Sum-rate maximization optimization method for hris-aided uplink NOMA URLLC system

Abstract

The application discloses a summation rate maximization optimization method for an HRIS auxiliary uplink NOMA URLLC system, and relates to the technical field of communication.The method specifically comprises the following steps: based on an HRIS auxiliary uplink NOMA URLLC system model and a signal transmission model, an HRIS unit selection model and a CSI uncertainty model are proposed, and a signal transmission mathematical expression is constructed; based on a communication theory, an uplink system summation rate maximization optimization problem is constructed; based on S lemma, Schur complement and SCA technology, non-convex constraints are converted, and an AO algorithm is proposed; and based on a single optimal solution generated by S4, a suboptimal solution of the original problem is obtained through an iterative convergence mode.The application solves the robust beamforming design of the HRIS auxiliary uplink NOMA URLLC system, and in particular solves the 'double fading' of pure passive RIS and the high power consumption problem of pure active RIS.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and more specifically to a summation rate maximization optimization method for HRIS-assisted uplink NOMA URLLC systems. Background Technology

[0002] The rapid development of autonomous systems and intelligent infrastructure has exacerbated the demand for Ultra-Reliable Low-Latency Communication (URLLC), which has become a fundamental pillar of the upcoming 6G wireless networks. Typically, URLLC uses short packet transmission to meet its stringent requirements for latency and reliability, such as latency below 1ms and reliability above 99.999%. Non-Orthogonal Multiple Access (NOMA) enables effective power allocation and better spectrum performance under conditions of limited spectrum resources, multi-user interference, and poor channel performance, and has become a key technology for meeting the reliability and latency requirements of future 6G services.

[0003] However, the user's channel gain determines the decoding order of Successive Interference Cancellation (SIC), posing a challenge for users with different quality of service requirements. Fortunately, Reconfigurable Intelligent Surface (RIS), as an emerging revolutionary technology, has the ability to reconfigure the wireless transmission environment, enabling coverage expansion and network performance improvement, and has attracted significant attention in mission-critical applications supporting short packet transmission. However, due to the "double fading" effect of RIS links and the inability of passive RIS to amplify signals, the network rate and coverage performance of URLLC networks assisted by passive RIS are limited.

[0004] Therefore, the Active RIS (Active RIS) architecture, which integrates active amplifiers into passive RIS units, has attracted much attention. It can achieve both signal reflection and amplification. However, the system performance improvements achieved by ARIS typically come at the cost of additional power consumption and hardware overhead. For RIS with a fixed number and fixed power overhead, neither fully active nor fully passive RIS can guarantee optimal system performance. To address these issues, the Hybrid RIS (Hybrid RIS) architecture, which integrates a small number of active and a large number of passive RIS units, has gained attention and has been extensively studied in downlink URLLC. However, research on uplink NOMA URLLC under imperfect channel state information (CSI) is limited. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for maximizing the summation rate of an HRIS-assisted uplink NOMA URLLC system.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This application discloses a summation rate maximization optimization method for HRIS-assisted uplink NOMA URLLC systems, comprising the following steps:

[0008] S1. Based on a hybrid reconfigurable smart surface (HRIS)-assisted uplink non-orthogonal multiple access ultra-reliable low-latency communication (NOMA URLLC) system, a signal transmission model is constructed. The HRIS-assisted uplink NOMA URLLC system includes... One antenna base station, HRIS and One single-antenna user;

[0009] S2. Establish a cell operating mode selection model for the Hybrid Reconfigurable Smart Surface (HRIS), and simultaneously use the norm-bounded channel state information (CSI) error model to characterize the channel uncertainty, thereby obtaining the base station received signal expression.

[0010] S3. Based on communication theory, construct the summation rate maximization optimization problem of the uplink NOMA URLLC system; introduce auxiliary variables to transform the summation rate maximization optimization problem into an easier-to-handle form, and obtain the equivalent optimization problem;

[0011] S4. The S-process lemma and Schur complement are used to handle the semi-infinite constraints in the equivalent optimization problem, and the continuous convex approximation (SCA) technique is used to handle the non-convex constraints in the equivalent optimization problem. Based on the processed equivalent optimization problem, the alternating optimization (AO) algorithm is used to decompose it into two convex optimization subproblems.

[0012] S5. Solve the two convex optimization subproblems generated in step S4 by iterative convergence until the objective function of the equivalent optimization problem converges, and obtain the suboptimal solution of the summation rate maximization optimization problem under the norm-bounded channel state information (CSI) error model.

[0013] Further, the HRIS mentioned in step S1 includes There are 10 reflective units, among which... Each reflective unit includes One active unit and One passive unit, namely The active unit dynamically adjusts the amplitude and phase of the incident signal, the passive unit only adjusts the phase of the incident signal without amplifying it, and the reflection unit can flexibly switch between active and passive modes.

[0014] Preferably, the construction of the signal transmission model in step S1 specifically includes: defining a user set. and HRIS reflection unit set Assuming that all channel gains in an HRIS-assisted uplink NOMA URLLC system are within a coherent block and satisfy quasi-static flat fading, the base station to user... Channel gain Channel gain from base station to HRIS HRIS to users Channel gain ,in, This represents a complex vector with dimensions N rows and 1 column. Let M represent a complex vector with dimensions M rows and 1 column. This represents a complex matrix with dimensions M rows and N columns.

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

[0016] S21. Based on the signal transmission model in step S1, define the user. The message sent is ,in, Indicates user The transmission power, Indicates user Send the unit information and meet the requirements. , This represents a Gaussian distribution with a mean of 0 and a variance of 1.

[0017] S22. Define a binary diagonal matrix. This indicates the operating mode of each reflection unit in HRIS, where, This represents a binary diagonal matrix with dimensions M rows and M columns. Indicates the first The operating mode of each reflective unit; if Then it means the first Each reflector unit operates in active mode, if... Then it means the first Each reflector unit operates in passive mode. Represents a diagonal matrix;

[0018] S23. Define the diagonal matrix of HRIS's reflection coefficients as follows: , by binary diagonal matrix Active RIS reflection coefficient diagonal matrix and passive RIS reflection coefficient diagonal matrix Composition, satisfying ,in, This indicates that the reflection unit in HRIS is operating in passive mode. , This represents a complex matrix with dimensions M rows and M columns. Indicates the first active unit in HRIS The formula for calculating each phase shift vector is: And satisfy , This represents the maximum complex amplitude of the active RIS unit. Indicates the first active unit in HRIS The magnification factor of each unit, ; , Represents the first passive unit in HRIS The formula for calculating each phase shift vector is: And satisfy , Represents the first reflection unit in HRIS One phase shift, and ; Indicates the first The phase shift vector corresponding to each reflecting unit is calculated using the following formula: , The imaginary unit representing Euler's formula; The formula for calculating the hybrid beamforming vector in HRIS is as follows: , Indicates the first in HRIS One phase shift vector, Indicates conjugate transpose;

[0019] S24, After that, the signal received by the base station is ,in, This represents additive white Gaussian noise in an active RIS, with a Gaussian distribution as follows: ,in, Represents an M x M matrix of 0. This represents the power of Gaussian white noise. Represents an M-row, M-column identity matrix; The additive white Gaussian noise representing the base station has the following Gaussian distribution: ,in Represents an N x N matrix of zeros. This represents the power of Gaussian white noise. Represents an N x N identity matrix;

[0020] S25, Assuming that the user is being restored When transmitting information, the base station uses SIC technology to reduce interference between users and satisfies the following:

[0021] ,in, Represents absolute value; This indicates the power of the transmitted signal from user 1; This represents the channel gain from the base station to the first user; This represents the channel gain from HRIS to User 1; This represents the transmitted signal power of user K; This represents the channel gain from the base station to user K; Represents the channel gain from HRIS to the Kth user; defines the receive beamforming of the base station. In addition, the base station uses perfect SIC to restore user data. Sending information to the user Signal-to-interference-to-noise ratio :

[0022] ,in, Describing the 2-norm, This indicates HRIS hybrid beamforming. Indicates the presence of direct links and cascaded links The equivalent channel, Indicates excluding users Afterwards, direct links are included. and cascaded links The equivalent channel, Indicates user The transmitted signal power, Indicates the base station to the user After recovering the signal using SIC technology, the user To users Signal accumulation;

[0023] S26. Based on the transmission rate expression for short packet transmission, the user... transmission rate for ,in, Indicates user Data packet length, Represents the Gaussian Q-function The reverse, Indicates user The probability of decoding errors;

[0024] S27. Using the norm-bounded CSI error model, obtain the perfect CSI in URLLC that supports short packet transmission. The expression for the norm-bounded CSI error model is:

[0025] ,

[0026] in, This represents the channel estimation from the base station to HRIS. This represents the channel estimation error from the base station to HRIS. This represents the maximum uncertainty bound of the channel error from the base station to HRIS. Indicates HRIS to user Channel estimation, Indicates HRIS to user Channel estimation error, Indicates HRIS to user The maximum uncertainty bound of the channel error, express Channel estimation, express Channel estimation error, express The maximum uncertainty bound of the channel error, Let Frobenius be the norm.

[0027] Preferably, step S3 specifically includes the following steps:

[0028] S31. Based on the signal transmission expression in step S2, construct the system summation rate maximization optimization problem, whose expression is:

[0029] Among them, the first constraint In This represents the maximum power of the active RIS unit in HRIS, the second constraint. Indicates to users The unit energy constraint corresponding to receive beamforming, the third constraint This represents the maximum amplitude constraint of the HRIS unit, the fourth constraint. In Indicates user Maximum transmission power, fifth constraint and the sixth constraint This represents the working mode selection matrix constraint in HRIS; Indicates from HRIS to user Channel estimation error The maximum value below; The optimization variable is Maximize the first optimization problem The system summation rate; Indicates the channel estimation error and Find the minimum summation rate of the system under the combined influence of these factors; express The element in the m-th row and m-th column, The first vector in the hybrid beamforming vector of HRIS represents the first vector. One phase shift vector, This represents the sum of the elements on the main diagonal of the matrix;

[0030] S32. Introducing auxiliary variables The first optimization problem The objective function is transformed into the following form:

[0031] ,in, Indicates the first child constraint. Indicates the second sub-constraint. Indicates a third-child constraint. Indicates the fourth child constraint. Indicates the fifth child constraint. Indicates the sixth child constraint. This indicates the seventh child constraint. This indicates the removal of users. Afterwards, direct links are included. and cascaded links The equivalent channel error; This parameter indicates the transmission rate that supports short packet transmission.

[0032] S33, Introducing Auxiliary Variables The first optimization problem The first constraint in Transform it into the following form:

[0033] ,

[0034] in, Indicates the eighth child constraint. Indicates the ninth child constraint. Indicates the tenth child constraint;

[0035] S34. Use continuous constraints The first optimization problem The fifth constraint Replacement is performed to resolve the fifth constraint. Integer constraints; at this point, the first optimization problem... The suboptimal solution is obtained by solving the second optimization problem. get:

[0036] ,in, Represents the second optimization problem The objective function.

[0037] Preferably, step S4 specifically includes:

[0038] S41. Using the S-process lemma, the second optimization problem is solved. In , and After transformation, we obtain the following linear matrix inequality:

[0039] ,

[0040] in, This represents the first inequality. This represents the second inequality. This represents the third inequality. Indicates and Related matrices, Indicates and and Related vectors, Indicates and and Related scalars, Indicates and and Related scalars, Indicates and and Related matrices; Indicates and , and Related vectors; Indicates and , and Related scalars; Indicates and , and Related scalars; Indicates and and Related matrices; Indicates and , and Related vectors; Indicates and , and Related scalars; Indicates and Related scalars; , and Indicates the scaling factor;

[0041] S42. Using Schur complement, solve the second optimization problem. In , and After transformation, we obtain the following linear matrix inequality: ,in, This represents the fourth inequality. This represents the fifth inequality. This represents the sixth inequality. express The value of the nth iteration. express The value of the nth iteration. This represents a 1-row, M+1-column matrix of zeros. This represents an M-row, 1-column matrix of zeros. express The value of the nth iteration. express The value of the nth iteration. , and Indicates the scaling factor. Indicates HRIS to user The maximum uncertainty bound of the mid-channel error is 0.5 to the power of the maximum uncertainty bound. Indicates excluding users Afterwards, direct links are included. and cascaded links The maximum uncertainty bound of the channel error in the equivalent channel is 0.5 to the power of the maximum uncertainty bound. This represents the 0.5 power of the maximum uncertainty bound of the channel error from HRIS to the base station;

[0042] S43. Introduce the continuous convex approximation (SCA) technique to solve the second optimization problem. In , and After transformation, we obtain the following linear matrix inequality: ,in, This represents the seventh inequality. This represents the eighth inequality. This represents the ninth inequality. express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration;

[0043] S44. Propose an alternating optimization AO algorithm, specifically including:

[0044] Will As a fixed variable, the received beamforming of the base station and users Transmission power First optimization subproblem Represented as: ,in, This represents maximizing the first optimization subproblem. The objective function; at the same time, due to the first optimization subproblem It is convex, and the convex optimization solver CVX is used to solve it;

[0045] Will As a fixed variable, regarding HRIS hybrid beamforming and binary diagonal matrix The second optimization subproblem Represented as: ,in, This represents maximizing the second optimization subproblem. The objective function, and at the same time, due to the second optimization subproblem It is convex, and the convex optimization solver CVX is used to solve it.

[0046] Preferably, step S5 specifically includes:

[0047] S51, will It is passed as a parameter and initialized, where, express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration, setting the number of iterations. Maximum number of iterations ;

[0048] S52, Given parameters Solve the first optimization subproblem And update parameters ;

[0049] S53, Given parameters Solve the second optimization subproblem And update parameters ;

[0050] S54, update iteration count, so that ; until the second optimization problem The objective function has converged or the number of iterations has reached the maximum number of iterations. .

[0051] The beneficial effects of this invention are:

[0052] 1) This application solves the problem of robust beamforming design for HRIS-assisted uplink NOMA URLLC systems, and in particular solves the problems of "double fading" in pure passive RIS and excessive power consumption in pure active RIS. Attached Figure Description

[0053] Figure 1 This is a schematic diagram illustrating the steps of the summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system according to an embodiment of the present invention.

[0054] Figure 2 This is a flowchart illustrating the alternating optimization AO algorithm according to an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram comparing simulation results of an embodiment of the present invention. Detailed Implementation

[0056] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0057] See Figures 1-2 This invention considers an HRIS-assisted uplink NOMA URLLC system and formulates a system summation rate maximization problem by jointly optimizing the user-side transmission power, the base station-side receive beamforming, the HRIS-side hybrid beamforming, and the active element selection parameters. Since this problem is highly non-convex, this invention uses S-lemma, Schur's complement, and Successive Convex Approximation (SCA) techniques to propose an Alternating Optimization (AO) algorithm. A summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system is disclosed, comprising the following steps:

[0058] S1. Based on a hybrid reconfigurable smart surface (HRIS)-assisted uplink non-orthogonal multiple access ultra-reliable low-latency communication (NOMA URLLC) system, a signal transmission model is constructed. The HRIS-assisted uplink NOMA URLLC system includes... One antenna base station, HRIS and One single-antenna user;

[0059] S2. Establish a cell operating mode selection model for the Hybrid Reconfigurable Smart Surface (HRIS), and simultaneously use the norm-bounded channel state information (CSI) error model to characterize the channel uncertainty, thereby obtaining the base station received signal expression.

[0060] S3. Based on communication theory, construct the summation rate maximization optimization problem of the uplink NOMA URLLC system; introduce auxiliary variables to transform the summation rate maximization optimization problem into an easier-to-handle form, and obtain the equivalent optimization problem;

[0061] S4. The S-lemma and Schur's complement are used to handle the semi-infinite constraints in the equivalent optimization problem, and the continuous convex approximation (SCA) technique is used to handle the non-convex constraints in the equivalent optimization problem. Based on the processed equivalent optimization problem, the alternating optimization (AO) algorithm is used to decompose it into two convex optimization subproblems.

[0062] S5. Solve the two convex optimization subproblems generated in step S4 by iterative convergence until the objective function of the equivalent optimization problem converges, and obtain the suboptimal solution of the summation rate maximization optimization problem under the norm-bounded channel state information (CSI) error model.

[0063] For example, the HRIS mentioned in step S1 includes There are 10 reflective units, among which... Each reflective unit includes One active unit and One passive unit, namely The active unit dynamically adjusts the amplitude and phase of the incident signal, the passive unit only adjusts the phase of the incident signal without amplifying it, and the reflection unit can flexibly switch between active and passive modes.

[0064] For example, the construction of the signal transmission model in step S1 specifically includes: defining a user set. and HRIS reflection unit set Assuming that all channel gains in an HRIS-assisted uplink NOMA URLLC system are within a coherent block and satisfy quasi-static flat fading, the base station to user... Channel gain Channel gain from base station to HRIS HRIS to users Channel gain ,in, This represents a complex vector with dimensions N rows and 1 column. Let M represent a complex vector with dimensions M rows and 1 column. This represents a complex matrix with dimensions M rows and N columns.

[0065] For example, step S2 specifically includes the following steps:

[0066] S21. Based on the signal transmission model in step S1, define the user. The message sent is ,in, Indicates user The transmission power, Indicates user Send the unit information and meet the requirements. , This represents a Gaussian distribution with a mean of 0 and a variance of 1.

[0067] S22. Define a binary diagonal matrix. This indicates the operating mode of each reflection unit in HRIS, where, This represents a binary diagonal matrix with dimensions M rows and M columns. Indicates the first The operating mode of each reflective unit; if Then it means the first Each reflector unit operates in active mode, if... Then it means the first Each reflector unit operates in passive mode. Represents a diagonal matrix;

[0068] S23. Define the diagonal matrix of HRIS's reflection coefficients as follows: , by binary diagonal matrix Active RIS reflection coefficient diagonal matrix and passive RIS reflection coefficient diagonal matrix Composition, satisfying ,in, This indicates that the reflection unit in HRIS is operating in passive mode. , This represents a complex matrix with dimensions M rows and M columns. Indicates the first active unit in HRIS The formula for calculating each phase shift vector is: And satisfy , This represents the maximum complex amplitude of the active RIS unit. Indicates the first active unit in HRIS The magnification factor of each unit, ; , Represents the first passive unit in HRIS The formula for calculating each phase shift vector is: And satisfy , Represents the first reflection unit in HRIS One phase shift, and ; Indicates the first The phase shift vector corresponding to each reflecting unit is calculated using the following formula: , The imaginary unit representing Euler's formula; , The formula for calculating the hybrid beamforming vector in HRIS is as follows: , Indicates the first in HRIS One phase shift vector, Indicates conjugate transpose;

[0069] S24, After that, the signal received by the base station is ,in, This represents additive white Gaussian noise in an active RIS, with a Gaussian distribution as follows: ,in, Represents an M x M matrix of 0. This represents the power of Gaussian white noise. Represents an M-row, M-column identity matrix; The additive white Gaussian noise representing the base station has the following Gaussian distribution: ,in Represents an N x N matrix of zeros. This represents the power of Gaussian white noise. Represents an N x N identity matrix;

[0070] S25, Assuming that the user is being restored When transmitting information, the base station uses SIC technology to reduce interference between users and satisfies the following:

[0071] ,

[0072] in, Represents absolute value; This indicates the power of the transmitted signal from user 1; This represents the channel gain from the base station to the first user; This represents the channel gain from HRIS to User 1; This represents the transmitted signal power of user K; This represents the channel gain from the base station to user K; Represents the channel gain from HRIS to the Kth user; defines the receive beamforming of the base station. In addition, the base station uses perfect SIC to restore user data. Sending information to the user Signal-to-interference-to-noise ratio :

[0073] ,in, Describing the 2-norm, This indicates HRIS hybrid beamforming. Indicates the presence of direct links and cascaded links The equivalent channel, Indicates excluding users Afterwards, direct links are included. and cascaded links The equivalent channel, Indicates user The transmitted signal power, Indicates the base station to the user After the user recovered the signal using SIC technology To users Signal accumulation;

[0074] S26. Based on the transmission rate expression for short packet transmission, the user... transmission rate for ,in, Indicates user Data packet length, Represents the Gaussian Q-function The inverse of the Gaussian Q function The calculation formula is ,in, It is the independent variable of the Gaussian Q-function. Represents the integral variable. Indicates user The probability of decoding errors;

[0075] S27. Using the norm-bounded CSI error model, obtain the perfect CSI in URLLC that supports short packet transmission. The expression for the norm-bounded CSI error model is:

[0076] ,

[0077] in, This represents the channel estimation from the base station to HRIS. This represents the channel estimation error from the base station to HRIS. This represents the maximum uncertainty bound of the channel error from the base station to HRIS. Indicates HRIS to user Channel estimation, Indicates HRIS to user Channel estimation error, Indicates HRIS to user The maximum uncertainty bound of the channel error, express Channel estimation, express Channel estimation error, express The maximum uncertainty bound of the channel error, Let Frobenius be the norm.

[0078] For example, step S3 specifically includes the following steps:

[0079] S31. Based on the signal transmission expression in step S2, construct the system summation rate maximization optimization problem, whose expression is:

[0080] Among them, the first constraint In This represents the maximum power of the active RIS unit in HRIS, the second constraint. Indicates to users The unit energy constraint corresponding to receive beamforming, the third constraint This represents the maximum amplitude constraint of the HRIS unit, the fourth constraint. In Indicates user Maximum transmission power, fifth constraint and the sixth constraint This represents the working mode selection matrix constraint in HRIS; Indicates from HRIS to user Channel estimation error The maximum value below; The optimization variable is Maximize the first optimization problem The system summation rate; Indicates the channel estimation error and Find the minimum summation rate of the system under the combined influence of these factors; express The element in the m-th row and m-th column, The first vector in the hybrid beamforming vector of HRIS represents the first vector. One phase shift vector, This represents the sum of the elements on the main diagonal of the matrix;

[0081] S32, Due to the first optimization problem This problem suffers from highly coupled optimization variables and integer constraints, making it difficult to find the optimal solution. Therefore, this application transforms it into a more manageable form by introducing auxiliary variables. The first optimization problem The objective function is transformed into the following form:

[0082] ,in, Indicates the first child constraint. Indicates the second sub-constraint. Indicates a third-child constraint. Indicates the fourth child constraint. Indicates the fifth child constraint. Indicates the sixth child constraint. This indicates the seventh child constraint. This indicates the removal of users. Afterwards, direct links are included. and cascaded links The equivalent channel error; This indicates the transmission rate parameter that supports short packet transmission, and its calculation formula is as follows: ,in, Indicates user The normalized reliability parameter is calculated using the following formula: , Represents the generalized Lambert W function;

[0083] S33, Introducing Auxiliary Variables The first optimization problem The first constraint in Transform it into the following form:

[0084] ,

[0085] in, Indicates the eighth child constraint. Indicates the ninth child constraint. Indicates the tenth child constraint;

[0086] S34. Use continuous constraints The first optimization problem The fifth constraint Replacement is performed to resolve the fifth constraint. Integer constraints; at this point, the first optimization problem... The suboptimal solution is obtained by solving the second optimization problem. get:

[0087] ,in, Represents the second optimization problem The objective function.

[0088] For example, step S4 specifically includes:

[0089] S41. Using the S-process lemma, the second optimization problem is solved. In , and After transformation, we obtain the following linear matrix inequality:

[0090] ,

[0091] in, This represents the first inequality. This represents the second inequality. This represents the third inequality. Indicates and Related matrices Indicates and and Related vectors, Indicates and and Related scalars, Indicates and and Related scalars, Indicates and and Related matrices; Indicates and , and Related vectors; Indicates and , and Related scalars; Indicates and , and Related scalars; Indicates and and Related matrices; Indicates and , and Related vectors; Indicates and , and Related scalars; Indicates and Related scalars; , and These represent scaling factors, all of which are non-negative real numbers; the calculation formulas are as follows: ,

[0092] in, Represents the Kronen product. To represent the real part of a complex number, Represents the vectorization of a matrix. express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration. Indicates the first The next iteration matrix.

[0093] S42. Using Schur complement, solve the second optimization problem. In , and After transformation, we obtain the following linear matrix inequality:

[0094] ,in, This represents the fourth inequality. This represents the fifth inequality. This represents the sixth inequality. This represents a 1-row, M+1-column matrix of zeros. This represents an M-row, 1-column matrix of zeros. express The value of the nth iteration. express The value of the nth iteration; , and Indicates the scaling factor. Indicates HRIS to user The maximum uncertainty bound of the mid-channel error is 0.5 to the power of 0.5. Indicates excluding users Afterwards, direct links are included. and cascaded links The maximum uncertainty bound of the channel error in the equivalent channel is 0.5 to the power of the maximum uncertainty bound. This represents the 0.5th power of the maximum uncertainty bound of the channel error from HRIS to the base station;

[0095] S43. Introduce the continuous convex approximation (SCA) technique to solve the second optimization problem. In , and After transformation, we obtain the following linear matrix inequality: ,in, This represents the seventh inequality. This represents the eighth inequality. This represents the ninth inequality. express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration;

[0096] S44. Propose an alternating optimization AO algorithm, specifically including:

[0097] Will As a fixed variable, the received beamforming of the base station and users Transmission power First optimization subproblem Represented as: ,in, This represents maximizing the first optimization subproblem. The objective function; at the same time, due to the first optimization subproblem It is convex, and the convex optimization solver CVX is used to solve it;

[0098] Will As a fixed variable, regarding HRIS hybrid beamforming and binary diagonal matrix The second optimization subproblem Represented as: ,in, This represents maximizing the second optimization subproblem. The objective function, and at the same time, due to the second optimization subproblem It is convex, and the convex optimization solver CVX is used to solve it.

[0099] For example, step S5 specifically includes:

[0100] S51, will It is passed as a parameter and initialized, where, express The value of the nth iteration, setting the number of iterations. Maximum number of iterations ;

[0101] S52, Given parameters Solve the first optimization subproblem And update parameters ;

[0102] S53, Given parameters Solve the second optimization subproblem And update parameters ;

[0103] S54, update iteration count, so that ; until the second optimization problem The objective function has converged or the number of iterations has reached the maximum number of iterations. .

[0104] See Figure 3 The robustness and effectiveness of this application have been demonstrated through experimental simulation.

[0105] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A summation rate maximization optimization method for HRIS-assisted uplink NOMA URLLC systems, characterized in that, Includes the following steps: S1. Based on a hybrid reconfigurable smart surface (HRIS)-assisted uplink non-orthogonal multiple access ultra-reliable low-latency communication (NOMA URLLC) system, a signal transmission model is constructed. The HRIS-assisted uplink NOMA URLLC system includes... One antenna base station, HRIS and One single-antenna user; S2. Establish a cell operating mode selection model for the Hybrid Reconfigurable Smart Surface (HRIS), and simultaneously use the norm-bounded channel state information (CSI) error model to characterize the channel uncertainty, thereby obtaining the base station received signal expression. S3. Based on communication theory, construct the summation rate maximization optimization problem of an uplink NOMA URLLC system; Introduction Auxiliary variables are used to transform the summation rate maximization optimization problem into an easier-to-handle form, resulting in an equivalent optimization problem. S4. The S-process lemma and Schur complement are used to handle the semi-infinite constraints in the equivalent optimization problem, and the continuous convex approximation (SCA) technique is used to handle the non-convex constraints in the equivalent optimization problem. Based on the processed equivalent optimization problem, the alternating optimization (AO) algorithm is used to decompose it into two convex optimization subproblems. S5. Solve the two convex optimization subproblems generated in step S4 by iterative convergence until the objective function of the equivalent optimization problem converges, and obtain the suboptimal solution of the summation rate maximization optimization problem under the norm-bounded channel state information (CSI) error model.

2. The summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system according to claim 1, characterized in that, The HRIS mentioned in step S1 includes There are 10 reflective units, of which... Each reflective unit includes One active unit and One passive unit, namely The active unit dynamically adjusts the amplitude and phase of the incident signal, the passive unit only adjusts the phase of the incident signal without amplifying it, and the reflection unit can flexibly switch between active and passive modes.

3. The summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system according to claim 2, characterized in that, The construction of the signal transmission model in step S1 specifically includes: defining the user set. and HRIS reflection unit set Assuming that all channel gains in an HRIS-assisted uplink NOMA URLLC system are within a coherent block and satisfy quasi-static flat fading, the base station to user... Channel gain Channel gain from base station to HRIS HRIS to users Channel gain ,in, This represents a complex vector with dimensions N rows and 1 column. Let M represent a complex vector with dimensions M rows and 1 column. This represents a complex matrix with dimensions M rows and N columns.

4. The summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system according to claim 3, characterized in that, Step S2 specifically includes the following steps: S21. Based on the signal transmission model in step S1, define the user. The message sent is ,in, Indicates user The transmission power, Indicates user Send the unit information and meet the requirements. , This represents a Gaussian distribution with a mean of 0 and a variance of 1. S22. Define a binary diagonal matrix. This indicates the operating mode of each reflection unit in HRIS, where, This represents a binary diagonal matrix with dimensions M rows and M columns. Indicates the first The operating mode of each reflective unit; if Then it means the first Each reflector unit operates in active mode, if... Then it means the first Each reflector unit operates in passive mode. Represents a diagonal matrix; S23. Define the diagonal matrix of HRIS's reflection coefficients as follows: , by binary diagonal matrix Active RIS reflection coefficient diagonal matrix and passive RIS reflection coefficient diagonal matrix Composition, satisfying ,in, This indicates that the reflection unit in HRIS is operating in passive mode. , This represents a complex matrix with dimensions M rows and M columns. Indicates the first active unit in HRIS The formula for calculating each phase shift vector is: And satisfy , This represents the maximum complex amplitude of the active RIS unit. Indicates the first active unit in HRIS The magnification factor of each unit, ; , Represents the first passive unit in HRIS The formula for calculating each phase shift vector is: And satisfy , Represents the first reflection unit in HRIS One phase shift, and ; Indicates the first The phase shift vector corresponding to each reflecting unit is calculated using the following formula: , The imaginary unit representing Euler's formula; The formula for calculating the hybrid beamforming vector in HRIS is as follows: , Indicates the first in HRIS One phase shift vector, Indicates conjugate transpose; S24, After that, the signal received by the base station is ,in, This represents additive white Gaussian noise in an active RIS, with a Gaussian distribution as follows: ,in, Represents an M x M matrix of 0. This represents the power of Gaussian white noise. Represents an M-row, M-column identity matrix; The additive white Gaussian noise representing the base station has the following Gaussian distribution: ,in Represents an N x N matrix of zeros. This represents the power of Gaussian white noise. Represents an N x N identity matrix; S25, Assuming that the user is being restored When transmitting information, the base station uses SIC technology to reduce interference between users and satisfies the following: ， in, Represents absolute value; This indicates the power of the transmitted signal from user 1; This represents the channel gain from the base station to the first user; This represents the channel gain from HRIS to User 1; This represents the transmitted signal power of user K; This represents the channel gain from the base station to user K; Represents the channel gain from HRIS to the Kth user; defines the receive beamforming of the base station. In addition, the base station uses perfect SIC to restore user data. Sending information to the user Signal-to-interference-to-noise ratio : ,in, Describing the 2-norm, This indicates HRIS hybrid beamforming. Indicates the presence of direct links and cascaded links The equivalent channel, Indicates excluding users Afterwards, direct links are included. and cascaded links The equivalent channel, Indicates user The transmitted signal power, Indicates the base station to the user After recovering the signal using SIC technology, the user To users Signal accumulation; S26. Based on the transmission rate expression for short packet transmission, the user... transmission rate for ,in, Indicates user Data packet length, Represents the Gaussian Q-function The reverse, Indicates user The probability of decoding errors; S27. Using the norm-bounded CSI error model, obtain the perfect CSI in URLLC that supports short packet transmission. The expression for the norm-bounded CSI error model is: ， in, This represents the channel estimation from the base station to HRIS. This represents the channel estimation error from the base station to HRIS. This represents the maximum uncertainty bound of the channel error from the base station to HRIS. Indicates HRIS to user Channel estimation, Indicates HRIS to user Channel estimation error, Indicates HRIS to user The maximum uncertainty bound of the channel error, express Channel estimation, express Channel estimation error, express The maximum uncertainty bound of the channel error, Let Frobenius be the norm.

5. The summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system according to claim 4, characterized in that, Step S3 specifically includes the following steps: S31. Based on the signal transmission expression in step S2, construct the system summation rate maximization optimization problem, whose expression is: Among them, the first constraint In This represents the maximum power of the active RIS unit in HRIS, the second constraint. Indicates to users The unit energy constraint corresponding to receive beamforming, the third constraint This represents the maximum amplitude constraint of the HRIS unit, the fourth constraint. In Indicates user Maximum transmission power, fifth constraint and the sixth constraint This represents the working mode selection matrix constraint in HRIS; Indicates from HRIS to user Channel estimation error The maximum value below; The optimization variable is Maximize the first optimization problem The system summation rate; Indicates the channel estimation error and Find the minimum summation rate of the system under the combined influence of these factors; express The element in the m-th row and m-th column, The first vector in the hybrid beamforming vector of HRIS represents the first vector. One phase shift vector, This represents the sum of the elements on the main diagonal of the matrix; S32. Introducing auxiliary variables The first optimization problem The objective function is transformed into the following form: ,in, Indicates the first child constraint. Indicates the second sub-constraint. Indicates a third-child constraint. Indicates the fourth child constraint. Indicates the fifth child constraint. Indicates the sixth child constraint. This indicates the seventh child constraint. This indicates the removal of users. Afterwards, direct links are included. and cascaded links The equivalent channel error; This parameter indicates the transmission rate that supports short packet transmission. S33, Introducing Auxiliary Variables The first optimization problem The first constraint in Transform it into the following form: ， in, Indicates the eighth child constraint. Indicates the ninth child constraint. Indicates the tenth child constraint; S34. Use continuous constraints The first optimization problem The fifth constraint Replacement is performed to resolve the fifth constraint. Integer constraints; at this point, the first optimization problem... The suboptimal solution is obtained by solving the second optimization problem. get: ,in, Represents the second optimization problem The objective function.

6. The summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system according to claim 5, characterized in that, Step S4 specifically includes: S41. Using the S-process lemma, the second optimization problem is solved. In , and After transformation, we obtain the following linear matrix inequality: ， in, This represents the first inequality. This represents the second inequality. This represents the third inequality. Indicates and Related matrices Indicates and and Related vectors, Indicates and and Related scalars, Indicates and and Related scalars, Indicates and and Related matrices; Indicates and , and Related vectors; Indicates and , and Related scalars; Indicates and , and Related scalars; Indicates and and Related matrices; Indicates and , and Related vectors; Indicates and , and Related scalars; Indicates and Related scalars; , and Indicates the scaling factor; S42. Using Schur complement, solve the second optimization problem. In , and After transformation, we obtain the following linear matrix inequality: ,in, This represents the fourth inequality. This represents the fifth inequality. This represents the sixth inequality. express The value of the nth iteration. express The value of the nth iteration. This represents a 1-row, M+1-column matrix of zeros. This represents an M-row, 1-column matrix of zeros. express The value of the nth iteration. express The value of the nth iteration. , and Indicates the scaling factor. Indicates HRIS to user The maximum uncertainty bound of the mid-channel error is 0.5 to the power of 0.

5. Indicates excluding users Afterwards, direct links are included. and cascaded links The maximum uncertainty bound of the channel error in the equivalent channel is 0.5 to the power of the maximum uncertainty bound. This represents the 0.5th power of the maximum uncertainty bound of the channel error from HRIS to the base station; S43. Introduce the continuous convex approximation (SCA) technique to solve the second optimization problem. In , and After transformation, we obtain the following linear matrix inequality: ,in, This represents the seventh inequality. This represents the eighth inequality. This represents the ninth inequality. express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration; S44. Propose an alternating optimization AO algorithm, specifically including: Will As a fixed variable, the received beamforming of the base station and users Transmission power First optimization subproblem Represented as: ,in, This represents maximizing the first optimization subproblem. The objective function; at the same time, due to the first optimization subproblem It is convex, and the convex optimization solver CVX is used to solve it; Will As a fixed variable, regarding HRIS hybrid beamforming and binary diagonal matrix The second optimization subproblem Represented as: ,in, This represents maximizing the second optimization subproblem. The objective function, and at the same time, due to the second optimization subproblem It is convex, and the convex optimization solver CVX is used to solve it.

7. The summation rate maximization optimization method for an HRIS-assisted uplink NOMA URLLC system according to claim 6, characterized in that, Step S5 specifically includes: S51, will It is passed as a parameter and initialized, where, express The value of the nth iteration. express The value of the nth iteration. express The value of the nth iteration, setting the number of iterations. Maximum number of iterations ; S52, Given parameters Solve the first optimization subproblem And update parameters ; S53, Given parameters Solve the second optimization subproblem And update parameters ; S54, update iteration count, so that ; until the second optimization problem The objective function has converged or the number of iterations has reached the maximum number of iterations. .

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