CN117176214B

CN117176214B - Method and device for optimizing sum rate of MIMO (multiple input multiple output) system assisted by RIS (radio resource locator)

Info

Publication number: CN117176214B
Application number: CN202311453886.0A
Authority: CN
Inventors: 孙福辉; 张迁; 王晓燕; 邵明杰; 刘琚
Original assignee: People's Court Information Technology Service Center; Shandong University
Current assignee: People's Court Information Technology Service Center; Shandong University
Priority date: 2023-11-03
Filing date: 2023-11-03
Publication date: 2024-01-16
Anticipated expiration: 2043-11-03
Also published as: CN117176214A

Abstract

The present specification relates to the technical field of mobile communications, and provides a method and a device for optimizing sum rate of a RIS-assisted MIMO system, where the method includes: after initialization, iteratively optimizing a sum rate objective function taking the RIS reflection matrix as a fixed value by adjusting a first punishment factor until a first punishment termination condition is met, so as to obtain candidate linear precoding vectors of a base station of the system to a user; iteratively optimizing a sum rate objective function taking the candidate linear precoding vector as a fixed value by adjusting a second penalty factor until a second penalty termination condition is met, so as to obtain a candidate RIS reflection matrix; judging whether the candidate linear precoding vector and the candidate RIS reflection matrix meet the alternate optimization termination condition; if not, continuing iteration to perform alternate optimization; if so, taking the two as the optimization result. The optimization efficiency of the RIS auxiliary MIMO system and the rate optimization can be improved through the embodiment of the specification.

Description

Method and device for optimizing sum rate of MIMO (multiple input multiple output) system assisted by RIS (radio resource locator)

Technical Field

The present disclosure relates to the field of mobile communications technologies, and in particular, to a method and apparatus for rate optimization of an RIS-assisted MIMO system.

Background

Due to various key enabling technologies such as ultra dense networks, massive Multiple-Input Multiple-Output (mimo), millimeter wave communication, and the like, fifth generation (5G) wireless networks have largely achieved a target increase of 1000 times network capacity and ubiquitous wireless connectivity of at least 1000 billions of devices. However, the high complexity and hardware cost required and the increased energy consumption remain as yet unresolved key issues. For example, densely deploying Base Stations (BS) or Access Points (APs) in an ultra-dense network may not only increase hardware expenditure and maintenance costs, but also exacerbate network interference problems. Furthermore, extending mimo from below 6GHz to the millimeter wave band generally requires more complex signal processing and more expensive and energy-consuming hardware (e.g., radio frequency chains, etc.). Thus, research to find innovative, spectrum and energy efficient and cost effective solutions for future/Byond-5G wireless networks is still imperative.

Recently, smart reflective surfaces (Reconfigurable Intelligent Surfaces, RIS) have been considered as a promising new technology for implementing functionality for reconfiguring a wireless propagation environment by software controlled signal reflection. Electromagnetic waves carrying information in wireless communications interact with objects and surfaces on their way from transmitters to receivers. While superposition of many propagation paths produces a random-like attenuation phenomenon, each propagation path has a constant behavior. However, some engineering materials are not constantly interacting with electromagnetic waves, but are reconfigurable. These materials do not exist naturally, but can be manufactured and deployed to shape a propagation environment, which is known as RIS. In particular, the RIS is a plane comprising a large number of low cost passive reflective elements, each capable of independently causing amplitude and/or phase changes of the incident signal, thereby cooperatively enabling fine-grained three-dimensional reflected beam forming. In sharp contrast to wireless link adaptation techniques at the transmitter/receiver, RIS actively modifies the wireless channel between them through highly controllable and intelligent signal reflection. In this way, a new degree of freedom (Degree of Freedom, doF) is provided to further improve wireless communication performance and pave the way for implementing intelligent and programmable wireless environments.

The conventional relay technology can implement reconfiguration of communication by adding a relay device between a Base Station (BS) and a user, but RIS is essentially different from the conventional relay technology. The current relay technology is mainly divided into active relay and back scattering communication, and is based on the active surface of large-scale MIMO. Active trunking requires a radio frequency link, typically operating in half-duplex communication mode, although full-duplex active trunking is currently under investigation, self-interference cancellation techniques are required, implementation costs are high, and RIS can implement full-duplex communication at low cost. Traditional backscatter communications (e.g., radio Frequency Identification (RFID) tags) communicate by modulating their reflected signals from a reader, which needs to perform self-interference cancellation at its receiver to decode the tag's information, RIS is mainly used to improve the existing communication link without sending any information of its own, and the direct link signal and the reflected link signal have the same useful information and can be coherently superimposed at the receiver to enhance the decoded signal strength; massive MIMO based on active surface has different array structure and different operation mechanism than RIS. Although RIS brings many possibilities for future communications, the presence of "multiplicative attenuation" can result in limited improvement in the performance of the communication system. In order to mitigate the effect of "multiplicative attenuation", the number of reflective units required for RIS is very large, difficult to implement and costly. Therefore, in order to solve the problem of "multiplicative attenuation", a structure of an active RIS, i.e., adding an active amplifier in each reflection unit, is proposed. Active RIS has proven to be effective in converting "multiplicative attenuation" into "additive attenuation".

Based on this, RIS has received extensive attention, and research into RIS-assisted communication systems has been very intensive. In general, optimization goals for various RIS-assisted communication scenarios are sum rate (i.e., reachable sum rate) maximization, energy efficiency maximization, spectral efficiency maximization, privacy rate maximization, mean square error minimization, etc. However, these problems are difficult to solve due to their non-convexity and variable coupling. Currently, the alternating optimization (Alternating Optimization, AO) algorithm is commonly used to decompose the coupling variables. The objective function may then be converted to a convex quadratic form using Weighted Minimum-Mean-Square-Error (WMMSE) or a fractional programming method. Based on the above solutions, more efficient optimization algorithms in passive RIS systems have been widely studied, such as lagrangian multiplier, gradient projection, riemann conjugate gradient, alternate multiplier, etc. However, due to the existence of coupled power constraints, there is currently limited research on efficient optimization algorithms in RIS systems. Active or passive beamforming optimization in RIS systems is typically solved using a CVX solver. In addition, for passive beamforming design in RIS systems, literature proposes a low complexity prime-to-even gradient algorithm to obtain a closed solution. However, these solution algorithms are complex and slow to solve.

In summary, the low optimization efficiency of sum rate optimization in an RIS-assisted MIMO communication system has become a technical problem to be solved.

Disclosure of Invention

An object of the embodiments of the present disclosure is to provide a method and an apparatus for optimizing a sum rate of an RIS-assisted MIMO system, so as to improve an optimization efficiency of the sum rate optimization of the RIS-assisted MIMO communication system.

To achieve the above object, in one aspect, an embodiment of the present disclosure provides a method for optimizing a sum rate of a RIS-assisted MIMO system, including:

initializing a RIS reflection matrix, a first penalty factor and a second penalty factor of a target MIMO system;

iteratively optimizing a sum rate objective function taking an RIS reflection matrix as a fixed value by adjusting the first penalty factor until a first penalty termination condition is met, so as to obtain candidate linear precoding vectors of a base station of the target MIMO system for users;

iteratively optimizing a sum rate objective function taking the candidate linear precoding vector as a constant value by adjusting the second penalty factor until a second penalty termination condition is met, so as to obtain a candidate RIS reflection matrix;

judging whether the candidate linear precoding vector and the candidate RIS reflection matrix meet the alternate optimization termination condition or not;

If the alternate optimization termination condition is not met, continuing to iterate the alternate optimization;

and if the alternate optimization termination condition is met, taking the candidate linear precoding vector as an optimal linear precoding vector corresponding to the maximized sum rate, and taking the candidate RIS reflection matrix as an optimal RIS reflection matrix corresponding to the maximized sum rate.

In the method for optimizing the sum rate of the RIS-aided MIMO system in the embodiment of the present disclosure, the sum rate objective function with the RIS reflection matrix as a constant value includes:

wherein min represents the minimum value, w is the candidate linear precoding vector of the base station to the user, Φ is the RIS reflection matrix,representing the sum rate objective function at a constant value of Φ,/->For a first penalty factor for w, +.>The linear precoding vector of the base station to the user, which is obtained for the last optimization w; />For the feasible region of w under the maximum transmission power constraint of the base station,is->Middle distance>Nearest vector, +.>Represents w and->Euclidean distance of>Is thatFeasible region of w under constraint, +.>Is the conjugate transpose of w, +.>，For K-dimensional identity matrix>Representing the kronecker product, G is the channel from the base station to the RIS, +.>Is the conjugate transpose of G>Is the conjugate transpose of phi >Is an intermediate variable +.>For RIS maximum reflected power, +.>F-norm of Φ>Is Gaussian white noise at the active smart reflective surface, +.>Is->Middle distance>The most recent vector is the one that,represents w and->Is a euclidean distance of (c).

In the method for optimizing the sum rate of the RIS-aided MIMO system according to the embodiments of the present disclosure, iteratively optimizing the sum rate objective function with the RIS reflection matrix as a constant value by adjusting the first penalty factor until a first penalty termination condition is satisfied, including: according to the formulaCalculate->And according to the formulaCalculate->；

Will beAnd->Input formula->Calculate->；

JudgingWhether a first penalty termination condition is satisfied; the first penalty termination condition includes；

If it isTriggering the optimization step of phi if the first punishment termination condition is met;

if it isIf the first penalty termination condition is not satisfied, increase +.>Is calculated again +.>Andfrom this, calculate +.>And judging the recalculated +.>Whether a first penalty termination condition is satisfied;

wherein,is->Is>For maximum transmission power of the base station +.>Is->Is conjugated toPut (I) at>For M-dimensional identity matrix->Is a constant obtained by one-dimensional search and +.>，/>K is the number of users, ">，/>For the auxiliary variable of the kth user, +. >Is->Conjugation of->Direct channel and cascade channel sum channel for kth user, +.>Is->Conjugate transpose of->，Is->Transpose of->，/>And the candidate linear precoding vector of the base station to the user is obtained.

In the method for optimizing the sum rate of the RIS-assisted MIMO system according to the embodiments of the present disclosure, the sum rate objective function with the candidate linear precoding vector as a constant value includes:

wherein min represents the minimum value, w is the candidate linear precoding vector of the base station to the user, Φ is the RIS reflection matrix,representing the sum rate objective function at a constant value of w,/for>For a second penalty factor for Φ, +.>RIS reflection matrix obtained for the last optimization Φ, < >>Is->Feasible region of w under constraint, +.>Is the conjugate transpose of phi>Is a diagonal matrix, and->K is the number of users, G is the channel from the base station to the RIS,candidate linearity for base station to kth userPrecoding vector,/->Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Is Gaussian white noise at the active smart reflective surface, +.>Is N-dimensional identity matrix->For RIS maximum reflected power, +.>Is->Intermediate distanceNearest vector, +. >Represents phi and +.>Euclidean distance of>Is->Feasible region of phi under constraint, +.>Phase shift coefficient of the nth reflection unit of the intelligent reflection surface, +.>For the maximum magnification factor of the nth reflection unit in RIS, < >>Is->Middle distance>Nearest vector, +.>Represents phi and +.>Is a euclidean distance of (c).

In the method for optimizing the sum rate of the RIS-aided MIMO system according to the embodiments of the present disclosure, iteratively optimizing a sum rate objective function with the candidate linear precoding vector as a constant value by adjusting the second penalty factor until a second penalty termination condition is satisfied, including: according to the formulaCalculate->And according to the formula->Calculate->；

Will beAnd->Input formula->Calculation ofThe method comprises the steps of carrying out a first treatment on the surface of the Judging->Whether a second penalty termination condition is satisfied; the second penalty termination condition includes；

If it isA judging step of triggering the alternate optimization termination condition when the second punishment termination condition is met;

if it isIf the second penalty termination condition is not satisfied, increase +.>Is calculated again +.>And->From this, calculate +.>And judging the recalculated +.>Whether a second penalty termination condition is satisfied; wherein lambda is a constant obtained by one-dimensional search and lambda is not less than 0, (-)>For the number of reflection units in RIS, +.>For the candidate RIS reflection matrix, ，/>As an auxiliary variable for the kth user,，/>is->Conjugation of->Direct channel and cascade channel sum channel for kth user, +.>Is->Conjugate transpose of->Transpose the conjugate of the RIS to user k channel,/->Is thatDiagonal matrix formed by elements of (a) as diagonal elements, < ->For the candidate linear precoding vector of the base station for the i-th user,is->Conjugate transpose of->For the RIS to user k channel, +.>Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->，/>Is the channel from the base station to the user.

In the method for optimizing the sum rate of the RIS-assisted MIMO system according to the embodiments of the present disclosure, the alternate optimization termination condition includes:

wherein,and->Respectively represent +.>Secondary and->Candidate linear precoding vectors obtained by the multiple iterations,and->Respectively represent +.>Secondary and->Candidate RIS reflection matrix obtained by multiple iterations, +.>Andrespectively represent +.>Secondary and->The sum rate obtained from the multiple iterations.

On the other hand, the embodiment of the specification also provides a device for optimizing the sum rate of the RIS auxiliary MIMO system, which comprises the following components:

the initialization module is used for initializing a RIS reflection matrix, a first penalty factor and a second penalty factor of the target MIMO system;

the first optimization module is used for iteratively optimizing a sum rate objective function taking the RIS reflection matrix as a fixed value by adjusting the first penalty factor until a first penalty termination condition is met so as to obtain candidate linear precoding vectors of the base station of the target MIMO system for users;

The second optimization module is used for iteratively optimizing a sum rate objective function taking the candidate linear precoding vector as a fixed value by adjusting the second penalty factor until a second penalty termination condition is met so as to obtain a candidate RIS reflection matrix;

the iteration control module is used for judging whether the candidate linear precoding vector and the candidate RIS reflection matrix meet the alternate optimization termination condition; if the alternate optimization termination condition is not met, continuing to iterate the alternate optimization; and if the alternate optimization termination condition is met, taking the candidate linear precoding vector as an optimal linear precoding vector corresponding to the maximized sum rate, and taking the candidate RIS reflection matrix as an optimal RIS reflection matrix corresponding to the maximized sum rate.

In another aspect, embodiments of the present disclosure further provide a computer device including a memory, a processor, and a computer program stored on the memory, which when executed by the processor, performs the instructions of the above method.

In another aspect, embodiments of the present disclosure also provide a computer storage medium having stored thereon a computer program which, when executed by a processor of a computer device, performs instructions of the above method.

In another aspect, the present description embodiment also provides a computer program product comprising a computer program which, when executed by a processor of a computer device, performs the instructions of the above method.

As can be seen from the technical solutions provided by the embodiments of the present specification above, in the embodiments of the present specification, the sum rate optimization is still decomposed into an alternating optimization of active beamforming and passive beamforming (i.e., an alternating optimization of linear precoding vectors and RIS reflection matrices); because the projection-based punishment function is adopted for solving (namely, the first punishment factor is adjusted to iteratively optimize the sum-rate objective function taking the RIS reflection matrix as a fixed value, and the second punishment factor is adjusted to iteratively optimize the sum-rate objective function taking the candidate linear precoding vector as a fixed value), the function corresponding to the constraint condition is required to be written into a square form to be put on the optimization problem, the constraint optimization problem is converted into the unconstrained optimization problem, the implementation complexity of sum-rate optimization in the RIS-assisted MIMO communication system is further reduced, and the optimization efficiency of sum-rate optimization in the RIS-assisted MIMO communication system is improved.

Drawings

In order to more clearly illustrate the embodiments of the present description or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some of the embodiments described in the present description, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. In the drawings:

FIG. 1 illustrates a downlink schematic diagram of a RIS-assisted MIMO system in some embodiments of the present description;

FIG. 2 illustrates a flow chart of a method of rate optimization and RIS-assisted MIMO systems in some embodiments of the present description;

FIG. 3 illustrates a flow chart of active beam honest optimization in the method of FIG. 2;

FIG. 4 illustrates a flow chart of active beam honest optimization in the method of FIG. 2;

FIG. 5 shows a plot of sum rate versus total power of the system for different sum rate optimization methods;

FIG. 6 shows a graph of average run time versus the number of RIS reflecting elements for different and rate optimization methods;

FIG. 7 is a graph showing average operating time for different and rate optimization methods as a function of the number of base station antennas;

FIG. 8 illustrates a block diagram of the structure of a RIS assisted MIMO system and rate optimizing apparatus in some embodiments of the present description;

fig. 9 illustrates a block diagram of a computer device in some embodiments of the present description.

[ reference numerals description ]

81. Initializing a module;

82. a first optimization module;

83. a second optimization module;

84. an iteration control module;

902. a computer device;

904. a processor;

906. a memory;

908. a driving mechanism;

910. an input/output interface;

912. an input device;

914. an output device;

916. a presentation device;

918. a graphical user interface;

920. a network interface;

922. a communication link;

924. a communication bus.

Detailed Description

In order to make the technical solutions in the present specification better understood by those skilled in the art, the technical solutions in the embodiments of the present specification will be clearly and completely described below with reference to the drawings in the embodiments of the present specification, and it is obvious that the described embodiments are only some embodiments of the present specification, not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are intended to be within the scope of the present disclosure.

The embodiments of the present specification relate to a target parameter optimization technique for an RIS-assisted MIMO system, so as to improve the optimization efficiency of target parameter optimization in the RIS-assisted MIMO communication system. Wherein, the RIS can be an active RIS or a passive RIS; target parameter optimization may include, but is not limited to, sum rate maximization, energy efficiency maximization, spectral efficiency maximization, privacy rate maximization, and the like. Therefore, the RIS-assisted MIMO system and rate optimization schemes described in the following embodiments of the present specification are merely illustrative of exemplary application scenarios of the embodiments of the present specification, and should not be construed as the only limitation of the embodiments of the present specification.

Before describing the sum rate optimization scheme of the RIS-aided MIMO system in the embodiments of the present specification, the following principle is explained.

A downlink schematic of a RIS-aided MIMO system is shown in fig. 1; the MIMO system includes a base station, an active RIS and a user terminal, taking a single cell (a region covered by a radio signal in mobile communication is called a cell) as an example of a large-scale active RIS-assisted multi-user MIMO downlink scenario, the base station is provided with M antennas, the active RIS is provided with N reflection units, and the user terminal (hereinafter referred to as a user) of each single antenna in the cell receives one data stream transmitted from the base station. The base station transmits the data stream to the user using linear precoding and uses perfect channel estimation to obtain channel state information. Is provided with Representing the channel from base station to user k (i.e. kth user in cell), active RIS to user k, and base station to RIS, respectively, wherein +.>K is the number of users in the cell, < >>Representing the complex matrix space in the N x M dimensions. In addition, it is assumed that the data symbol transmitted by the base station is +.>And meet the followingAnd->Wherein->Mean value of s>Represents the conjugate transpose of s, < >>Representing a K-dimensional identity matrix. The base station transmission signal x can be expressed as:

（1）

wherein,representing the linear precoding vector of the base station for user k, a>Data symbols for user k transmitted by the base station.

Received signal of user kThe method can be expressed as follows:

（2）

wherein,representation->Conjugate transpose of>，/>A sum channel representing a direct channel and a concatenated channel, < ->Is->Conjugate transpose of->Is->Phi represents the RIS reflection matrix,，/>representing the reflection amplitude of the active RIS, +.>Is->Conjugate transpose of->Representing the reflection phase of the active RIS, n=1, 2, …, N. v and->Representing the active RIS and the additive Gaussian white noise introduced by user k, respectively, where v and +.>Obeys a circularly symmetric complex gaussian distribution.

Assume that the maximum transmission power of an active RIS-assisted massive MIMO system isWherein the maximum transmission power of the base station is +. >The maximum reflected power of the active RIS is +.>. The following power constraints may be obtained:

（3）

wherein,feasible region representing the base station transmission power constraint, < >>Feasible domain representing active RIS power constraint,/->Representing the mean of the variables s,/->Representing the mean of the variables s and v, +.>F-norm of Φ>Is gaussian white noise at the active smart reflective surface.

The achievable rate for user k is expressed as:

（4）

wherein,for the achievable rate of user k as a function of w and phi,，/>for the linear precoding vector of the base station to user i,transpose of the linear precoding vector for user K for base station,/>Is gaussian white noise at the base station.

Then, the sum rate maximization problem can be expressed as follows:

（5a）

（5b）

wherein,phase shift coefficient of the nth reflection unit of the intelligent reflection surface, +.>For the maximum magnification factor of the nth reflection unit in RIS, the constraint corresponding to equation (5 b) is about w or ΦConvex, but not jointly convex with respect to (w, Φ). Meanwhile, the objective function f (w, Φ) (i.e., the sum rate function that varies with w and Φ) is non-convex. Thus, alternating optimization solutions and rate maximization problems can be employed; alternate optimization solution and rate maximization includes: active beamforming optimization and passive beamforming optimization.

(1) Active beamforming optimization

Given Φ, equation (5 a) for w can be expressed as follows:

（6a）

（6b）

（6c）

wherein,represents f (w, phi) at fixed phi, where F is a constant phi>，/>，Representation->The feasible region of w under constraint.

However, the process is not limited to the above-described process,still non-convex, which can be solved using a weighted least mean square error method, as will be explained in more detail below. Now, attention is paid to constraint->And->. The feasible region is the sphere->And ellipsoids->This intersection is convex, but its projection is not easy to calculate, but can be calculated efficiently for a single projection of the sphere and ellipsoid. Therefore, the problem of equation (6 a) is solved using a penalty approach based on the nearest distance. Specifically, equation (6 a) is restated as:

（7）

wherein the method comprises the steps ofRepresent w to set->Y is +.>In the presence of an element of the group,is a penalty factor for w. From the exact penalty method and the regularization conditions of the convex set, it is known that when +.>When sufficiently large and finite, equation (7) is equivalent to equation (6) because they have the same optimum value.

The distance function in equation (7) is not easy to calculate and is non-smooth; the following approximations can be considered:

（8）

next, distance optimization is applied to solve this problem. Assuming the optimal value for the previous iteration, consider the current iteration: Wherein->Expressed in feasible region->Middle distance>The most recent vector. Therefore, equation (8) can be rewritten as:

（9）

（10）

（11）

wherein,is indicated at->Middle distance>Nearest vector, +.>Is indicated at->Middle distance>Nearest vector, +.>Representing Cronecker product, metropolyl>Is a constant greater than or equal to zero, which can be obtained by one-dimensional search whenThe search terminates. For convenience of symbolization, the +.>And->Are abbreviated as +.>And->。

The termination conditions for the penalty method for solving the optimal w are as follows:

（12）

(2) Passive beamforming optimization

Given w, equation (5 a) for Φ can be expressed as follows:

（13a）

（13b）

（13c）

wherein,is a diagonal matrix. />Represents f (w, phi) at the fixed w, -where w is fixed>Representation->Constrained->Is (are) feasible domain->Representation->Constrained->Is a feasible region of (2). Constraint->Is convex but is difficult to solve due to its complex round fashion. Likewise, the->Restricted feasible region and->The projection of the intersection of the feasible regions of the constraint is difficult to calculate. Thus, the optimal Φ can be solved using the same penalty method as solving the optimal. Thus, equation (12) can be approximated as:

（14）

（15）

（16）

wherein,representation is directed at->Penalty factor of->The phase shift coefficient of the nth reflection unit in the RIS reflection matrix obtained for the last optimization phi, lambda is a constant obtained by one-dimensional search and lambda is not less than 0, >Is->Middle distance>Nearest vector, +.>Is->Middle distance>The nearest vector, for convenience of symbology, will be described in the followingAnd->Are abbreviated as +.>And->。

Solving for the optimumThe termination conditions of the penalty method of (2) are as follows:

（17）

(3) Sum rate maximization

In the embodiment of the specification, a weighted least mean square error method is adopted to solve non-convex。

Introducing auxiliary variablesSetting:

（18）

wherein,representation->Conjugation of (2);

（19）

wherein, the bestEqual to->；

Variable(s)eAndρfor any one ofe>0, the following results are satisfied:

（20）

according to equation (18) and equation (19), equation (5 a) is equivalent to

（21a）

（21b）

Assume thatThe minimum value of equation (19) isObtained at that time. Using a weighted least mean square error method, equation (9) can be converted into: />

（22）

Wherein,（23）

wherein,representation->Is a transpose of (a).

Solving the steady state point of equation (22), the optimal value can be obtained as follows:

（24）

also, using the weighted least mean square error method, equation (14) can be converted to:

(25）

wherein,

（26）

solving the steady state point of equation (25), the optimal value can be obtained as follows:

（27）

the alternate optimization termination conditions are as follows:

（28）

wherein,and->Respectively represent +.>And obtaining optimal w and phi through multiple iterations.

Based on the above principle, the embodiments of the present disclosure provide a method for optimizing the sum rate of an RIS-assisted MIMO system, which may be applied to the MIMO system described above, and referring to fig. 2, in some embodiments of the present disclosure, the method for optimizing the sum rate of an RIS-assisted MIMO system may include the following steps:

Step 201, initializing a RIS reflection matrix, a first penalty factor and a second penalty factor of a target MIMO system;

step 202, iteratively optimizing a sum rate objective function with an RIS reflection matrix as a fixed value by adjusting the first penalty factor until a first penalty termination condition is met, so as to obtain candidate linear precoding vectors of a base station of the target MIMO system to a user;

step 203, iteratively optimizing a sum rate objective function taking the candidate linear precoding vector as a fixed value by adjusting the second penalty factor until a second penalty termination condition is met, so as to obtain a candidate RIS reflection matrix;

step 204, judging whether the candidate linear precoding vector and the candidate RIS reflection matrix meet an alternate optimization termination condition; if the alternate optimization termination condition is not satisfied, then step 202 is performed; otherwise, step 205 is performed.

Step 205, taking the candidate linear precoding vector as an optimal linear precoding vector corresponding to the maximization sum rate, and taking the candidate RIS reflection matrix as an optimal RIS reflection matrix corresponding to the maximization sum rate.

In the embodiment of the present disclosure, when the linear precoding vector of the base station to the user is controlled according to the optimal linear precoding vector and the RIS reflection matrix is set according to the optimal RIS reflection matrix, downlink communication of the RIS-assisted MIMO system may be facilitated to reach the maximum combining rate, thereby improving the communication performance of the RIS-assisted MIMO system.

In the embodiments of the present description, the sum rate optimization is still broken down into an alternating optimization of active beamforming and passive beamforming (i.e., alternating optimization of linear precoding vectors and RIS reflection matrices); because the projection-based punishment function is adopted for solving (namely, the first punishment factor is adjusted to iteratively optimize the sum-rate objective function taking the RIS reflection matrix as a fixed value, and the second punishment factor is adjusted to iteratively optimize the sum-rate objective function taking the candidate linear precoding vector as a fixed value), the function corresponding to the constraint condition is required to be written into a square form to be put on the optimization problem, the constraint optimization problem is converted into the unconstrained optimization problem, the implementation complexity of sum-rate optimization in the RIS-assisted MIMO communication system is further reduced, and the optimization efficiency of sum-rate optimization in the RIS-assisted MIMO communication system is improved.

For example, toAn order representing the computational complexity of the algorithm; the computational complexity of the optimization method of the embodiments of the present specification is +.>The method comprises the steps of carrying out a first treatment on the surface of the The computational complexity of the CVX solver is +.>The method comprises the steps of carrying out a first treatment on the surface of the The computational complexity of the PDS solution is +.>Therefore, the optimization method of the embodiments of the present specification has higher optimization efficiency than the CVX solver and PDS solver methods.

In the embodiment of the present specification, the candidate linear precoding vector may be an initialized linear precoding vector, or whether the linear precoding vector to be confirmed obtained after each active beamforming optimization is an optimal linear precoding vector (i.e., an optimal linear precoding vector of the base station to the user); the candidate RIS reflection matrix is an RIS reflection matrix which is obtained after each passive beam forming optimization and is to be confirmed whether the RIS reflection matrix is optimal or not.

In some embodiments of the present description, the sum-rate objective function with the RIS reflection matrix as a constant value may include:

wherein min represents the minimum value, w is the candidate linear precoding vector of the base station to the user, Φ is the RIS reflection matrix,representing the sum rate objective function at a constant value of Φ,/->For a first penalty factor for w, +.>The linear precoding vector of the base station to the user, which is obtained for the last optimization w; />For the feasible region of w under the maximum transmission power constraint of the base station,is->Middle distance>Nearest vector, +.>Represents w and->Euclidean distance of>Is thatFeasible region of w under constraint, +.>Is the conjugate transpose of w, +.>，/>For K-dimensional identity matrix>Representing the kronecker product, G is the channel from the base station to the RIS, +.>Is the conjugate transpose of G>Is the conjugate transpose of phi >Is an intermediate variable +.>For RIS maximum reflected power, +.>F-norm of Φ>Is Gaussian white noise at the active smart reflective surface, +.>Is->Middle distance>The most recent vector is the one that,represents w and->Is a euclidean distance of (c).

Referring to fig. 3, in some embodiments of the present disclosure, on the basis of the foregoing sum-rate objective function with a value of the RIS reflection matrix, by adjusting the first penalty factor, iteratively optimizing the sum-rate objective function with a value of the RIS reflection matrix until a first penalty termination condition is satisfied may include the following steps:

step 301, calculateAnd->。

In some embodiments of the present description, the formula may be followedCalculate->And according to the formula->Calculate->。/>

Step 302, according toAnd->Calculate->。

In some embodiments of the present description, one may applyAnd->Input formulaCalculate->。

Step 303, judgingWhether a first penalty termination condition is satisfied; if->Executing step 304 if the first penalty termination condition is not satisfied; otherwise, go to step 305;

wherein the first penalty termination condition may includeStep 304, adjust->The method comprises the steps of carrying out a first treatment on the surface of the And performs step 301 after the adjustment.

I.e. ifIf the first penalty termination condition is not satisfied, increase +.>Is calculated iteratively on the basis of the value of (2); in this way, the optimal w can ultimately be projected into the feasible domain of w.

Wherein the increase isThe strategy of (2) can be customized, e.g. can be increased by a fixed increment +.>For example, if initialized +.>Then +.>Can be +.>Second time after enlargement +.>May beIn this way.

Step 305, triggering an optimization step of Φ.

Steps 301-305 pertain to active beamforming optimization (i.e., optimization); if the first penalty termination condition is met, the method can be shifted to passive beam forming optimization (i.e. optimization), namely, the step of performing ' iterative optimization of a sum rate objective function taking a RIS reflection matrix as a constant value by adjusting the first penalty factor ' until the first penalty termination condition is met, so as to obtain candidate linear precoding vectors of the base station of the target MIMO system to a user '.

In steps 301-305, the method comprises, among other things,is->Is>For maximum transmission power of the base station +.>Is thatConjugate transpose of->For M-dimensional identity matrix->Is a constant obtained by one-dimensional search and +.>，K is the number of users, ">，/>For the auxiliary variable of the kth user, +.>Is->Conjugation of->Direct channel and cascade channel sum channel for kth user, +.>Is->Conjugate transpose of->，/>Is->Transpose of- >，/>And the candidate linear precoding vector of the base station to the user is obtained.

In some embodiments of the present specification, the sum rate objective function with the candidate linear precoding vector as a constant value may include:

wherein min represents the minimum value, w is the candidate linear precoding vector of the base station to the user, Φ is the RIS reflection matrix,representing the sum rate objective function at a constant value of w,/for>For a second penalty factor for Φ, +.>RIS reflection matrix obtained for the last optimization Φ, < >>Is->Feasible region of w under constraint, +.>Is the conjugate transpose of phi>Is a diagonal matrix, and->K is the number of users, G is the channel from the base station to the RIS,candidate linear precoding vectors for the base station for the kth user, +.>Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Is Gaussian white noise at the active smart reflective surface, +.>Is N-dimensional identity matrix->For RIS maximum reflected power, +.>Is->Intermediate distanceNearest vector, +.>Represents phi and +.>Euclidean distance of>Is->Feasible region of phi under constraint, +.>Phase shift coefficient of the nth reflection unit of the intelligent reflection surface, +.>For the maximum magnification factor of the nth reflection unit in RIS, < > >Is->Middle distance>Nearest vector, +.>Represents phi and +.>Is a euclidean distance of (c).

Referring to fig. 4, in some embodiments of the present disclosure, on the basis of the foregoing sum rate objective function with the candidate linear precoding vector as a constant value, by adjusting the second penalty factor to iteratively optimize the sum rate objective function with the candidate linear precoding vector as a constant value until a second penalty termination condition is satisfied, a step of obtaining a candidate RIS reflection matrix may include:

step 401, calculatingAnd->。

In some embodiments of the present description, the formula may be followedCalculate->And according to the formula->Calculate->。

Step 402, according toAnd->Calculate->。

Step 403, judgingWhether a second penalty termination condition is satisfied; if->If the second penalty termination condition is not satisfied, then step 404 is performed; otherwise, step 405 is performed.

Wherein the second penalty termination condition includes。

Step 404, adjustThe method comprises the steps of carrying out a first treatment on the surface of the And performs step 401 after adjustment.

I.e. ifIf the first penalty termination condition is not satisfied, increase +.>Is calculated iteratively on the basis of the value of (2); thus, finally the optimal +. >Projection to +.>Is a feasible domain of (c).

Step 405, triggering a judgment step of alternately optimizing termination conditions.

I.e. ifAnd if the second punishment termination condition is met, judging whether the newly obtained candidate linear precoding vector and the candidate RIS reflection matrix meet the alternate optimization termination condition so as to confirm whether the newly obtained candidate linear precoding vector and the candidate RIS reflection matrix are optimal.

In steps 401 to 405, wherein λ is a constant obtained by one-dimensional search and λ is not less than 0,for the number of reflection units in RIS, +.>For the candidate RIS reflection matrix,/I>，/>For the auxiliary variable of the kth user, +.>，/>Is->Conjugation of->Direct channel and cascade channel sum channel for kth user, +.>Is->Conjugate transpose of->Transpose the conjugate of the RIS to user k channel,/->Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Candidate linear precoding vector for base station to ith user, +.>Is->Conjugate transpose of->For the RIS to user k channel, +.>Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->，/>Is the channel from the base station to the user.

In some embodiments of the present description, the alternate optimization termination condition may include:

wherein,and->Respectively represent +.>Secondary and->Candidate linear precoding vectors obtained by the multiple iterations, And->Respectively represent +.>Secondary and->Candidate RIS reflection matrix obtained by multiple iterations, +.>Andrespectively represent +.>Secondary and->The sum rate obtained from the multiple iterations.

In the alternate optimization of the embodiments of the present description, by performing active beamforming optimization (i.e., optimizing first) followed by passive beamforming optimization (i.e., re-optimizing), the sequential consistency of precoding vectors required for downlink communication of the RIS-aided MIMO system can be ensured.

To demonstrate the effectiveness of the proposed algorithm, consider the following scenario, with a system model as shown in FIG. 1. Setting r=8m, l=100deg.m in fig. 1; the small scale fading in the system is modeled as rice fading; the large scale fading between base station to user is denoted pl=41.2+28.7log (d), the large scale fading between base station to active RIS is denoted pl=37.3+22.0log (d), where d represents the distance between the two devices; additive white gaussian noise The method comprises the steps of carrying out a first treatment on the surface of the The penalty coefficient initial value is set to 0.01.

By simulation, it can be obtained: a plot of sum rate versus total system power for different sum rate optimization methods as shown in fig. 5 (m=128, n=128, k=16 is set in fig. 5); the average run time of the different and rate optimization methods shown in FIG. 6 varies with the number of RIS reflective elements Is shown (in fig. 6, set m=128, k=16,) The method comprises the steps of carrying out a first treatment on the surface of the And a graph of average running time of different and rate optimization methods as shown in fig. 7 as a function of the number of base station antennas (n=128, k=16,/in fig. 7 is set up>). As can be seen from fig. 5, the total power +.of the different systems obtained with the sum rate optimization method of the embodiments of the present specification>The sum rate is equal to the total power of different systems obtained based on the optimization of a CVX solver and a PDS solving method>The following sum rates are almost the same, thereby verifying the feasibility of the sum rate optimization method of the embodiments of the present specification; meanwhile, as can be seen in conjunction with fig. 6 and 7, the average time consumption of the algorithms of the CVX solver and the PDS solver method is at least 20 times that of the algorithms of the rate optimization method and the embodiment of the present specification; thus, the sum rate optimization method of the embodiment of the specification has higher optimization efficiency.

While the process flows described above include a plurality of operations occurring in a particular order, it should be apparent that the processes may include more or fewer operations, which may be performed sequentially or in parallel (e.g., using a parallel processor or a multi-threaded environment).

Corresponding to the above method for optimizing the sum rate of the RIS-assisted MIMO system, the embodiments of the present disclosure further provide a device for optimizing the sum rate of the RIS-assisted MIMO system, which may be configured on the above RIS-assisted MIMO system, as shown in fig. 8, and in some embodiments of the present disclosure, the device for optimizing the sum rate of the RIS-assisted MIMO system may include:

an initialization module 81, configured to initialize a RIS reflection matrix, a first penalty factor, and a second penalty factor of the target MIMO system;

a first optimizing module 82, configured to iteratively optimize a sum rate objective function with the RIS reflection matrix as a constant value by adjusting the first penalty factor until a first penalty termination condition is satisfied, so as to obtain a candidate linear precoding vector of the base station of the target MIMO system for the user;

a second optimizing module 83, configured to iteratively optimize a sum rate objective function with the candidate linear precoding vector as a constant value by adjusting the second penalty factor until a second penalty termination condition is satisfied, so as to obtain a candidate RIS reflection matrix;

an iteration control module 84, configured to determine whether the candidate linear precoding vector and the candidate RIS reflection matrix satisfy an alternate optimization termination condition; if the alternate optimization termination condition is not met, continuing to iterate the alternate optimization; and if the alternate optimization termination condition is met, taking the candidate linear precoding vector as an optimal linear precoding vector corresponding to the maximized sum rate, and taking the candidate RIS reflection matrix as an optimal RIS reflection matrix corresponding to the maximized sum rate.

For convenience of description, the above devices are described as being functionally divided into various units, respectively. Of course, the functions of each element may be implemented in one or more software and/or hardware elements when implemented in the present specification.

In the embodiments of the present disclosure, the user information (including, but not limited to, user device information, user personal information, etc.) and the data (including, but not limited to, data for analysis, stored data, presented data, etc.) are information and data that are authorized by the user and are sufficiently authorized by each party.

Embodiments of the present description also provide a computer device. As shown in fig. 9, in some embodiments of the present description, the computer device 902 may include one or more processors 904, such as one or more Central Processing Units (CPUs) or Graphics Processors (GPUs), each of which may implement one or more hardware threads. The computer device 902 may also include any memory 906 for storing any kind of information, such as code, settings, data, etc., and in a particular embodiment, a computer program on the memory 906 and executable on the processor 904, which when executed by the processor 904, may perform the instructions of the RIS-assisted MIMO system and rate optimization method described in any of the embodiments above. For example, and without limitation, the memory 906 may include any one or more of the following combinations: any type of RAM, any type of ROM, flash memory devices, hard disks, optical disks, etc. More generally, any memory may store information using any technique. Further, any memory may provide volatile or non-volatile retention of information. Further, any memory may represent fixed or removable components of computer device 902. In one case, when the processor 904 executes associated instructions stored in any memory or combination of memories, the computer device 902 can perform any of the operations of the associated instructions. The computer device 902 also includes one or more drive mechanisms 908 for interacting with any memory, such as a hard disk drive mechanism, optical disk drive mechanism, and the like.

The computer device 902 may also include an input/output interface 910 (I/O) for receiving various inputs (via an input device 912) and for providing various outputs (via an output device 914). One particular output mechanism may include a presentation device 916 and an associated graphical user interface 918 (GUI). In other embodiments, input/output interface 910 (I/O), input device 912, and output device 914 may not be included, but merely as a computer device in a network. The computer device 902 may also include one or more network interfaces 920 for exchanging data with other devices via one or more communication links 922. One or more communication buses 924 couple the above-described components together.

The communication link 922 may be implemented in any manner, for example, through a local area network, a wide area network (e.g., the internet), a point-to-point connection, etc., or any combination thereof. Communication link 922 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc., governed by any protocol or combination of protocols.

The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), computer-readable storage media, and computer program products according to some embodiments of the specification. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processor to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processor, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processor to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processor to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

In a typical configuration, a computer device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.

The memory may include volatile memory in a computer-readable medium, random Access Memory (RAM) and/or nonvolatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). Memory is an example of computer-readable media.

Computer readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of storage media for a computer include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Disks (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium, which can be used to store information that can be accessed by a computer device. Computer readable media, as defined in the specification, does not include transitory computer readable media (transmission media), such as modulated data signals and carrier waves.

It will be appreciated by those skilled in the art that embodiments of the present description may be provided as a method, system, or computer program product. Accordingly, the present specification embodiments may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present description embodiments may take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present embodiments may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The embodiments of the specification may also be practiced in distributed computing environments where tasks are performed by remote processors that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.

It should also be understood that, in the embodiments of the present specification, the term "and/or" is merely one association relationship describing the association object, meaning that three relationships may exist. For example, a and/or B may represent: a exists alone, A and B exist together, and B exists alone. In addition, the character "/" herein generally indicates that the front and rear associated objects are an "or" relationship.

In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, as relevant to see a section of the description of method embodiments.

In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the embodiments of the present specification. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.

The foregoing is merely exemplary of the present application and is not intended to limit the present application. Various modifications and changes may be made to the present application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc. which are within the spirit and principles of the present application are intended to be included within the scope of the claims of the present application.

Claims

1. A method for rate optimization for a RIS-aided MIMO system, comprising:

2. The method for sum-rate optimization of an RIS-aided MIMO system of claim 1, wherein said sum-rate objective function with the RIS reflection matrix as a constant value comprises: ；

Wherein min represents the minimum value, w is the candidate linear precoding vector of the base station to the user, Φ is the RIS reflection matrix,representing the sum rate objective function at a constant value of Φ,/->For a first penalty factor for w, +.>The linear precoding vector of the base station to the user, which is obtained for the last optimization w; />For the feasible region of w under the maximum transmission power constraint of the base station,is->Middle distance>Nearest vector, +.>Represents w and->Euclidean distance of>Is->Feasible region of w under constraint, +.>Is the conjugate transpose of w, +.>，For K-dimensional identity matrix>Representing the kronecker product, G is the channel from the base station to the RIS, +.>Is the conjugate transpose of G>Is the conjugate transpose of phi>Is an intermediate variable +.>For RIS maximum reflected power, +.>F-norm of Φ>Is Gaussian white noise at the active smart reflective surface, +.>Is->Middle distance>The most recent vector is the one that,represents w and->Is a euclidean distance of (c).

3. The RIS aided MIMO system sum rate optimization method of claim 2, wherein iteratively optimizing a sum rate objective function with a RIS reflection matrix as a constant value by adjusting the first penalty factor until a first penalty termination condition is met, comprises:

according to the formulaCalculate->And according to the formula Calculate->；

Will beAnd->Input formula->Calculate->；

if it isDoes not satisfy the firstPenalty termination condition, then increase->Is calculated again +.>And->From this, calculate +.>And judging the recalculated +.>Whether a first penalty termination condition is satisfied;

wherein,is->Is>For maximum transmission power of the base station +.>Is->Conjugate transpose of->For M-dimensional identity matrix->Is a constant obtained by one-dimensional search and +.>，/>K is the number of users, ">，/>For the auxiliary variable of the kth user, +.>Is->Conjugation of->Direct channel and cascade channel sum channel for kth user, +.>Is->Conjugate transpose of->，/>Is->Transpose of->，/>Candidate linear precoding vectors for base station to user, < > for>And the candidate linear precoding vector of the kth user is the base station.

4. The RIS aided MIMO system sum rate optimization method of claim 1, wherein said sum rate objective function with said candidate linear precoding vector as a constant value comprises:；

wherein min represents the minimum value, w is the candidate linear precoding vector of the base station to the user, Φ is the RIS reflection matrix, Representing the sum rate objective function at a constant value of w,/for>For a second penalty factor for Φ, +.>RIS reflection matrix obtained for the last optimization Φ, < >>Is->Feasible region of w under constraint, +.>Is the conjugate transpose of phi>Is a diagonal matrix, and->K is the number of users, G is the channel from the base station to the RIS,candidate linear precoding vectors for the base station for the kth user, +.>Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Is Gaussian white noise at the active smart reflective surface, +.>Is N-dimensional identity matrix->For RIS maximum reflected power, +.>Is->Intermediate distanceNearest vector, +.>Represents phi and +.>Is of Euclidean distance of (2)Leave, go up>Is->Feasible region of phi under constraint, +.>Phase shift coefficient of the nth reflection unit of the intelligent reflection surface, +.>For the maximum magnification factor of the nth reflection unit in RIS, < >>Is->Middle distance>Nearest vector, +.>Represents phi and +.>Is a euclidean distance of (c).

5. The RIS aided MIMO system sum rate optimization method of claim 4, wherein iteratively optimizing a sum rate objective function with said candidate linear precoding vector as a constant by adjusting said second penalty factor until a second penalty termination condition is met, comprises:

According to the formulaCalculate->And according to the formulaCalculate->；

Will beAnd->Input formula->Calculate->；

JudgingWhether a second penalty termination condition is satisfied; the second penalty termination condition includes；

if it isIf the second penalty termination condition is not satisfied, increase +.>Is calculated again +.>And->From this, calculate +.>And judging the recalculated +.>Whether a second penalty termination condition is satisfied;

wherein lambda is a constant obtained by one-dimensional search and lambda is not less than 0,for the number of reflection units in RIS, +.>For the candidate RIS reflection matrix,

，/>as an auxiliary variable for the kth user,，/>is->Conjugation of->The sum channel of the direct channel and the concatenated channel of the kth user,is->Conjugate transpose of->Transpose the conjugate of the RIS to user k channel,/->Is->Diagonal matrix formed by elements of (a) as diagonal elements, < ->Candidate linear precoding vector for base station to ith user, +.>Is->Conjugate transpose of->For the RIS to user k channel, +.>Is->As a diagonal matrix formed by diagonal elements,，/>is the channel from the base station to the user.

6. As claimed inThe method for sum rate optimization of a RIS-aided MIMO system of claim 1, wherein the alternate optimization termination conditions include: ；

Wherein,and->Respectively represent +.>Secondary and->Candidate linear precoding vector obtained by multiple iterations, +.>Andrespectively represent +.>Secondary and->Candidate RIS reflection matrix obtained by multiple iterations, +.>Andrespectively represent +.>Secondary and->The sum rate obtained from the multiple iterations.

7. A device for rate optimization of a RIS-aided MIMO system, comprising:

8. A computer device comprising a memory, a processor, and a computer program stored on the memory, characterized in that the computer program, when being executed by the processor, performs the instructions of the method according to any of claims 1-6.

9. A computer storage medium having stored thereon a computer program, which, when executed by a processor of a computer device, performs the instructions of the method according to any of claims 1-6.