[0108] in, ,when , ;when , .

[0109] Similarly, during the transmission / reflection period, the closed-form expression for the optimal transmission power of the central user is further obtained as follows:

[0110]

[0111] in, ,when , ;when , , .

[0112] (2) When the user transmits power and time allocation coefficient Fix, bundle the original optimization problem into a semi-definite programming problem, use the convex optimization solver to solve the optimization problem after bundle, then perform eigenvalue decomposition on the optimal solution of the bundle problem, take the eigenvector corresponding to the maximum eigenvalue as the approximate solution, make it meet the rank-one constraint, and further normalize each element to make it meet the unit module constraint, so as to obtain the reflection / projection coefficient matrix The optimal solution of .

[0113] For a given user transmit power and time allocation coefficient , the optimization problem P1 can be transformed into problem P3:

[0114] P3:

[0115] It is worth noting that the optimization problem P3 can be decoupled according to the different time slots of transmission and reflection, that is, it can be optimized independently. and to solve the problem.

[0116] In order to further write the objective function into a compressed form, a new set of vectors is defined, namely and ,in , here represents the Hadamard product operation. Therefore, the optimization The problem can be simplified to the optimization problem P4, as follows:

[0117] P4:

[0118] The objective function in the optimization problem P4 can be transformed into ,in, is the distribution coefficient of the kth transmission / reflection area user.

[0119] In addition, by introducing an auxiliary matrix, as follows:

[0120]

[0121] is a positive semidefinite matrix, and we can deduce that

[0122]

[0123] in, is a matrix traces.

[0124] In order to simplify the objective function, a new auxiliary matrix is ​​further introduced , and it satisfies and ,in, A matrix with only one non-zero element. Specifically, the non-zero element is located at the i-th diagonal element position and its value is 1, and the other elements are all zero. Further rewrite the objective function of P4 as Similarly, an auxiliary matrix can be introduced for the kth transmission / reflection area user , converting the constraint into the following expression: Therefore, question P4 can be equivalently replaced by question P5 as follows:

[0125] P5:

[0126] In the optimization problem P5, there is only one non-convex constraint. After ignoring the rank-one constraint, the CVX toolkit can be used to obtain the optimal solution of the semi-definite programming problem. It represents the optimal solution of the semi-positive programming problem, which needs to be further corrected into a feasible solution of the optimization problem P5. The specific correction process is as follows:

[0127] If the conditions are met ,according to , we can get the optimal solution of optimization problem P5 If this condition is not met, you need to implement the following method: Set and Represents matrices respectively The maximum eigenvalue and the eigenvector corresponding to the maximum eigenvalue, therefore, an approximate optimal solution can be obtained: If satisfied , approximate solution It is feasible, otherwise, the elements need to be normalized Through the above operations, each element of STAR-RIS satisfies the unit module constraint.

[0128] (3) When the user transmits power and the reflection / projection coefficient matrix Fixed, by using the Lagrange multiplier method to transform the original constrained optimization problem into an unconstrained optimization problem, and further using the one-dimensional search method to obtain the time allocation coefficient The optimal solution of .

[0129] For a given transmit power and the reflection / projection coefficient matrix , the original optimization problem P1 can be rewritten as the optimization problem P6 as follows:

[0130] P6:

[0131] Then, the problem with the equality constraint Q1 is transformed into an unconstrained nonlinear optimization problem by using the Lagrange multiplier method and further solved using the one-dimensional search method. Therefore, the optimal value of the optimization problem P6 can be further obtained.

[0132] (4) Iterate the above (1), (2), and (3) in sequence until the optimization objective function value converges, thereby obtaining the optimal user transmission power, reflection / projection coefficient matrix, and time allocation coefficient of the system.

[0133] Example

[0134] The following simulation experiments illustrate the performance of the STAR-RIS assisted uplink NOMA system proposed in this invention. The system parameters are as follows: cell coverage radius , the number of users in the central area, edge reflection area and edge transmission area , noise power , path loss index from central user to base station , the path loss index from edge users to base stations is , path loss index from STAR-RIS to base station , path loss index from edge users to STAR-RIS , the Rice K factor of each channel is 4, and the coverage radius of STAR-RIS is , near field radius , the distance between BS and STAR-RIS .

[0135] like Figure 2 As shown in the figure, the total transmission power consumption curve under different minimum signal-to-noise ratio conditions is given, where the number of STAR-RIS reconstruction units Five scenarios were considered: a NOMA system uplink transmission method without RIS assistance, a traditional RIS-assisted NOMA system uplink transmission method, a STAR-RIS-assisted orthogonal multiple access (OMA) system uplink transmission method, a STAR-RIS-assisted NOMA uplink transmission method with ignoring the rank-one constraint, and the STAR-RIS-assisted NOMA system uplink transmission method proposed in this invention. It can be seen that the total system transmit power consumption is essentially the same whether or not the rank-one constraint is ignored, indicating that this constraint has little impact on the total system power consumption. Furthermore, the total transmit power under the OMA scheme is consistently greater than that of the NOMA system, demonstrating the improved performance of the NOMA system. Finally, the figure shows that the performance of the system without or with the traditional RIS is significantly worse, fully demonstrating the advantages of the STAR-RIS-assisted NOMA system.

[0136] Figure 3 The influence of different numbers of STAR-RIS reconstruction units on the total transmission power consumption and the minimum signal-to-noise ratio of the user are given. Five cases were considered: the NOMA system uplink transmission method without RIS assistance, the traditional RIS-assisted NOMA system uplink transmission method, the STAR-RIS-assisted OMA system uplink transmission method, the STAR-RIS-assisted NOMA uplink transmission method when the rank 1 constraint is ignored, and the STAR-RIS-assisted NOMA system uplink transmission method proposed in the present invention. It is not difficult to find that as the number of reconstruction units in STAR-RIS increases, the total transmission power tends to decrease. Under different conditions of the number of reconstruction units, the total transmission power consumption of the method of the present invention is lower than that of various other benchmark methods.

[0137] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A STAR-RIS-assisted NOMA system uplink low-power transmission method, characterized in that: The steps include: Establish the channel models required by the system between the central user and the base station, between STAR-RIS and the base station, and between the transmission area user / reflection area user and STAR-RIS; According to the channel model, calculate the mathematical expression of the total received signal at the base station receiving end; Based on the demodulation order of the NOMA system and the mathematical expression of the total received signal, different users are sorted to obtain the signal-to-interference-noise ratio and achievable rate expressions of different users; Establish the original optimization problem of user transmit power, transmission / reflection beamformer and time allocation, and alternately optimize the user transmit power, reflection / transmission coefficient matrix and time allocation coefficient variables; The original optimization problem is solved after convergence to obtain the minimized total transmit power of the NOMA system; The original optimization problem is expressed as follows: ， in, represents the reflection / transmission coefficient matrix of STAR-RIS; Indicates the time allocation coefficient for transmission of users in the transmission area or the reflection area; represents the transmission power of the kth central user in the reflection time slot / transmission time slot, represents the transmission power of the kth transmission area user / reflection area user; Indicates the number of central users; Indicates the number of users in the transmission area / reflection area; represents the transmission rate of the kth central user in the reflection time slot / transmission time slot, represents the transmission rate of the kth transmission / reflection area user, represents the minimum transmission rate required by the kth transmission area user / reflection area user, represents the minimum transmission rate required by the kth central user, where , , M represents the number of reconfigurable units; constraint Q1 indicates that STAR-RIS uses an orthogonal time slot protocol; constraints Q2 and Q3 indicate that the user's transmission rate is higher than the minimum rate requirement; constraint Q4 indicates that each reflective element only changes the phase shift of the incident signal; Constraints Q5 and Q6 represent the strength order of user channels in the NOMA system; represents the communication link between BS and STAR-RIS, represents the channel link between BS and the first central user, Indicates the channel link between STAR-RIS and the first transmission zone user or reflection zone user.

2. A STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 1, characterized in that: The mathematical expression of the total received signal at the base station receiving end is: ， in, represents the transmission data of the kth central user, Represents the transmission data of the kth transmission area user / reflection area user; represents the transmission power of the kth central user in the reflection time slot / transmission time slot, represents the transmission power of the kth transmission area user / reflection area user; represents the reflection / transmission coefficient matrix of STAR-RIS; The mean is 0 and the variance is Complex Gaussian noise; represents the channel link between the kth transmission area user / reflection area user and STAR-RIS, represents the communication link between BS and STAR-RIS, represents the channel link between the BS and the kth central user.

3. A STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 1, characterized in that: The achievable rate expression is as follows: ， ， in, represents the transmission rate of the kth central user in the reflection time slot / transmission time slot, represents the transmission rate of the kth transmission / reflection area user, Indicates the time allocation coefficient for transmission of users in the transmission area or the reflection area; represents the signal-to-interference-and-noise ratio of the kth central user in the reflection time slot / transmission time slot, It represents the signal-to-interference-and-noise ratio of the kth transmission area user / reflection area user.

4. A STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 1, characterized in that: The specific steps to converge the original optimization problem are as follows: When the reflection / transmission coefficient matrix and time allocation coefficient are fixed, the original optimization problem is transformed into the first sub-optimization problem and solved using the contradiction method to obtain the optimal user transmission power; When the user transmission power and time allocation coefficient are fixed, the original optimization problem is transformed into a second sub-optimization problem to obtain the optimal solution of the reflection / transmission coefficient matrix; When the user transmission power and reflection / transmission coefficient matrix are fixed, the original optimization problem is transformed into a third sub-optimization problem by using the Lagrange multiplier method, and the optimal solution of the time allocation coefficient is obtained by a one-dimensional search method.

5. A STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 4, characterized in that: The steps for obtaining the optimal transmit power of a user are as follows: The first sub-optimization problem is solved using the contradiction method. The first sub-optimization problem is expressed as follows: ； When the optimal solution of the first sub-optimization problem is obtained, the constraint condition takes the equal sign, and the closed-form expression of the optimal transmission power of the transmission area user / reflection area user is obtained, which is expressed as follows: ， in, ,when , ;when , ; Substituting the optimal transmit power of users in the transmission / reflection areas into the minimum rate requirement of users in the central area, the closed-form expression for the optimal transmit power of users in the central area is obtained as follows: ， in, ,when , ;when , , .

6. A STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 4, characterized in that: The specific steps to obtain the optimal solution of the reflection / transmission coefficient matrix are as follows: The original optimization problem is constrained to a semi-definite programming problem, and the convex optimization solving tool is used to solve the semi-definite programming problem. By performing eigenvalue decomposition on the optimal solution of the semidefinite programming problem, the eigenvector corresponding to the maximum eigenvalue is taken as the approximate solution to satisfy the rank-one constraint; Each element after decomposition is normalized to satisfy the unit modulus constraint and obtain the optimal solution of the reflection / transmission coefficient matrix.

7. A STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 4 or 6, characterized in that: The second sub-optimization problem is expressed as follows: ； definition and ,in , represents the Hadamard product operation, and the second sub-optimization problem is simplified to the optimization problem P4. The optimization problem P4 is expressed as follows: ； On the basis of satisfying the rank-one constraint, the auxiliary matrix is ​​introduced to transform the objective function in the optimization problem P4; According to the objective function, the optimization problem P4 is converted into the optimization problem P5. The optimization problem P5 is expressed as follows: ， Ignoring the rank-one constraint, the CVX toolkit is used to obtain the optimal solution to the semidefinite programming problem, where , represents the distribution coefficient of the kth transmission area user / reflection area user, represents a positive semidefinite matrix that satisfies and ; Representation matrix The rank 1 constraint must be satisfied. Represents a matrix with only one nonzero element.

8. A STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 4, characterized in that: The steps for finding the optimal solution to the time allocation coefficient are as follows: The Lagrange multiplier method is used to transform the original optimization problem into a third sub-optimization problem. The third sub-optimization problem is an unconstrained nonlinear optimization problem, which is specifically expressed as follows: ， The third sub-optimization problem is solved by a one-dimensional search method to obtain the optimal solution of the time allocation coefficient.

9. The STAR-RIS-assisted NOMA system uplink low-power transmission method according to claim 1, characterized in that: Converging the original optimization problem includes sequentially iterating the steps described in claim 4, repeatedly converging the optimization problem until the optimization objective function value converges, and obtaining the optimal user transmission power, reflection / transmission coefficient matrix and time allocation coefficient of the system.

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