Ris-assisted downlink urllc beamforming method with discrete phase shift

Abstract

The application discloses a RIS-aided downlink URLLC beamforming method with discrete phase shift, relates to the technical field of wireless communication, and comprises the following steps: S1, constructing a RIS-aided downlink multi-user MISO URLLC system model; S2, based on communication theory and optimization theory, constructing a BS transmission power minimization problem model, and improving the model through parameter replacement and problem conversion; S3, introducing a first variable, converting integer constraints and non-convex constraints into an easy-to-handle form, and rewriting the optimization problem model through a penalty method; S4, based on variable decoupling conversion non-convex constraints, adopting S lemma and SCA technology to propose an AO algorithm; and S5, based on the single-time optimal solution generated in step S4, obtaining a suboptimal solution of the original problem beamforming through iterative convergence. The application solves the RIS-aided multi-user MISO URLLC beamforming optimization problem, also considers the influence of RIS unit discrete phase shift on beamforming, and proves that, under the influence of 2-bit quantization resolution, the ideal RIS unit performance is approximated with a small performance loss.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically to a RIS-assisted downlink URLLC beamforming method with discrete phase shift. Background Technology

[0002] With the rapid development of 5G technology, the number of IoT devices worldwide is experiencing explosive growth, expected to reach 22 billion units by 2025, laying the foundation for the iterative upgrade of industrial IoT and smart home technologies. However, most IoT applications require the use of short packet communication with a transmission latency of less than 1ms and a reliability of greater than 99.9999%, known as Ultra-Reliable Low-Latency Communication (URLLC).

[0003] Currently, most wireless channels in typical 5G applications suffer from strong multipath fading due to blocked line-of-sight links, resulting in poor connectivity and failing to meet the quality of service requirements of URLLC. In recent years, reconfigurable intelligent surfaces (RIS), composed of a large number of electromagnetic units, have become the most promising technology for URLLC networks due to their ability to intelligently control electromagnetic waves, attracting widespread attention from the academic community. However, most current research is based on the assumptions of perfect Channel State Information (CSI) and ideal RIS unit phase shift, and has not yet solved the problems of robust transmission scheme design under imperfect CSI and discrete phase shift design of RIS units under the influence of low quantization resolution. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a RIS-assisted downlink URLLC beamforming method with discrete phase shift.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a RIS-assisted downlink URLLC beamforming method with discrete phase shift, comprising the following steps:

[0007] S1. Construct a RIS-assisted downlink multi-user MISO URLLC system model;

[0008] S2. Based on communication theory and optimization theory, a model for minimizing BS transmission power is constructed, and the model is improved through parameter substitution and problem transformation.

[0009] S3, introduce the first variable, convert the integer constraint and non-convex constraint into a form easy to handle, and rewrite the optimization problem model by the penalty method;

[0010] S4, convert the non-convex constraint based on variable decoupling, and propose an AO algorithm by using S lemma and SCA technology;

[0011] S5, based on the single optimal solution generated in step S4, the suboptimal solution of the original problem beamforming is obtained by iteration convergence.

[0012] Further, in step S1, the BS is equipped with N antennas, serving K single-antenna users, and defining as a set of single-antenna users, specifically including the following steps:

[0013] S11, let the number of RIS reflecting units be M, the index be , define that the RIS reflecting unit adopts a discrete phase shifter, and satisfies uniform quantization within interval, the phase shift of the RIS reflecting unit satisfies , wherein represents the sequential index of any RIS unit in the set ; represents the discrete phase shift set, represents the quantization interval, and the calculation formula is , represents the number of phase shift levels, and the calculation formula is , represents the quantization resolution; the phase shift vector of the RIS reflecting unit satisfies , wherein represents Euler's formula, , and the imaginary satisfies ;

[0014] S12, define the first complex-valued equivalent channel from the BS to the RIS as , the second complex-valued equivalent channel from the BS to the user as , and the third complex-valued equivalent channel from the RIS to the user as , wherein represents a complex vector with a dimension of N rows and 1 column; represents a complex vector with a dimension of M rows and 1 column; represents a complex matrix with a dimension of M rows and N columns;

[0015] S13, BS to users Message sent satisfy ,in, This represents a Gaussian distribution with mean 0 and variance 1, and the complex baseband signal transmitted at point BS. for ,in, This indicates that the BS is for the user Linear precoding;

[0016] S14, User Received signal for , ,in, This indicates the process from BS to RIS to the user. The cascaded channel link is calculated using the following formula: , H represents the diagonal matrix transformation of a vector, and H denotes the conjugate transpose. Indicates user Additive white Gaussian noise at the location, user The signal-to-interference-plus-noise ratio is , Represents a single-antenna user set In addition to single-antenna users The sum of all other single-antenna users, excluding those mentioned above; Indicates a single-antenna user The precoded vector;

[0017] S15. According to the finite block length coding theory, the user The achievable transmission rate is ,in, The channel dispersion is represented by the following formula: ; Indicates user The length of the transmission block, Indicates user The probability of decoding errors; Gaussian function The reverse;

[0018] S16, Definition The first channel link is ,definition The second channel link is ,in, express The estimated value, express The estimated value; express The estimated channel error, denotes the estimated channel error of ; denotes the uncertainty region radius of , denotes the uncertainty region radius of , denotes the F-norm of a matrix, denotes the 2-norm of a vector.

[0019] Preferably, step S2 specifically comprises the following steps:

[0020] S21, constructing a BS transmission power minimization problem model, i.e. wherein, denotes the first optimization problem, denotes the total power of BS transmission; denotes the minimum transmission rate of users satisfying the URLLC service quality under the influence of the norm-bounded CSI error model, denotes the minimum transmission rate constraint; denotes the RIS unit discrete phase shift vector constraint, denotes the minimization of the objective function of when and are taken as optimization variables; denotes the minimum transmission power of users under the influence of imperfect CSI;

[0021] S22, proving by lemma that is equivalent to its corresponding signal-to-noise ratio constraint, satisfying wherein the signal-to-noise ratio threshold satisfies ; wherein the calculation formula of the generalized function is , denotes a function, and the calculation formula thereof is wherein, and respectively denote the internal parameters of the function denotes a positive integer ranging from , denotes a positive integer ranging from ;

[0022] S23, defining the matrix , and satisfying and then calculating the RIS beamforming vector after integrating the cascade channel link and the second channel link , , the RIS beamforming matrix after integrating the cascaded channel link and the second channel link , , and satisfying and , the desired signal of the user is:

[0023]

[0024] wherein, represents taking the real part of a complex variable; represents the rank operation of a matrix; represents the system channel after integrating the cascaded channel link and the second channel link, and the calculation formula is , based on the influence of imperfect CSI, at this time satisfies:

[0025] ;

[0026] wherein, represents the estimated value of ; represents the channel error of ; and there is , represents the maximum norm value of the system channel estimation error after integrating the cascaded channel link and the second channel link;

[0027] After that, is modeled to obtain the channel error set , after integrating the cascaded channel link and the second channel link;

[0028] S24, rewrite the signal-to-interference-and-noise ratio of the user , that is, introduce an auxiliary variable , and equivalent to:

[0029] ;

[0030] wherein, represents the second optimization problem, and the constraint represents the minimum expected power of the user under the influence of imperfect CSI; the constraint represents the maximum interference and noise power of the user under the influence of imperfect CSI; the constraint represents the RIS unit vector after considering the cascaded channel and the direct channel; and the constraint represents the matrix It is a Hermitian matrix; constraints The matrix representing the discrete phase shift vectors of the RIS units; constraints Representation matrix A solution satisfying rank 1; This represents the rank operation on a matrix. This represents the maximum sum of multi-user interference and noise under the influence of channel error. ; Indicates will and Minimize when used as an optimization variable The objective function; This indicates the impact of imperfect CSI on users. The minimum expected transmission power; This indicates the impact of imperfect CSI on users. The maximum value of interference and noise power.

[0031] Preferably, step S3 includes the following steps:

[0032] S31. Introducing the first variable and define a binary matrix. Used to solve Constraints ,Will Constraints Equivalent to: ,in, Represents scalar Located in the binary matrix The Rows m columns Represents the set of phase shift levels, when When, the m-th unit of RIS selects the first... One working mode, otherwise satisfy ;constraint There are still 0 / 1 integer constraints, which can be addressed through inequalities. Replace, where and Indicates constraints; This represents the m-th element in the RIS beamforming vector after integrating the first and second channel links;

[0033] S32, Using equality constraints Replacement constraints ,in, and Indicates constraints; This represents the Hermitian matrix constructed under the influence of discrete phase shift in the RIS unit. Representing Hermitian matrices the element in the mth row and mth column in the matrix , and is rewritten as ;

[0034] wherein denotes a third optimization problem, denotes a penalty factor, denotes the sum of eigenvalues of the Hermitian matrix ; denotes the maximum eigenvalue of the Hermitian matrix , denotes an objective function of maximizing when is taken as an optimization variable.

[0035] Preferably, step S4 specifically comprises the following steps:

[0036] S41, respectively vectorize and to obtain a vectorized matrix , a vectorized channel estimation matrix , and a vectorized channel estimation error matrix , wherein , indicates that the maximum norm value of the channel estimation error vector does not exceed , and the third optimization problem is solved; the constraints and are converted into a form easy to handle by using an equality transformation: ; wherein denotes a Kronecker product, denotes vectorization of a matrix;

[0037] S42, the constraints and are transformed by using the S lemma to solve the influence of the CSI uncertainty in the form easy to handle in step S41: ; wherein denotes the result of transforming the constraint by using the S lemma, denotes the result of transforming the constraint by using the S lemma, denotes and Kronecker products, denotes and the sum of the remaining beamforming matrices after eliminating the beamforming matrix at the user , and denote auxiliary variables introduced, respectively; express OK Column identity matrix; express A matrix with 1 row and 0 columns; Indicates 1 row 0-column matrix;

[0038] S43. Based on SCA technology and using first-order Taylor series, expand the constraints respectively. and the third optimization problem The penalty item in the middle, namely , ;in, , and Let represent the nth iteration point, This represents the eigenvector corresponding to the largest eigenvalue; then the third optimization problem... Rewrite: ,in, This represents the fourth optimization problem. ; Indicates will Maximize when used as an optimization variable The objective function;

[0039] S44. Design the AO algorithm to solve... Lieutenant General and When used as an optimization variable, under constraints and The variable coupling that exists in it.

[0040] Preferably, step S44 specifically includes the following steps:

[0041] S441, Given parameters Regarding The optimization subproblem, with the optimization variable as the optimization variable, is written as: ; This represents the fifth optimization problem. Indicates will Maximize when used as an optimization variable The objective function is then used; subsequently, the relaxation constraints are proved using a theorem. After It exhibits compactness and can be solved using CVX;

[0042] S442, will As optimization variables, regarding parameters The optimization subproblem can be written as: , This represents the sixth optimization problem, which is solved using CVX.

[0043] Preferably, step S5 specifically comprises: initializing parameters , setting and , and then respectively performing outer loop and inner loop to output a suboptimal value of the second optimization problem ;

[0044] The inner loop comprises: firstly, given the second variable , solving the fifth optimization problem and updating the third variable ; then, given the third variable , solving the sixth optimization problem and updating the fourth variable ; letting , until the objective function in the fourth optimization problem converges or the number of inner loop iterations reaches , ending the inner loop;

[0045] The outer loop comprises: updating the penalty factor , until converges, ending the outer loop.

[0046] The beneficial effects of the present application are:

[0047] 1) The present application solves the RIS-aided multi-user MISO URLLC beamforming optimization problem, in particular, solves the coupling problem of beamforming vectors at the BS and phase shift vectors at the RIS. At the same time, the present application comprehensively considers the influence of RIS unit discrete phase shift on beamforming, and proves that under the influence of 2-bit quantization resolution, the system performance approximates the ideal RIS unit performance with small performance loss. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 is a step schematic diagram of the RIS-aided downlink URLLC beamforming method with discrete phase shift of an embodiment of the present application;

[0049] Figure 2 is an AO algorithm step schematic diagram of the RIS-aided downlink URLLC beamforming method with discrete phase shift of an embodiment of the present application;

[0050] Figure 3 is a comparison result schematic diagram of the RIS unit with discrete phase shift and the ideal RIS unit phase shift system performance of an embodiment of the present application. DETAILED DESCRIPTION

[0051] The technical solutions of the present application will be described clearly and completely below in connection with the embodiments. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0052] The present application considers an RIS-aided downlink multi-user multiple input single output (MISO) URLLC system, under the influence of imperfect CSI, by jointly optimizing the beamforming at the base station (BS) and the RIS, a system BS transmission power minimization problem is formulated. Due to the existence of variable coupling and mixed integer constraints, the optimization problem is a mixed integer non-convex optimization problem. In order to solve this problem, the present application proposes an alternating optimization (AO) algorithm by variable decoupling and based on S lemma, successive convex approximation (SCA) technique and penalty method, and the robustness and effectiveness of the proposed algorithm are proved by simulation analysis under different parameters. The steps of the method are shown in Figure 1 The specific steps include the following steps:

[0053] S1, construct an RIS-aided downlink multi-user MISO URLLC system model;

[0054] S2, based on the communication theory and optimization theory, construct a BS transmission power minimization problem model, and improve the model by parameter substitution and problem conversion;

[0055] S3, introduce a first variable, convert the integer constraint and non-convex constraint into an easy-to-handle form, and rewrite the optimization problem model by the penalty method;

[0056] S4, based on variable decoupling conversion non-convex constraint, AO algorithm is proposed by using S lemma and SCA technique;

[0057] S5, based on the single optimal solution generated in step S4, the suboptimal solution of the original problem beamforming is obtained by iterative convergence.

[0058] Specifically, in step S1, the BS is equipped with N antennas, serving K single-antenna users, define as a set of single-antenna users, which includes the following steps:

[0059] S11, let the number of RIS reflecting elements be M, and the index be The RIS reflection unit is defined to use a discrete phase shifter, and in Uniform quantization is satisfied within the interval, and the phase shift of the RIS reflector unit is achieved. satisfy ,in, Represents any RIS unit in the set Middle sequential index, Represents the discrete phase shift set. The quantization interval is represented by the formula: , The number of phase shift levels is represented by the following formula: , Indicates quantization resolution; phase shift vector of the RIS reflector unit. satisfy ,in, This represents Euler's formula. , imaginary number satisfy ;

[0060] S12. Define the first complex-valued equivalent channel from BS to RIS as follows: BS to user The second complex-valued equivalent channel is RIS to users The third complex-valued equivalent channel 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;

[0061] S13, BS to users Message sent satisfy ,in, This represents a Gaussian distribution with mean 0 and variance 1, and the complex baseband signal transmitted at point BS. for ,in, This indicates that the BS is for the user Linear precoding;

[0062] S14, User Received signal for , ,in, This indicates the process from BS to RIS to the user. The cascaded channel link is calculated using the following formula: , H represents the diagonal matrix transformation of a vector, and H represents the conjugate transpose. Indicates user The additive white Gaussian noise at the location follows a distribution. ,here This indicates that the mean is 0 and the variance is... The Gaussian distribution. (User) The signal-to-interference-plus-noise ratio is , Represents a single-antenna user set In addition to single-antenna users The sum of all other single-antenna users, excluding those mentioned above; Indicates a single-antenna user The precoded vector;

[0063] S15. According to the finite block length coding theory, the user The achievable transmission rate is ,in, The channel dispersion is represented by the following formula: ; Indicates user The length of the transmission block, Indicates user The probability of decoding errors; Gaussian function The reverse;

[0064] S16. Consider the norm-bounded CSI error model to characterize the channel uncertainty, and define... The first channel link is ,definition The second channel link is ,in, express The estimated value, express The estimated value; express The estimated channel error, express The estimated channel error; express The radius of the uncertainty region, express The radius of the uncertainty region, Denotes the F-norm of a matrix. It represents the 2-norm of a vector.

[0065] Specifically, step S2 includes the following steps:

[0066] S21. Based on the signal transmission model in step S1, construct a model for minimizing the BS transmission power problem, i.e. ,in, This represents the first optimization problem. This indicates the total power transmitted by the BS. Indicates user The minimum transmission rate that satisfies URLLC quality of service under the influence of the norm-bounded CSI error model. This indicates a minimum transmission rate constraint. This represents the discrete phase shift vector constraint of the RIS unit. Indicates will and Minimize when used as an optimization variable The objective function; This indicates the impact of imperfect CSI on users. Minimize transmission power;

[0067] S22, Proof using lemmas Equivalent to its corresponding signal-to-noise ratio constraint, satisfying Among them, the signal-to-noise ratio threshold satisfy In a broad sense function The calculation formula is: , The function is represented by the formula: ,in, and Representing functions respectively Internal parameters, The range is indicated in positive integers, The range is indicated in Positive integers;

[0068] S23, Define the matrix and satisfy and Then, the RIS beamforming vector after integrating the cascaded channel link and the second channel link is calculated. , Calculate the RIS beamforming matrix after integrating the cascaded channel links and the second channel link. , and satisfy and ,user The expected signal is:

[0069]

[0070] in, denotes the real part of a complex variable; denotes the rank operation on a matrix; denotes the system channel after integrating the cascaded channel link and the second channel link, and its calculation formula is , based on the influence of imperfect CSI, at this time satisfies:

[0071] ;

[0072] wherein, denotes the estimation value of ; denotes the channel error of ; and there exists , denotes the maximum norm value of the system channel estimation error after integrating the cascaded channel link and the second channel link;

[0073] After that, is modeled, and the channel error set after integrating the cascaded channel link and the second channel link is obtained , ;

[0074] S24, rewrite the signal-to-interference-and-noise ratio of the user , that is, , introduce an auxiliary variable , and equivalent to:

[0075] ;

[0076] wherein, denotes a second optimization problem, and constraints denote the minimum expected power of the user under the influence of imperfect CSI; constraints denote the maximum interference and noise power of the user under the influence of imperfect CSI; constraints denote the RIS unit vector considering the cascaded channel and the direct channel; constraints denote the matrix is a Hermitian matrix; constraints denote the matrix composed of RIS unit discrete phase shift vectors; constraints denote the matrix satisfies a rank 1 solution; denotes the rank operation on a matrix; denotes the maximum value of the multi-user interference and noise summation under the influence of channel error, ; denotes the minimum value of and as optimization variables The objective function; This indicates the impact of imperfect CSI on users. The minimum expected transmission power; This indicates the impact of imperfect CSI on users. The maximum value of interference and noise power.

[0077] Specifically, step S3 includes the following steps:

[0078] S31. Introducing the first variable And define a binary matrix. Used to solve Constraints ,Will Constraints Equivalent to: ,in, Represents scalar Located in the binary matrix The Rows m columns Represents the set of phase shift levels, when When, the m-th unit of RIS selects the first... One working mode, otherwise satisfy ;constraint There are still 0 / 1 integer constraints, which can be addressed through inequalities. Replace, where and Indicates constraints; This represents the m-th element in the RIS beamforming vector after integrating the first and second channel links;

[0079] S32, Using equality constraints Replacement constraints ,in, and Indicates constraints; This represents the Hermitian matrix constructed under the influence of discrete phase shifts in RIS units. Representing Hermitian matrices The element in the m-th row and m-th column; resolving constraints using a penalty method. and will Rewrite: ;

[0080] in, This represents the third optimization problem. Indicates the penalty factor. Representing Hermitian matrices The sum of eigenvalues; Representing Hermitian matrices the maximum eigenvalue of denotes maximizing as the objective function.

[0081] Specifically, step S4 specifically comprises the following steps:

[0082] S41, respectively vectorizing and to obtain the vectorization matrix , the vectorization channel estimation matrix , and the vectorization channel estimation error matrix , wherein , denotes that the maximum norm value of the channel estimation error vector does not exceed , for solving the third optimization problem ; using equation transformation to convert the constraints and into an easily handled form respectively: ; wherein, denotes the Kronecker product, denotes the vectorization of the matrix;

[0083] S42, using the S lemma to transform the constraints and respectively, for solving the influence of the easily handled form CSI uncertainty in step S41: ; wherein denotes the result of transforming the constraint using the S lemma, denotes the result of transforming the constraint using the S lemma, denotes and Kronecker product, , denotes and the sum of the remaining beamforming matrices after eliminating the beamforming matrix of user , , denotes the sum of the beamforming matrices for different users at the BS, and denote the introduced auxiliary variables respectively; denotes row column unit matrix; denotes row 1 column 0 matrix; denotes 1 row column 0 matrix;

[0084] S43. Based on SCA technology and using first-order Taylor series, expand the constraints respectively. and the third optimization problem The penalty item in the middle, namely , ;in, , and Let represent the nth iteration point, This represents the eigenvector corresponding to the largest eigenvalue; then the third optimization problem will be discussed. Rewrite: ,in, This represents the fourth optimization problem. ; Indicates will Maximize when used as an optimization variable The objective function;

[0085] S44. Design the AO algorithm to solve... Lieutenant General and When used as an optimization variable, under constraints and The variable coupling that exists in it.

[0086] Specifically, step S44 includes the following steps:

[0087] S441, Given parameters Regarding The optimization subproblem, with the optimization variable as the optimization variable, is written as: ; This represents the fifth optimization problem. Indicates will Maximize when used as an optimization variable The objective function is then used; subsequently, the relaxation constraints are proved using a theorem. After It exhibits compactness and can be solved using CVX;

[0088] S442, will As optimization variables, regarding parameters The optimization subproblem can be written as: , This represents the sixth optimization problem, which is solved using CVX.

[0089] Specifically, the steps of the AO algorithm are illustrated in the diagram below. Figure 2 As shown, step S5 includes: initializing parameters. ,set up and Then, perform outer and inner loops respectively, and output the second optimization problem. suboptimal value ;

[0090] The inner loop comprises: first, given the second variable , the fifth optimization problem is solved and the third variable is updated ; then, given the third variable , the sixth optimization problem is solved and the fourth variable is updated ; let , until the objective function in the fourth optimization problem converges or the number of inner loop iterations reaches , the inner loop is ended;

[0091] The outer loop comprises: updating the penalty factor , until converges, the outer loop is ended.

[0092] Specifically, the RIS unit in the present application has a discrete phase shift and a comparison result diagram of ideal RIS unit phase shift system performance as shown in Figure 3 The present application combines RIS with multi-user MISO URLLC under the influence of non-perfect CSI, formulates a BS transmission power minimization problem, and proposes a beamforming solution based on the AO algorithm. The RIS-assisted multi-user MISO URLLC constructs an optimization problem formula, and through parameter substitution and problem conversion, the original unsolvable optimization problem is converted into an easy-to-handle form; the present application also considers the full channel link uncertainty problem model, and uniformly analyzes the direct link and cascaded link; the discrete phase shift of the RIS unit is comprehensively considered and integrated into the optimization problem model; in order to solve the non-convex optimization problem, the present application proposes an AO algorithm based on the SCA technology, the penalty method and the S lemma, and obtains a suboptimal solution of the original problem.

[0093] 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, and should not be considered as excluding other embodiments, but 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 appended claims of the present application.

Claims

1. A RIS-assisted downlink URLLC beamforming method with discrete phase shift, characterized in that, Includes the following steps: S1. Construct a RIS-assisted downlink multi-user MISO URLLC system model; S2. Based on communication theory and optimization theory, a model for minimizing BS transmission power is constructed, and the model is improved through parameter substitution and problem transformation. S3. Introduce the first variable to transform integer constraints and non-convex constraints into easily manageable forms, and rewrite the optimization problem model using a penalty method. S4. Based on variable decoupling transformation nonconvex constraints, the AO algorithm is proposed using S-lemma and SCA techniques; S5. Based on the single optimal solution generated in step S4, the suboptimal solution of beamforming for the original problem is obtained through iterative convergence. In step S1, the BS is equipped with N antennas, serving simultaneously K A single-antenna user, defined For a single-antenna user set, the specific steps include: S11. Let the number of RIS reflection units be M, and the index be... The RIS reflection unit is defined to use a discrete phase shifter, and in Uniform quantization is satisfied within the interval, and the phase shift of the RIS reflector unit is achieved. satisfy ,in, Represents any RIS unit in the set Middle sequential index; Represents the discrete phase shift set. The quantization interval is represented by the formula: , The number of phase shift levels is represented by the following formula: , Indicates quantization resolution; phase shift vector of the RIS reflector unit. satisfy ,in, This represents Euler's formula. , imaginary number satisfy ; S12. Define the first complex-valued equivalent channel from BS to RIS as follows: BS to user The second complex-valued equivalent channel is RIS to users The third complex-valued equivalent channel 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, BS to users Message sent satisfy ,in, This represents a Gaussian distribution with mean 0 and variance 1, and the complex baseband signal transmitted at point BS. for ,in, This indicates that the BS is for the user Linear precoding; S14, User Received signal for , ,in, This indicates the process from BS to RIS to the user. The cascaded channel link is calculated using the following formula: , H represents the diagonal matrix transformation of a vector, and H represents the conjugate transpose. Indicates user Additive white Gaussian noise at the location, user The signal-to-interference-plus-noise ratio is , Represents a single-antenna user set In addition to single-antenna users The sum of all other single-antenna users, excluding those mentioned above; Indicates a single-antenna user The precoded vector; S15. According to the finite block length coding theory, the user The achievable transmission rate is ,in, The channel dispersion is represented by the following formula: ; Indicates user The length of the transmission block, Indicates user The probability of decoding errors; Gaussian function The reverse; S16, Definition The first channel link is ,definition The second channel link is ,in, express The estimated value, express The estimated value; express The estimated channel error, express The estimated channel error; express The radius of the uncertainty region, express The radius of the uncertainty region, Denotes the F-norm of a matrix. The 2-norm of a vector; Step S2 specifically includes the following steps: S21. Construct a model for minimizing the transmission power of the BS (Browser-Based Switch) problem, i.e. ,in, This represents the first optimization problem. This indicates the total power transmitted by the BS. Indicates user The minimum transmission rate that satisfies URLLC quality of service under the influence of the norm-bounded CSI error model. This indicates a minimum transmission rate constraint. This represents the discrete phase shift vector constraint of the RIS unit. Indicates will and Minimize when used as an optimization variable The objective function; This indicates the impact of imperfect CSI on users. Minimize transmission power; S22, Proof by referencing the lemma Equivalent to its corresponding signal-to-noise ratio constraint, satisfying Among them, the signal-to-noise ratio threshold satisfy In a broad sense function The calculation formula is: , The function is represented by the formula: ,in, and Representing functions respectively Internal parameters, The range is indicated in positive integers, The range is indicated in Positive integers; S23, Define the matrix and satisfy and Then, the RIS beamforming vector after integrating the cascaded channel link and the second channel link is calculated. , Calculate the RIS beamforming matrix after integrating the cascaded channel links and the second channel link. , and satisfy and ,user The expected signal is: in, This indicates taking the real part of the complex variable; This represents the rank operation on a matrix. The system channel, representing the integrated cascaded channel link and the second channel link, is calculated using the following formula: Due to the impact of imperfect CSI, at this time satisfy: ； in, express The estimated value; express Channel error; and there exists , This represents the maximum norm of the system channel estimation error after integrating the cascaded channel link and the second channel link; After that, Modeling to obtain the channel error set after integrating the cascaded channel links and the second channel link. , ; S24, will the user The signal-to-interference-to-noise ratio is rewritten, that is... Introducing auxiliary variables ,Will Equivalent to: ； in, This represents the second optimization problem, with constraints. Indicates user Minimum expected power under the influence of imperfect CSI; constraints Indicates user Maximum interference plus noise power under the influence of imperfect CSI; constraints Represents the RIS cell vector considering cascaded and direct channels; constraints Representation matrix It is a Hermitian matrix; constraints The matrix representing the discrete phase shift vectors of the RIS units; constraints Representation matrix A solution satisfying rank 1; This represents the rank operation on a matrix. This represents the maximum sum of multi-user interference and noise under the influence of channel error. ; Indicates will and Minimize when used as an optimization variable The objective function; This indicates the impact of imperfect CSI on users. The minimum expected transmission power; This indicates the impact of imperfect CSI on users. The maximum value of interference and noise power; Step S3 also includes the following steps: S31. Introducing the first variable And define a binary matrix. Used to solve Constraints ,Will Constraints Equivalent to: ,in, Represents scalar Located in the binary matrix The Rows m columns Represents the set of phase shift levels, when When, the m-th unit of RIS selects the first... One working mode, otherwise satisfy ;constraint There are still 0 / 1 integer constraints, which can be addressed through inequalities. Replace, where and Indicates constraints; This represents the m-th element in the RIS beamforming vector after integrating the first and second channel links; S32, Using equality constraints Replacement constraints ,in, and Indicates constraints; This represents the Hermitian matrix constructed under the influence of discrete phase shifts in RIS units. Representing Hermitian matrices The element in the m-th row and m-th column; resolving constraints using a penalty method. ; and will Rewrite, ; in, This represents the third optimization problem. Indicates the penalty factor. Representing Hermitian matrices The sum of eigenvalues; Representing Hermitian matrices The largest eigenvalue, Indicates will Maximize when used as an optimization variable The objective function; Step S4 specifically includes the following steps: S41, respectively and Vectorization to obtain a vectorized matrix. Vectorized channel estimation matrix Vectorized channel estimation error matrix , in This indicates that the maximum norm of the channel estimation error vector does not exceed [a certain value]. Used to solve the third optimization problem The constraints are transformed using equations. and Convert to an easier-to-process form: ;in, Indicates the Kronecker product. Vectorization of matrices; S42. Using Lemma S, the constraints are respectively... and A transformation is performed to address the impact of easily tractable CSI uncertainty in step S41: ;in Representing constraints The result of transformation using S-lemma Representing constraints The result of transformation using S-lemma express and Kronen product, express With eliminating users The Kronen product of the summation of the remaining beamforming matrices after the beamforming matrix is ​​applied. and These represent the introduced auxiliary variables; express OK Column identity matrix; express A matrix with 1 row and 0 columns; Indicates 1 row 0-column matrix; S43. Based on SCA technology and using first-order Taylor series, expand the constraints respectively. and the third optimization problem The penalty item in the middle, namely , ;in, , and Let represent the nth iteration point, This represents the eigenvector corresponding to the largest eigenvalue; then the third optimization problem will be discussed. Rewrite: ,in, This represents the fourth optimization problem. ; Indicates will Maximize when used as an optimization variable The objective function; S44. Design the AO algorithm to solve... Lieutenant General and When used as an optimization variable, under constraints and The variables that exist in the process.

2. The RIS-assisted downlink URLLC beamforming method with discrete phase shift according to claim 1, characterized in that, Step S44 specifically includes the following steps: S441, Given parameters Regarding The optimization subproblem, with the optimization variable as the optimization variable, is written as: ; This represents the fifth optimization problem. Indicates will Maximize when used as an optimization variable The objective function is then used; subsequently, the relaxation constraints are proved using a theorem. After It exhibits compactness and can be solved using CVX; S442, will As optimization variables, regarding parameters The optimization subproblem can be written as: , This represents the sixth optimization problem, which is solved using CVX.

3. The RIS-assisted downlink URLLC beamforming method with discrete phase shift according to claim 2, characterized in that, Step S5 specifically includes: initializing parameters ,set up and Then, perform outer and inner loops respectively, and output the second optimization problem. suboptimal value ; The inner loop includes: first, a second variable is given. For the fifth optimization problem Solve and update the third variable Then a third variable is given. For the sixth optimization problem Solve and update the fourth variable ;make Until the fourth optimization problem The objective function in the loop converges or the number of iterations in the inner loop reaches a certain threshold. End the inner loop; The outer loop includes: updating the penalty factor. ,until Convergence occurs, ending the outer loop.

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