An optimization method for sum-rate maximization of ris-aided uplink urllc system

Abstract

The application discloses an optimization method for sum rate maximization of a RIS-aided uplink URLLC system, and relates to the technical field of wireless communication, and comprises the following steps: S1, a reconfigurable intelligent surface (RIS)-aided uplink multi-user URLLC system model is constructed, the URLLC system model is a single-input multiple-output (SIMO) architecture, and a signal transmission mathematical expression is established according to the system model; S2, a system sum rate maximization problem model is constructed based on communication theory and optimization theory, and the problem model is improved through problem conversion; S3, constraints are converted through SCA technology, and a single optimal solution is obtained through a BCD algorithm; and S4, based on the single optimal solution obtained in step S3, a suboptimal solution of the original problem is obtained through an iterative convergence method. The application solves the beamforming optimization problem of the RIS-aided uplink URLLC system, especially provides a closed-form solution of the receive beamforming at the BS for the uplink URLLC, and the superiority of the algorithm is verified through parameter simulation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to an optimization method for sum-rate maximization of RIS-aided uplink URLLC system. BACKGROUND

[0002] The upcoming 6G wireless network is expected to develop towards intelligence and software reconfigurability, realizing seamless and ubiquitous communication between humans and devices, and realizing the vision of low power consumption, high throughput, high energy efficiency, large-scale connection, high reliability and low delay communication through perception, control and optimization of wireless environment. At present, Ultra-Reliable Low-Latency Communication (URLLC) is one of the important standards to support 6G, which meets its strict requirements on reliability and latency through limited block length transmission. In recent years, Reconfigurable Intelligent Surface (RIS) composed of a large number of electromagnetic units has become one of the most promising technologies for 6G URLLC network due to its ability to intelligently control electromagnetic waves. However, most of the current researches are focused on RIS-aided downlink URLLC system, and there are few studies on resource optimization in uplink. SUMMARY

[0003] The purpose of the present application is to overcome the shortcomings of the prior art and provide an optimization method for sum-rate maximization of RIS-aided uplink URLLC system.

[0004] The purpose of the present application is achieved by the following technical solutions:

[0005] The present application discloses an optimization method for sum-rate maximization of RIS-aided uplink URLLC system, comprising:

[0006] S1, a reconfigurable intelligent surface (RIS) aided uplink multi-user URLLC system model is constructed, the URLLC system model is a single-input multiple-output (SIMO) architecture, and a signal transmission mathematical expression is established according to the system model;

[0007] S2, a system sum-rate maximization problem model is constructed based on communication theory and optimization theory, and the problem is improved through problem conversion;

[0008] S3, the constraints are converted through SCA technology, and a single optimal solution is obtained through BCD algorithm;

[0009] S4, based on the single optimal solution obtained in step S3, a suboptimal solution of the original problem is obtained by iterative convergence.

[0010] Furthermore, in step S1, the URLLC system consists of a base station (BS) and a reconfigurable smart surface (RIS), which coordinate to provide services. There are single-antenna uplink users, and the user set is defined as follows: Meanwhile, the base station (BS) is equipped with One antenna, specifically including:

[0011] S11, Assume RIS includes It consists of several reflective units, and the unit set is as follows: The RIS phase shift matrix is ,in, The dimension is M OK M A complex matrix of columns, This represents a diagonal matrix, where the phase shift vector corresponds to the m-th reflecting unit. The angle of the phase shift generation range of RIS , , The imaginary unit representing Euler's formula;

[0012] S12. Assume that the system channel gain satisfies quasi-static flat fading within the coherent block, and define RIS up to the th... The channel gain for each user is The channel gain from BS to RIS is BS to the The channel gain for each user is ,in, The dimension is N A complex vector with 1 row and 1 column; The dimension is M A complex vector with 1 row and 1 column. The dimension is M OK N A complex matrix of columns;

[0013] S13, Define User The signal sent to the BS is The signal received at BS for: ;in, This represents the sum of signals from all users after passing through the channel link. This represents the additive white Gaussian noise received at BS, where H represents the conjugate transpose. (User) Signal-to-interference-to-noise ratio at the location for: , ;in, Represents a set of users In addition to users All other users, denotes the recovered user at the BS, denotes the transmit signal power of user , denotes the receive beamforming vector of single-antenna user , denotes the transmit signal power of single-antenna user , denotes the 2-norm, denotes the Gaussian white noise power; denotes the channel gain from the BS to the set of users excluding user ; denotes the channel gain from the RIS to the set of users excluding user ;

[0014] S14, according to the finite block length coding theory, the achievable transmission rate of user is denoted as , where denotes the channel dispersion; denotes the block length of user , denotes the decoding error probability of user , denotes the inverse of the Gaussian function if , the achievable transmission rate of user is .

[0015] Preferably, the step S2 specifically comprises the following steps:

[0016] S21, constructing a system sum-rate maximization problem, i.e. , where denotes the first optimization problem, denotes the receive beamforming unit energy constraint of user , denotes the maximum transmit power constraint of user , denotes the phase shift vector constraint of the RIS, denotes the objective function of the first optimization problem maximized when is taken as the optimization variable;

[0017] S22, obtaining the cascaded channel from the BS to the RIS to user in the uplink , where This indicates the process from BS to RIS to the user. The cascaded channel link is calculated using the following formula: , Represents the phase shift vector of RIS. Then define the first covariance channel matrix. , ,in The expectation operator is represented here; it is assumed that the channel gain is constant within each coherent block, and the expectation operator is ignored. , will users The signal-to-noise ratio is rewritten as , Let the second channel covariance matrix be represented, and then the first optimization problem will be addressed. Equivalently transformed into a second optimization problem ,Right now: ;in, This represents the m-th element in the phase shift vector of RIS. Indicates user Maximum power threshold for transmission.

[0018] Preferably, step S3 specifically includes the following steps:

[0019] S31, will As a parameter, for users recovering at BS Receive beamforming vector of transmitted signal Optimize the second optimization problem. Transform into a third optimization problem ,Right now ;

[0020] in, Indicates will Maximizing the third optimization problem when used as an optimization variable. The objective function;

[0021] S32. Based on the relevant lemmas in the paper, find... Closed-form solution , Representation matrix The reverse; This represents the composite channel gain; its calculation formula is: ;

[0022] S33, will As a parameter, for the user Transmitted signal power Optimize the second optimization problem. Transform into the fourth optimization problem ,Right now ;in, denotes maximizing the objective function of the fourth optimization problem as the optimization variable.

[0023] S34, optimizing as the parameters, respectively, and and , converts the second optimization problem into the sixth optimization problem , that is ; wherein, denotes maximizing the objective function of the sixth optimization problem as the optimization variable.

[0024] Preferably, the non-convexity of the fourth optimization problem in step S33 comes from the first objective function, and the optimal solution of the fourth optimization problem is obtained using SCA iteration, specifically comprising the following steps:

[0025] S331, rewriting the first objective function as , wherein the first ln logarithm sum of the expected power and the noise power in the user set is calculated as , , denotes the first function, and the calculation formula is , and the calculation formula of the receive beamforming matrix at the BS is , denotes the rank of the matrix;

[0026] S332, using SCA iteration, the first feasible point of the nth iteration is , and the lower bound of the first function is expanded by the first order Taylor series: ; wherein, wherein denotes the convex lower bound inequality of the first function , denotes the derivative of , and the product of the first function is ; wherein, denotes the remaining users in the user set except for the user and the user ; denotes the third channel covariance matrix; denotes the fourth channel covariance matrix; denotes the user set except for the user​​ all other users except user represents a set of users all other users except user

[0027] S333, the fourth optimization problem is converted into a fifth optimization problem by using the BCD algorithm ; wherein the fifth optimization problem is convex and is solved by CVX.

[0028] Preferably, step S34 comprises the following steps:

[0029] S341, the expected signal power of user is written as:

[0030] ;

[0031] wherein, represents the real part of a complex variable, represents the cascade channel link from the BS to the RIS to the user , and its calculation formula is ; represents the RIS beamforming vector integrated with the cascade channel link and the channel gain from the BS to the kth user, and its calculation formula is ; represents the system channel gain representation integrated with the cascade channel link and the channel gain from the BS to the kth user, and its calculation formula is ; the calculation formula of the Hermitian matrix ; ;

[0032] S342, the signal-to-noise ratio of user is rewritten as: , and the second objective function is ; wherein, represents the second ln logarithm sum of the expected power and the noise power in the set of users , and its calculation formula is , represents the system channel gain representation integrated with the cascade channel link and the channel gain from the BS to the kth user, and its calculation formula is ; ;

[0033] S343, using the SCA iteration, the second feasible point of the nth iteration is defined as​​​​​​​ , the lower bound of the second function is expanded by the first order Taylor series: ; where denotes the convex lower bound inequality of the second function , the derivative of , the product of and the second function is ; the sixth optimization problem is converted into the seventh optimization problem : ; where denotes the rank of the matrix; denotes the objective function of the seventh optimization problem maximizing when is taken as the optimization variable;

[0034] S344, the constraint of the seventh optimization problem is non-convex rank-1 constraint, which is replaced using the equation into the form of difference of convex functions, obtaining the non-convex constraint ; where denotes the sum of eigenvalues of the Hermitian matrix ; denotes the largest eigenvalue of the Hermitian matrix ;

[0035] S345, using SCA iteration, and expanding the convex lower bound inequality of the left side of the inequality in the non-convex constraint by the first order Taylor series: ; where denotes the eigenvector corresponding to the largest eigenvalue, denotes the convex lower bound of the largest eigenvalue of the Hermitian matrix , and finally the BCD algorithm is used to transform the seventh optimization problem into the eighth optimization problem : ; where the eighth optimization problem is convex, which is solved by CVX.

[0036] Preferably, step S4 specifically comprises:

[0037] taking as a parameter and initializing, setting the iteration number n to 0, and the maximum iteration number to 100;

[0038] taking as a parameter, updating by the formula ; denotes the n+1th iteration of recovering users at the BS receive beamforming vectors of the transmitted signals;

[0039] Let solving the eighth optimization problem with the parameter and updating the fourth feasible point of the n+1th iteration , denotes the nth iteration of recovering users at the BS receive beamforming vectors of the transmitted signals;

[0040] Let solving the eighth optimization problem with the parameter and updating the fourth feasible point of the n+1th iteration ;

[0041] until the objective function of the second optimization problem converges.

[0042] The beneficial effects of the present application are:

[0043] 1) The present application solves the beamforming optimization problem of the RIS-aided uplink URLLC system, and especially provides a closed-form solution of the receive beamforming at the BS for the uplink URLLC. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is a step schematic diagram of an optimization method for sum-rate maximization of a RIS-aided uplink URLLC system according to an embodiment of the present application;

[0045] Figure 2 is a flowchart of a BCD algorithm according to an embodiment of the present application;

[0046] Figure 3 is a schematic diagram of a comparison result of the performance of a conventional single-input single-output URLLC system according to an embodiment of the present application.DETAILED DESCRIPTION

[0047] The technical solutions of the present application will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0048] The application discloses an optimization method for sum rate maximization of a RIS-aided uplink URLLC system, and relates to a RIS-aided uplink multi-user single-input multi-output (SIMO) URLLC system. By jointly optimizing the transmission power at the user, the receive beamforming at the base station (BS) and the passive beamforming at the RIS, a system sum rate maximization optimization problem is formulated. Since the problem is highly non-convex, the application uses successive convex approximation (SCA) to convert the non-convex constraint, and proposes a block coordinate descent (BCD) iterative algorithm. Finally, the superiority of the algorithm in the application is proved through multi-parameter experimental simulation. The steps of the method are shown in the schematic diagram Figure 1 and specifically include the following steps:

[0049] S1, a reconfigurable intelligent surface (RIS)-aided uplink multi-user URLLC system model is constructed, the URLLC system model is a single-input multi-output (SIMO) architecture, and a signal transmission mathematical expression is established according to the system model;

[0050] S2, a system sum rate maximization problem model is constructed based on communication theory and optimization theory, and the model is improved through problem conversion;

[0051] S3, the constraint is converted through SCA technology, and a single optimal solution is obtained through a BCD algorithm;

[0052] S4, based on the single optimal solution obtained in step S3, a suboptimal solution of the original problem is obtained through iterative convergence.

[0053] Specifically, in step S1, the URLLC system is composed of a base station (BS) and a reconfigurable intelligent surface (RIS), and cooperatively serves a single-antenna uplink user, and the user set is defined as Meanwhile, the base station (BS) is equipped with antennas, including:

[0054] S11, it is assumed that the RIS includes a reflection unit, the unit set is , and the RIS phase shift matrix is , wherein represents a complex matrix with a dimension of M rows M columns, represents a diagonal matrix, and the phase shift vector corresponding to the mth reflection unit is , and the solution is obtained through Euler formula . , , The angle representing the phase shift range of RIS, with a value ranging from 0 to... ,Right now , , The imaginary unit representing Euler's formula;

[0055] S12. Without loss of generality, assume that the system channel gain satisfies quasi-static flat fading within the coherent block, and define RIS up to the th... The channel gain for each user is The channel gain from BS to RIS is BS to the The channel gain for each user is ,in, The dimension is N A complex vector with 1 row and 1 column; The dimension is M A complex vector with 1 row and 1 column. The dimension is M OK N A complex matrix of columns;

[0056] S13, Define User The signal sent to the BS is ,in, This indicates that the distribution follows a Gaussian distribution with a mean of 0 and a variance of 1. The signal received at BS for: ;in, This represents the sum of signals from all users after passing through the channel link. This represents the additive white Gaussian noise received at BS, i.e. ,in This represents the power of Gaussian white noise. Represents an N x N matrix of zeros. Let H represent an N x N identity matrix, where H denotes the conjugate transpose. Signal-to-interference-to-noise ratio at the location for: , ;in, Represents a set of users In addition to users All other users, This indicates that the user has been restored at the BS. The receiving beamforming vector of the transmitted signal, Indicates user The transmitted signal power, Indicates a single-antenna user a receive beamforming vector of the user denotes a single-antenna user a transmit signal power of the user denotes a 2-norm; denotes a channel gain from the BS to the user except the user ; denotes a channel gain from the RIS to the user except the user ;

[0057] S14, according to the limited block length coding theory, the achievable transmission rate of the user is represented as , where denotes a channel dispersion; denotes a block length of the user ; denotes a decoding error probability of the user ; denotes an inverse of a Gaussian function , and a calculation formula of the Gaussian function is , where t denotes a variable of an integral function; if , then can be approximated as 1, and the achievable transmission rate of the user can be represented as .

[0058] Specifically, the step S2 comprises the following steps.

[0059] S21, a system sum rate maximization problem, i.e. , is constructed, where denotes a first optimization problem, denotes a receive beamforming unit energy constraint of the user ; denotes a maximum transmit power constraint of the user ; denotes a phase shift vector constraint of the RIS, denotes a target function of maximizing the first optimization problem when taking as an optimization variable;

[0060] S22, in order to solve the above-mentioned non-convex first optimization problem , this step proposes a problem conversion; firstly, a cascade channel from the BS to the RIS to the user in the uplink is obtained, and a calculation process thereof is ; wherein denotes a channel from the BS to the RIS The cascaded channel link is calculated using the following formula: , Represents the phase shift vector of RIS. Then define the first covariance channel matrix. , ,in Let this represent the expectation operator, assuming the channel gain is constant within each coherent block, and ignore the expectation operator. , will users The signal-to-noise ratio rewritten as , Represents the second channel covariance matrix (i.e. Represents the covariance channel matrix Excluded users The channel covariance matrix (followed by the first optimization problem) Equivalently transformed into a second optimization problem ,Right now: ;in, This represents the m-th element in the RIS phase shift vector. Indicates user Maximum power threshold for transmission.

[0061] Specifically, in order to solve the aforementioned non-convex second optimization problem This step transforms the non-convex constraints using SCA technology and proposes the BCD algorithm to solve the optimal solutions to each subproblem; step S3 includes the following steps:

[0062] S31, will As a parameter, for users recovering at BS Receive beamforming vector of transmitted signal Optimize the second optimization problem. Transform into a third optimization problem ,Right now ;

[0063] in, Indicates will Maximizing the third optimization problem when used as an optimization variable. The objective function;

[0064] S32, Although this is the third optimization problem It is still nonconvex, but it can be explained based on the relevant lemmas in the paper. Here, we will explain the relevant lemmas in the paper: Although the third optimization problem It remains non-convex, but note the difference in... The third optimization problem involves scaling by any positive factor. The objective function remains unchanged; therefore, the third optimization problem can be safely removed. the resulting is made . Subsequently, the optimization problem will become a standard eigenvalue problem, i.e. BS receives The closed-form solution of is The closed-form solution of , denotes the inverse of the matrix , and the calculation formula of the matrix is ; denotes the composite channel gain; its calculation formula is , which represents the integrated cascade channel gain and the channel gain from the BS to the user;

[0065] S33, taking as a parameter, optimizing the transmission signal power of the user , and converting the second optimization problem into a fourth optimization problem , i.e. ; wherein denotes the objective function of the fourth optimization problem when is taken as the optimization variable, and is maximized;

[0066] S34, taking as a parameter, respectively optimizing and , and converting the second optimization problem into a sixth optimization problem , i.e. ; wherein denotes the objective function of the sixth optimization problem when is taken as the optimization variable, and is maximized.

[0067] Specifically, the non-convexity of the fourth optimization problem in step S33 comes from the first objective function, and the optimal solution of the fourth optimization problem is obtained using SCA iteration, including the following steps:

[0068] S331, rewriting the first objective function as , wherein the first ln logarithm of the expected power in the user set and the noise power is calculated as , denotes the first function, and its calculation formula is a receive beamforming matrix at the BS The formula for calculating , denotes the rank of a matrix;

[0069] S332, at this time, the non-convexity of the first objective function comes from the first function ; therefore, using SCA iteration, the first feasible point of the nth iteration is , the lower bound of the first function is expanded by the first order Taylor series: ; wherein, wherein denotes the convex lower bound inequality of the first function , denotes the derivative of , and the product of the first function is ; denotes the remaining users in the user set after removing user and user ; denotes the third channel covariance matrix (i.e., the channel covariance matrix after removing user in the user set ); denotes the fourth channel covariance matrix (i.e., the remaining channel covariance matrix after removing user and user in the user set ); denotes all other users in the user set except user ; denotes all other users in the user set except user ;

[0070] S333, the fourth optimization problem is converted into the fifth optimization problem : ; wherein, the fifth optimization problem is convex, which is solved by CVX, a commonly used matlab convex optimization solver.

[0071] Specifically, it is noted that the non-convexity in the sixth optimization problem comes from the second objective function and the constraint , and the suboptimal solution of the sixth optimization problem is obtained by using SCA iteration. Step S34 includes the following steps:

[0072] S341, User The expected signal power is written as:

[0073] ;

[0074] in, This indicates taking the real part of the complex variable; Indicates the integration of cascaded channel links and BS to the first The RIS beamforming vector after channel gain for each user is calculated using the following formula: ; Indicates the integration of cascaded channel links and BS to the first The system channel gain characterization after the channel gain of each user is expressed by the following formula: Hermitian matrix The calculation formula is ;

[0075] S342, will the user Rewrite the signal-to-interference-plus-noise ratio: At this point, the second objective function is ;in, Represents a set of users The sum of the second ln logarithms of the expected power and the noise power is calculated using the following formula: , Indicates the integration of cascaded channel links and BS to the first The system channel gain representation after excluding user k, using the channel gain of each user, is represented by the second function. The calculation formula is: ;

[0076] S343. At this point, the nonconvexity of the second objective function comes from the second function. Using SCA iteration, the second feasible point in the nth iteration is defined as... The second function is derived using a first-order Taylor series. The lower bound expansion is: ; where, Indicates the second function The convex lower bound inequality The derivative is represented by . With the second function The product is The sixth optimization problem Transform into the seventh optimization problem : ;in, Describes the rank of a matrix; Indicates will Maximizing the seventh optimization problem when used as an optimization variable. The objective function;

[0077] S344, Constraints The seventh optimization problem Non-convex rank 1 constraints, using equations By replacing it and transforming it into the form of the difference of convex functions, we obtain the non-convex constraint. ;in, Representing Hermitian matrices The sum of eigenvalues; Representing Hermitian matrices The largest eigenvalue;

[0078] S345. Using SCA iteration and expanding the convex lower bound inequality on the left side of the inequality in the non-convex constraint using a first-order Taylor series: ;in, express The eigenvector corresponding to the largest eigenvalue. Representing Hermitian matrices The convex lower bound of the largest eigenvalue is calculated using the following formula: Finally, the BCD algorithm is used to solve the seventh optimization problem. Transformed into the eighth optimization problem : The eighth optimization problem It is convex, and it is solved using CVX.

[0079] Specifically, the BCD algorithm flowchart is as follows: Figure 2 As shown, step S4 specifically includes:

[0080] Will As a parameter and initialized, the iteration count n is set to 0, and the maximum iteration count is set to 0. Set to 100;

[0081] Will As a parameter, through the formula right Update; This indicates the (n+1)th time the user is restored at the BS. The receiving beamforming vector of the transmitted signal;

[0082] Will As a parameter, for the fifth optimization problem Solve the problem and update the third feasible point in the (n+1)th iteration. , This indicates the nth time the user is restored at the BS. The receiving beamforming vector of the transmitted signal;

[0083] Will As a parameter, for the eighth optimization problem solving and updating the fourth feasible point of the n+1th iteration ;

[0084] until the objective function of the second optimization problem converges.

[0085] Exemplarily, as shown in a comparison result diagram of a traditional single-input single-output URLLC system performance and the present application Figure 3 , the present application has a better system sum rate compared with the traditional method; the present application combines the RIS with the uplink multi-antenna URLLC system, formulates a system sum rate maximization problem, and especially provides a closed-form solution of the receive beamforming at the BS for the uplink URLLC.

[0086] The above only describes the preferred embodiments of the present application, and it should be understood that the present application is not limited to the forms disclosed herein, should not be regarded as excluding other embodiments, and can be used in various other combinations, modifications and environments, and can be modified within the scope of the concepts described herein by the above-mentioned teaching or related art or knowledge. Any modification and change made by those skilled in the art without departing from the spirit and scope of the present application shall be within the protection scope of the claims of the present application.

Claims

1. An optimization method for maximizing the summation rate of a RIS-assisted uplink URLLC system, characterized in that, The application relates to a method for constructing a reconfigurable intelligent surface (RIS) assisted uplink multi-user (URLLC) system model, and the method comprises the following steps: S1, constructing a reconfigurable intelligent surface (RIS) assisted uplink multi-user (URLLC) system model, the system model is a single-input multi-output (SIMO) architecture, and a signal transmission mathematical expression is established according to the system model; S2, constructing a system sum rate maximization problem model based on a communication theory and an optimization theory, and improving the problem model through problem conversion; S3, converting the constraint through an SCA technology, and obtaining a single optimal solution through a BCD algorithm; S4, obtaining a suboptimal solution of the original problem through an iterative convergence method based on the single optimal solution obtained in step S3; The URLLC system in step S1 is composed of a base station BS and a reconfigurable intelligent surface RIS, and cooperates with a service An individual antenna uplink user, define a user set as At the same time, the base station BS is equipped with Antennas, specifically including: S11, the RIS includes a plurality of reflecting units, the units being , the phase shift matrix of the RIS is , wherein represents a complex matrix with dimensions M rows M columns, represents a diagonal matrix, the phase shift vector corresponding to the mth reflecting unit is , the angle of the phase shift range of the RIS is , , represents the imaginary unit of Euler's formula; S12. Assume that the system channel gain satisfies quasi-static flat fading within the coherent block, and define RIS up to the th... The channel gain for each user is The channel gain from BS to RIS is BS to the The channel gain for each user is ,in, The dimension is N A complex vector with 1 row and 1 column; The dimension is M A complex vector with 1 row and 1 column; The dimension is M OK N A complex matrix of columns; S13, define users The transmitted signal to the BS is The received signal at the BS is where ; where denotes the accumulated signal of all users after the channel link, denotes the additive white Gaussian noise received at the BS, H denotes the conjugate transpose, and The signal-to-interference-plus-noise ratio at user is , ; where denotes all users in the user set except user , denotes the receive beamforming vector at the BS to recover the transmitted signal of user , denotes the transmit signal power of user , denotes the receive beamforming vector of single-antenna user , denotes the transmit signal power of single-antenna user , denotes the 2-norm, denotes the Gaussian white noise power; denotes the channel gain from the BS to all users in the user set except user ; denotes the channel gain from the RIS to all users in the user set except user ; S14. According to the limited block length coding theory, the achievable transmission rate of a user is expressed as where denotes the channel dispersion; denotes the block length of the user ; denotes the decoding error probability of the user ; denotes the inverse of the Gaussian function if , the achievable transmission rate of the user is ; Step S2 specifically comprises the following steps: S21. Construct a system summation rate maximization problem, i.e. ,in, This represents the first optimization problem. Indicates user Receive beamforming unit energy constraint Indicates user Maximum transmit power constraint This represents the phase shift vector constraint of RIS. Indicates will When used as an optimization variable, it maximizes the first optimization problem. The objective function; S22, obtaining the cascade channel of BS-to-RIS-to-user in uplink where denotes the cascade channel link of BS-to-RIS-to-user , whose calculation formula is , denotes the phase shift vector of RIS, and then the first covariance channel matrix , is defined, where denotes the expectation operator; assuming that the channel gain is constant within each coherence block, the expectation operator is ignored , the signal-to-interference-plus-noise ratio of user is rewritten as , denotes the second channel covariance matrix, and then the first optimization problem is equivalently converted into the second optimization problem , that is: ; where denotes the mth element in the phase shift vector of RIS, denotes the maximum power threshold of user transmission;​ Step S3 specifically comprises the following steps: S31, to As a parameter, the user The receive beamforming vector of the transmitted signal Optimization, the second optimization problem Convert to a third optimization problem That is ; wherein, represents maximizing the objective function of the third optimization problem as the optimization variable; and as the optimization variable; and S32, based on the paper's relevant lemma, the paper's relevant lemma is to any positive factor scaling, the third optimization problem The objective function remains unchanged, the third optimization problem The constraints are deleted safely, and then scale So that The third optimization problem Become a standard eigenvalue problem, that is, BS receives Closed form solution, find Closed form solution , Indicates the inverse of the matrix ; Indicates the composite channel gain; its calculation formula is ; S33, will As a parameter, for the user Transmitted signal power Optimize the second optimization problem. Transform into the fourth optimization problem ,Right now ;in, Indicates will When used as an optimization variable, it maximizes the fourth optimization problem. The objective function; S34, will As parameters, respectively and Optimize the second optimization problem. Transform into the sixth optimization problem ,Right now ;in, Indicates will Maximizing the sixth optimization problem when used as an optimization variable. The objective function; The fourth optimization problem in step S33 The non-convexity comes from the first objective function, and the optimal solution of the fourth optimization problem is obtained using SCA iteration , specifically comprising the following steps: S331, rewrite the first target function as where the user set the first ln logarithm of the expected power and the noise power in the medium The calculation formula of , denotes the first function, and the calculation formula is The receive beamforming matrix at the BS The calculation formula of , denotes the rank of the matrix; S332, using the SCA iteration, the first feasible point of the nth iteration is , the lower bound of the first function is expanded by the first order Taylor series: ; wherein, wherein represents the convex lower bound inequality of the first function , represents the derivative of , and the product of the first function is ; wherein, represents the remaining users in the user set after removing the user and the user ; represents the third channel covariance matrix; represents the fourth channel covariance matrix; represents all other users in the user set except the user ; represents all other users in the user set except the user ; S333, the fourth optimization problem is converted into a fifth optimization problem using the BCD algorithm ; wherein the fifth optimization problem is convex and is solved by CVX;​​ Step S34 comprises the following steps: S341、write the expected signal power of the user as: ； wherein, denotes the real part of a complex variable, denotes the BS-to-RIS-to-user cascade channel link, whose computational formula is ; denotes the RIS beamforming vector integrated with the cascade channel link and the channel gain from the BS to the first user, whose computational formula is ; denotes the system channel gain representation integrated with the cascade channel link and the channel gain from the BS to the first user, whose computational formula is ; the computational formula of the Hermitian matrix is ; S342, rewriting the signal-to-interference-and-noise ratio of the user , at this time the second target function is ; wherein, represents the second ln logarithm sum of the expected power and the noise power in the user set , and the calculation formula is , represents the system channel gain representation after excluding the user k after the integrated cascade channel link and the channel gain of the BS to the first user, and the calculation formula of the second function is ;​ S343, using the SCA iteration, define a second feasible point of the n-th iteration as , expand the lower bound of the second function by the first order Taylor series: ; where, denotes the convex lower bound inequality of the second function , denotes the derivative of , and the product of ; convert the sixth optimization problem into the seventh optimization problem : ; where, denotes the rank of the matrix; denotes the objective function of the seventh optimization problem when is taken as the optimization variable; S344, constraint For the seventh optimization problem of non-convex rank 1 constraints, using the equality replace it, into the form of difference of convex functions, obtain the non-convex constraint ; Where, denotes the sum of eigenvalues of the Hermitian matrix ; denotes the maximum eigenvalue of the Hermitian matrix ; S345, using SCA iteration, and expanding the convex lower bound inequality of the left side of the inequality in the non-convex constraint by the first order Taylor series: ; wherein, represents the eigenvector corresponding to the maximum eigenvalue, represents the Hermitian matrix the convex lower bound of the maximum eigenvalue, and finally the seventh optimization problem is transformed into the eighth optimization problem : ; wherein the eighth optimization problem is convex, and is solved by CVX. Step S4 specifically comprises: Set As a parameter and initialize, the iteration number n is set to 0, the maximum iteration number Set to 100; will be updated as parameters by the formula ; and represents the n+1th time the user signal is received at the BS;​ The as parameters, the fifth optimization problem is solved and the third feasible point of the n+1 iteration is updated , denotes the n-th recovered user at the BS; the receive beamforming vector for the transmitted signal; Solve the eighth optimization problem as a parameter, the eighth optimization problem is solved and the fourth feasible point of the n+1 iteration is updated ; until the objective function of the second optimization problem converges.

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