An optimization method for maximizing energy efficiency of IRS-assisted downlink URLLC system

Abstract

The invention discloses an optimization method for maximizing the energy efficiency of an IRS-assisted downlink URLLC system, comprising: assisting in constructing a multi-input single-output URLLC system on an intelligent reflecting surface; constructing a system energy efficiency maximization problem model to obtain a non-convex optimization problem; based on parameter substitution and problem conversion, converting the integer constraints and fractional constraints of the original problem into an easily tractable form; solving the variable coupling problem by an alternating optimization method, converting the non-convex problem into a convex optimization problem by using an SCA iterative algorithm and an SDR technology, and solving the convex optimization problem by using a BCD algorithm; obtaining a suboptimal solution of the multi-input single-output URLLC system parameter based on the generated iterative optimization variable values ​​and using the BCD iterative algorithm, and in the process of obtaining the suboptimal solution, obtaining the maximum energy efficiency of a single antenna user and the optimal solution of the reliability constraint by iteration; proposing an alternating optimization method to solve the variable coupling problem, and converting the non-convex constraint into a convex constraint by using the SCA algorithm and the SDR technology; and solving the local optimal solution based on the BCD iterative algorithm.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an optimization method for maximizing energy efficiency of an IRS-assisted downlink URLLC system. Background Art

[0002] With the rapid development of wireless networks, 5G has been commercialized and is striding towards the 6G era. New applications of future 6G networks, such as autonomous driving, factory automation, and real-time human-computer interaction, will require more stringent reliability and latency than 5G. However, due to the fading nature of channels in wireless environments, the finite block length (FBL) transmission in ultra-reliable low-latency communication (URLLC) is inevitably affected by the decrease in transmission rate and the probability of packet errors. However, current studies are all based on the system design of the Shannon capacity expression of infinite block length (IFBL) transmission, while ignoring the requirements of URLLC in 6G. At the same time, current studies all consider the ideal constant power consumption of the intelligent reflecting surface (IRS), while ignoring the actual power consumption when there is a discrete phase shift. Summary of the invention

[0003] The purpose of the present invention is to overcome the deficiencies of the prior art and provide an optimization method for maximizing the energy efficiency of an IRS-assisted downlink URLLC system.

[0004] The objective of the present invention is achieved through the following technical solutions:

[0005] The present invention provides an optimization method for maximizing energy efficiency of an IRS-assisted downlink URLLC system, comprising:

[0006] S1, constructing a multi-input single-output URLLC system with the assistance of smart reflector;

[0007] S2. Construct a system energy efficiency maximization problem model and obtain a non-convex optimization problem;

[0008] S3, based on parameter substitution and problem transformation, the integer constraints and fraction constraints of the original problem are converted into a tractable form;

[0009] S4, solve the variable coupling problem through the alternating optimization method, use the SCA iterative algorithm and SDR technology to convert the non-convex problem into a convex optimization problem, and solve the convex optimization problem through the BCD algorithm;

[0010] S5. Based on the iterative optimization variable values ​​generated in S4, the BCD iterative algorithm is used to obtain the suboptimal solution of the multi-input single-output URLLC system parameters. In the process of obtaining the suboptimal solution, the maximum energy efficiency of the single antenna user and the optimal solution of the reliability constraint are obtained through iteration.

[0011] Furthermore, the multiple-input single-output URLLC system comprises For a single-antenna user, N-antenna base stations and M reflection units IRS, step S1 specifically includes:

[0012] definition For user collection, It is a collection of IRS units; the data transmission link from the antenna base station to the single antenna user through the IRS Reflection link from IRS to base station and IRS user reflection link The data transmission link from the antenna base station to the single antenna user is: ;in, The dimension is N A complex vector with 1 row and 1 column; The dimension is M A complex vector with 1 row and 1 column; The dimension is M OK N A complex matrix of columns;

[0013] Assume that the base station uses linear precoding and define the precoding vector of the base station to the user as , the phase shift matrix at the IRS is defined as , the phase shift variable at the IRS is defined as , the passive beamforming at the IRS is defined as ;in, , represents a diagonal matrix function, represents the phase shift of the mth unit of IRS, , T represents transpose; The phase shift of the mth reflection unit IRS is converted into a complex function, that is, the Euler transformation formula , It represents the phase shift of the first reflection unit IRS converted into a complex function, Indicates M The phase shift of each reflection unit IRS is converted into a complex function, represents an imaginary unit;

[0014] The actual power consumption of the IRS unit is defined as ,in, Indicates the encoding of the IRS unit; Indicates encoding The number of Indicates that the code is Power consumption when It represents the accumulation of all IRS units. The actual power consumption of the IRS unit is determined by the working state of the PIN diode pin;

[0015] user The signal-to-noise ratio is defined as , ;in, represents the intensity of received Gaussian white noise; the symbol represents conjugate transpose; represents the single antenna user set Except for single antenna users All other single-antenna users except Indicates a single antenna user The precoding vector of

[0016] According to the finite block length coding theory, user The achievable transmission rate is expressed as ;in, represents channel dispersion; Indicates user The block length indicates that the user The probability of packet transmission error; Gauss The inverse function of a function is defined as ;when hour, user The achievable transmission rate is further expressed as ;in, ;

[0017] Use imperfect CSI to build a system covariance uncertainty channel model; for downlink users The covariance matrix of is defined as ;in, represents the expectation operator;

[0018] When the system considers the impact of imperfect CSI, the channel gain is constant in each coherent block, and the expectation operator is ignored. The true covariance channel matrix is ;in, represents the channel covariance uncertainty matrix, and its dimension is N OK N A complex matrix with columns; and , represents the maximum norm value of the corresponding covariance channel estimation error, ;user The signal-to-noise ratio can be rewritten as ; The total power consumption of the downlink URLLC system is defined as , and satisfy the formula ;in, It represents the power amplification factor; Indicates the circuit power introduced by deploying an antenna in a base station; Indicates the power of a single user under a single antenna; Represents static circuit power consumption.

[0019] Preferably, constructing a mathematical model for maximizing system energy efficiency in step S2 specifically includes: ;in, Indicates the number of phase shift levels, represents the quantization resolution, Represents quantization interval; constraints represents the minimum transmission rate of the user, represents the required transmission rate threshold; constraint Indicates the maximum transmit power of the system. Indicates the actual maximum transmit power threshold; constraint Indicates the maximum transmission block length of the user, Indicates the maximum threshold value for limited block length transmission; constraint Indicates the reliability of the user, represents the maximum reliability threshold of a finite block length transmission system; constraint Represents the discrete phase shift of the IRS unit supporting phase shift encoding; constraint Represents the IRS unit discrete beam constraint vector; constraint represents the channel uncertainty level; Represents maximization P1 The objective function and the optimization variables are the user's precoding vector , discrete phase shift of IRS unit , the discrete beam vector of the IRS unit , the packet transmission error probability of a single antenna user under limited block length transmission and the transmission block length of a single-antenna user , Represents the square of the matrix norm.

[0020] Preferably, step S3 comprises:

[0021] By replacing parameters and transforming the problem, the integer constraints and fractional constraints of the original problem are transformed into a tractable form for solving the non-convex optimization problem P1. First, the constraints are proved by contradiction. At the optimal solution, the equation holds true, satisfying ;

[0022] Then by proving the constraint Equivalent to its corresponding signal-to-noise ratio constraint, satisfying ;in, Represents the signal-to-noise ratio threshold and satisfies ; ; ; Finally, the function Defined as ,in, , and Respectively The internal parameters of the function, Indicates the range A positive integer, Indicates the range A positive integer of ;

[0023] When considering the impact of imperfect CSI, users Signal-to-noise ratio Re-expressed as: ;in, Represents the BS-side precoding vector The active beamforming matrix composed of Indicates that the dimension is N OK N The identity matrix of columns;

[0024] Introduction To solve discrete constraints ;in, represents the selection variable of the reflection unit IRS; Represents a reflection set, the range is ; The selection variable of the reflection unit IRS can only select binary numbers 0 or 1; Translates to:

[0025]

[0026] in, Representing a collection The elements; at this time the constraint There are still discrete variables, and the following transformation is used to constrain Convert to a continuous constraint:

[0027]

[0028] Then, the Dinkelbach method was used to P1 Fractional objective function Convert to subtractive form of parameters; introduce new auxiliary variables , defined as the fraction at the corresponding number of iterations ; The objective function is rewritten as ; At this point, the original optimization problem P1 Equivalently transformed into the following optimization problem: ;in, The function represents the rank of the matrix; Represents maximization P2 The objective function and the optimization variables are the user's active beamforming matrix , discrete phase shift of IRS unit , the discrete beam vector of the IRS unit , the transmission block length of a single-antenna user under limited block length transmission and the selection variables of the IRS unit .

[0029] Preferably, step S4 comprises:

[0030] The alternating optimization method is used to solve the variable coupling problem. Then, for each sub-problem, the SCA iterative algorithm and SDR technology are used to convert the non-convex optimization problem into a convex optimization problem, and the BCD algorithm is used to solve the optimal solution of each sub-problem to solve the non-convex optimization problem. P2 ;

[0031] Given parameters Optimization parameters , a non-convex optimization problem P2 Convert to ;in, Represents maximization P3 The objective function and the optimization variable is the transmission block length of the single-antenna user , using the first-order Taylor series expansion P3 The non-convex objective function is converted to a convex objective function: , in, express The nth iteration value; then, using the BCD algorithm, the problem P3 Convert to ;in Represents maximization P4 The objective function and the optimization variable is the transmission block length of the single-antenna user ; P4 It is a LP subproblem;

[0032] Given parameters Optimization parameters , a non-convex optimization problem P2 Convert to ;in Represents maximization P5The objective function and the optimization variable is the user's precoding vector , Represents the trace of a matrix; introduces the symbol , and are defined as Using a first-order Taylor series expansion And find its convex lower bound: in, express The nth iteration value, express Approximation of Indicates about A derivation of Representation function About variables A derivative of The value at ,in, represents the single antenna user set Except for single antenna users All other single-antenna users except represents the single antenna user set Except for single antenna users For all other single-antenna users except express;

[0033] Will P5 Constraints in Transform and rewrite as:

[0034] Then the BCD algorithm is used, the problem P5 The equivalent conversion is: ; Represents maximization P6 The objective function and the optimization variable is the user's precoding vector At this time, the SDR algorithm is used to relax the constraint C7. P6 Convert to the first SDP question;

[0035] Given parameters Optimization parameters , a non-convex optimization problem P2 Translates to: ;in Represents maximization P7 The objective function and the optimization variables are the discrete phase shifts of the IRS unit , the discrete beam vector of the IRS unit and the selection variables of the IRS unit ;

[0036] The expected signal of a single-antenna user can be expressed as ;in, ; It indicates the deformation of the user-base station channel including direct link and reflection link. represents the passive beamforming vector of the IRS reflection unit after the direct link and the reflection link deformation; at this time, the user The signal-to-noise ratio at is reformulated as: ;

[0037] Importing symbols and , and are defined as:

[0038]

[0039] The actual power consumption of IRS is a complex function of quantization resolution and discrete phase shift encoding, which can be expressed by the following approximate function: ;

[0040] Discrete Phase Shift Variables of IRS Converted to discrete beam constraints, Further expressed as: in, Represents the newly introduced slack variable, which represents the new matrix when IRS discrete phase shift adopts encoding, and its dimension is M OK M List, express M A row vector with 1 row and 1 column and all internal elements are 1. Represents real part operations of complex numbers;

[0041] The approximate expression of is: ; Using a first-order Taylor series expansion And find its convex lower bound: in, express The nth iteration value, express The approximation of Indicates about A derivation of Representation function About variables A derivation of The value at in, represents the single antenna user set Except for single antenna users For all other single-antenna users except express;

[0042] Will P7 Constraints in Transform and rewrite as: constraint This also equivalently converts to: , in, express The nth iteration value;

[0043] question P7 The equivalent conversion is: ; Represents maximization P8 The objective function and the optimization variables are the discrete beamforming vector matrices of the IRS unit. , discrete phase shift coding matrix of IRS unit and the selection variables of the IRS unit At the same time, P8 Non-convex constraints in Replace it with the following constraints: represents a new matrix composed of the passive beamforming matrix and the passive beamforming vector of the reflection unit IRS, with a dimension of M+2 OK M+2 Column; Use the first-order Taylor series to expand the non-convex constraint C9b to convert it into the following convex constraint: in, represents the nuclear norm of matrix Y, represents the norm of matrix Y, represents the eigenvector corresponding to the largest eigenvalue of matrix Y, Represents the nth iteration value of matrix Y;

[0044] Using a first-order Taylor series to expand the non-convex constraint C8, it is equivalent to the following convex constraint: in, represents the nuclear norm of matrix X, represents the norm of the matrix X, represents the eigenvector corresponding to the largest eigenvalue of matrix X, Represents the nth iteration value of matrix X;

[0045] Then the BCD algorithm is used, the problem P8 The equivalent conversion is: ; Represents maximization P9 The objective function and the optimization variables are the discrete beamforming vector matrices of the IRS unit. , discrete phase shift coding matrix of IRS unit , and the selection variables of the IRS unit ;at this time, P9 It is the second SDP question.

[0046] Preferably, the step S5 comprises:

[0047] Initialization parameters , set n=0;

[0048] Obtaining the optimal parameters by proof by contradiction ;

[0049] pass Calculate and update ;

[0050] Given parameters , solve P4 and update the parameters ;

[0051] Given parameters , solve P6 and update the parameters ;

[0052] Given parameters , solve P9 and update the parameters ;

[0053] By parameters ,renew ;

[0054] Until convergence.

[0055] The beneficial effects of the present invention are:

[0056] 1) The present invention solves the problem of maximizing user energy efficiency in the URLLC system, innovatively adds IRS technology, makes the wireless channel controllable, increases the channel gain of the system, and improves the system performance.

[0057] 2) For the reliability constraints of users in the URLLC system, the present invention proves based on contradiction that the constraint equation holds true at the optimal solution.

[0058] 3) Regarding the impact of non-ideal IRS and actual power consumption of IRS, the present invention proposes an alternating optimization method to solve the variable coupling problem, and uses the SCA algorithm and SDR technology to convert non-convex constraints into convex constraints, solving the problem of difficulty in calculating the actual power consumption of non-ideal IRS.

[0059] 4) For the user transmission block length constraint in the URLLC system, the present invention adopts the SCA method to convert the objective function into the form of the difference of convex functions to facilitate the algorithm solution, thereby solving the problem of solving the optimal solution of the reliability constraint of the URLLC system.

[0060] 5) The non-ideal IRS optimization model with actual power consumption proposed in the present invention shows better system performance gain compared with the existing constant power consumption IRS optimization model when the number of BS antennas changes.

[0061] 6) By combining IRS and URLLC, a model for maximizing the system energy efficiency under the influence of non-ideal IRS, actual IRS power consumption and imperfect CSI is proposed, and a BCD iterative algorithm is developed to solve the local optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A flowchart of a method for optimizing the energy efficiency of an IRS-assisted downlink URLLC system according to an embodiment of the present invention;

[0063] Figure 2 A detailed flow chart of step S5 of an optimization method for maximizing energy efficiency of an IRS-assisted downlink URLLC system according to an embodiment of the present invention;

[0064] Figure 3 The figure is a comparison chart of simulation results of the non-ideal IRS optimization model and the existing constant power consumption IRS optimization model. DETAILED DESCRIPTION

[0065] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0066] Exemplarily, the present invention provides an optimization method for maximizing the energy efficiency of an IRS-assisted downlink URLLC system. The present invention is based on non-ideal IRS and actual IRS power consumption, considers imperfect channel state information (CSI), is based on the user's FBL transmission mechanism, and takes maximizing the system's energy efficiency as the research goal. A non-convex optimization problem is formulated to jointly optimize the user transmission block length and decoding error probability, the precoder at the BS, the discrete phase shifter at the IRS, and the discrete phase shift coding. The present invention proposes an iterative algorithm based on block coordinatedescent (BCD), which exhibits better system performance and robustness than existing algorithms. The specific step flow chart is shown in FIG. Figure 1 As shown, including:

[0067] S1, constructing a multi-input single-output URLLC system with the assistance of smart reflector;

[0068] S2. Construct a system energy efficiency maximization problem model and obtain a non-convex optimization problem;

[0069] S3, based on parameter substitution and problem transformation, the integer constraints and fraction constraints of the original problem are converted into a tractable form;

[0070] S4, solve the variable coupling problem through the alternating optimization method, use the SCA iterative algorithm and SDR technology to convert the non-convex problem into a convex optimization problem, and solve the convex optimization problem through the BCD algorithm;

[0071] S5. Based on the iterative optimization variable values ​​generated in S4, the BCD iterative algorithm is used to obtain the suboptimal solution of the multi-input single-output URLLC system parameters. In the process of obtaining the suboptimal solution, the maximum energy efficiency of the single antenna user and the optimal solution of the reliability constraint are obtained through iteration.

[0072] Specifically, the multiple-input single-output URLLC system includes For a single-antenna user, N-antenna base stations and M reflection units IRS, step S1 specifically includes:

[0073] definition For user collection, It is a collection of IRS units; the data transmission link from the antenna base station to the single antenna user through the IRS Reflection link from IRS to base station and IRS user reflection link The data transmission link from the antenna base station to the single antenna user is: ;in, The dimension is N A complex vector with 1 row and 1 column; The dimension is M A complex vector with 1 row and 1 column; The dimension is M OK N A complex matrix of columns.

[0074] Assume that the base station uses linear precoding and define the precoding vector of the base station to the user as , the phase shift matrix at the IRS is defined as , the phase shift variable at the IRS is defined as , the passive beamforming at the IRS is defined as ;in, , represents a diagonal matrix function, represents the phase shift of the mth unit of IRS, , T represents transpose; The phase shift of the mth reflection unit IRS is converted into a complex function, that is, the Euler transformation formula , It represents the phase shift of the first reflection unit IRS converted into a complex function, Indicates M The phase shift of each reflection unit IRS is converted into a complex function, Represents an imaginary unit.

[0075] Then consider the actual power consumption of the IRS unit, which is determined by the working state of the PIN diode pin. The actual power consumption of the IRS unit is defined as , which is given by the formula Indicates. Among them, Indicates encoding The number of Indicates that the code is Power consumption when Represents the accumulation of all units of IRS.

[0076] user The signal-to-noise ratio is defined as , ;in, Indicates the intensity of received Gaussian white noise; symbol represents conjugate transpose; represents the single antenna user set Except for single antenna users All other single-antenna users except Indicates a single antenna user The precoding vector of

[0077] According to the finite block length coding theory, user The achievable transmission rate is expressed as ;in, represents channel dispersion; Indicates user The block length indicates that the user The probability of packet transmission error; Gauss The inverse function of a function is defined as ;when hour, user The achievable transmission rate is further expressed as ;in, .

[0078] The system covariance uncertainty channel model is constructed using imperfect CSI. Definition: Downlink user The covariance matrix of . Among them, the symbol represents the expected operator. In the calculation process of the system, since the channel gain is assumed to be constant in each coherent block, the expected operator can be ignored. Since this system considers the impact of imperfect CSI, it is assumed that the true covariance channel matrix is .in, represents the channel covariance uncertainty matrix, and its dimension is N OK N A complex matrix with columns. And it satisfies , represents the maximum norm value of the corresponding covariance channel estimation error, .

[0079] user The signal-to-noise ratio can be rewritten as ; The total power consumption of the downlink URLLC system is defined as , and satisfy the formula ;in, It represents the power amplification factor; Indicates the circuit power introduced by deploying an antenna in a base station; Indicates the power of a single user under a single antenna; Represents static circuit power consumption.

[0080] Specifically, the construction of the mathematical model of the system energy efficiency maximization problem in step S2 specifically includes: ;in, Indicates the number of phase shift levels, represents the quantization resolution, Represents quantization interval; constraints represents the minimum transmission rate of the user, represents the required transmission rate threshold; constraint Indicates the maximum transmit power of the system. Indicates the actual maximum transmit power threshold; constraint Indicates the maximum transmission block length of the user, Indicates the maximum threshold value for limited block length transmission; constraint Indicates the reliability of the user, represents the maximum reliability threshold of a finite block length transmission system; constraint Represents the discrete phase shift of the IRS unit supporting phase shift encoding; constraint Represents the IRS unit discrete beam constraint vector; constraint represents the channel uncertainty level; Represents maximization P1 The objective function and the optimization variables are the user's precoding vector , discrete phase shift of IRS unit , the discrete beam vector of the IRS unit , the packet transmission error probability of a single antenna user under limited block length transmission and the transmission block length of a single-antenna user , Represents the square of the matrix norm.

[0081] Specifically, step S3 includes:

[0082] By replacing parameters and transforming the problem, the integer constraints and fractional constraints of the original problem are transformed into a tractable form for solving the non-convex optimization problem P1. First, the constraints are proved by contradiction. At the optimal solution, the equation holds true, satisfying ;

[0083] Then by proving the constraint Equivalent to its corresponding signal-to-noise ratio constraint, satisfying ;in, Represents the signal-to-noise ratio threshold and satisfies ; ; ; Finally, the function Defined as ,in, , and Respectively The internal parameters of the function, Indicates the range A positive integer, Indicates the range A positive integer.

[0084] When considering the impact of imperfect CSI, users Signal-to-noise ratio Re-expressed as: ;in, Represents the BS-side precoding vector The active beamforming matrix composed of The dimension is N OK N The identity matrix of the columns.

[0085] Introduction To solve discrete constraints ;in, represents the selection variable of the reflection unit IRS; Represents a reflection set, the range is ; The selection variable of the reflection unit IRS can only select binary numbers 0 or 1; Converts to:

[0086]

[0087] in, Representing a collection The elements; at this time the constraint There are still discrete variables, and the following transformation is used to constrain Convert to a continuous constraint:

[0088]

[0089] Then, the Dinkelbach method was used to P1 Fractional objective function Convert to subtractive form of parameters; introduce new auxiliary variables , defined as the fraction at the corresponding number of iterations ; The objective function is rewritten as .

[0090] At this point, the original optimization problem P1 Equivalently transformed into the following optimization problem: ;in, The function represents the rank of the matrix; Represents maximization P2 The objective function and the optimization variables are the user's active beamforming matrix , discrete phase shift of IRS unit , the discrete beam vector of the IRS unit , the transmission block length of a single-antenna user under limited block length transmission and the selection variables of the IRS unit .

[0091] Specifically, step S4 includes:

[0092] The alternating optimization method is used to solve the variable coupling problem. Then, for each sub-problem, the SCA iterative algorithm and SDR technology are used to convert the non-convex optimization problem into a convex optimization problem, and the BCD algorithm is used to solve the optimal solution of each sub-problem to solve the non-convex optimization problem. P2 ;

[0093] The alternating optimization method is used to solve the variable coupling problem. Then, for each sub-problem, the SCA iterative algorithm and SDR technology are used to convert the non-convex optimization problem into a convex optimization problem, and the BCD algorithm is used to solve the optimal solution of each sub-problem to solve the non-convex optimization problem. P2 ;

[0094] Given parameters Optimization parameters , a non-convex optimization problem P2 Convert to ;in, Represents maximization P3 The objective function and the optimization variable is the transmission block length of the single-antenna user , using the first-order Taylor series expansion P3 The non-convex objective function is converted to a convex objective function: , in, express The nth iteration value; then, using the BCD algorithm, the problem P3 Convert to ;in Represents maximization P4 The objective function and the optimization variable is the transmission block length of the single-antenna user ; P4 It is a LP subproblem;

[0095] Given parameters Optimization parameters , a non-convex optimization problem P2 Convert to ;in Represents maximization P5 The objective function and the optimization variable is the user's precoding vector , Represents the trace of a matrix; introduces the symbol , and are defined as Using a first-order Taylor series expansion And find its convex lower bound: in, express The nth iteration value, express Approximation of Indicates about A derivation of Representation function About variables A derivative of The value at ,in, represents the single antenna user set Except for single antenna users All other single-antenna users except represents the single antenna user set Except for single antenna users For all other single-antenna users except express.

[0096] Will P5 Constraints in Transform and rewrite as: Then the BCD algorithm is used, the problem P5 The equivalent conversion is: ; Represents maximization P6 The objective function and the optimization variable is the user's precoding vector At this time, the SDR algorithm is used to relax the constraint C7. P6 Convert to the first SDP question.

[0097] Given parameters Optimization parameters , a non-convex optimization problem P2 Translates to: ;in Represents maximization P7 The objective function and the optimization variables are the discrete phase shifts of the IRS unit , the discrete beam vector of the IRS unit and the selection variables of the IRS unit .

[0098] The expected signal of a single-antenna user can be expressed as ;in, ; It indicates the deformation of the user-base station channel including direct link and reflection link. represents the passive beamforming vector of the IRS reflection unit after the direct link and the reflection link deformation; at this time, the user The signal-to-noise ratio at is reformulated as: ; Introduce symbols and , and are defined as: The actual power consumption of IRS is a complex function of quantization resolution and discrete phase shift encoding, which can be expressed by the following approximate function: ; Discrete phase shift variables of IRS Converted to discrete beam constraints, Further expressed as: in, Represents the newly introduced slack variable, which represents the new matrix when IRS discrete phase shift adopts encoding, and its dimension is M OK M List, express M A row vector with 1 row and 1 column and all internal elements are 1. Represents real part operations of complex numbers; The approximate expression of is: .

[0099] Using a first-order Taylor series expansion And find its convex lower bound: in, express The nth iteration value, express Approximation of Indicates about A derivation of Representation function About variables A derivative of The value at in, represents the single antenna user set Except for single antenna users For all other single-antenna users except express.

[0100] Will P7 Constraints in Transform and rewrite as: constraint This also equivalently converts to: , in, express The nth iteration value.

[0101] question P7 The equivalent conversion is: ; Represents maximization P8 The objective function and the optimization variables are the discrete beamforming vector matrices of the IRS unit. , discrete phase shift coding matrix of IRS unit and the selection variables of the IRS unit At the same time, P8 Non-convex constraints in Replace it with the following constraints: represents a new matrix composed of the passive beamforming matrix and the passive beamforming vector of the reflection unit IRS, with a dimension of M+2 OK M+2 Column; Use the first-order Taylor series to expand the non-convex constraint C9b to convert it into the following convex constraint: in, represents the nuclear norm of matrix Y, represents the norm of matrix Y, represents the eigenvector corresponding to the largest eigenvalue of matrix Y, Represents the nth iteration value of matrix Y.

[0102] Using a first-order Taylor series to expand the non-convex constraint C8, it is equivalent to the following convex constraint: in, represents the nuclear norm of matrix X, represents the norm of the matrix X, represents the eigenvector corresponding to the largest eigenvalue of matrix X, Represents the nth iteration value of matrix X.

[0103] Then the BCD algorithm is used, the problem P8 The equivalent conversion is: ; Represents maximization P9 The objective function and the optimization variables are the discrete beamforming vector matrix of the IRS unit and the discrete phase shift coding matrix of the IRS unit. and the selection variables of the IRS unit ;at this time, P9 It is the second SDP question.

[0104] Specifically, the specific flow chart of step S5 is as follows: Figure 2 As shown, the following steps are included:

[0105] Initialization parameters , set n=0;

[0106] Obtaining the optimal parameters by proof by contradiction ;

[0107] pass Calculate and update ;

[0108] Given parameters , solve P4 and update the parameters ;

[0109] Given parameters , solve P6 and update the parameters ;

[0110] Given parameters , solve P9 and update the parameters ;

[0111] By parameters ,renew ;

[0112] Until convergence.

[0113] For example, the simulation comparison diagram of the non-ideal IRS optimization model with actual power consumption in the present invention and the existing constant power consumption IRS optimization model is as follows: Figure 3As shown, the solid line is the simulation result of the non-ideal IRS optimization model with actual power consumption in the present invention, and the dotted line is the simulation result of the existing constant power consumption IRS optimization model. It can be seen that the present invention solves the problem of maximizing the energy efficiency of users in the URLLC system, especially the innovative addition of IRS technology, which makes the wireless channel controllable, increases the channel gain of the system, and improves the system performance. At the same time, the problem of the difficulty in calculating the actual power consumption of the non-ideal IRS is solved. In addition, the problem of solving the optimal solution of the reliability constraint of the URLLC system is solved. The non-ideal IRS optimization model with actual power consumption proposed by the present invention shows a better system performance gain than the existing constant power consumption IRS optimization model under the change of the number of antennas at the BS end.

[0114] The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art shall not deviate from the spirit and scope of the present invention, and shall be within the scope of protection of the claims attached to the present invention.

Claims

1. An optimization method for maximizing energy efficiency of an IRS-assisted downlink URLLC system, characterized in that: include: S1, constructing a multi-input single-output URLLC system with the assistance of smart reflector; S2. Construct a system energy efficiency maximization problem model and obtain a non-convex optimization problem; S3, based on parameter substitution and problem transformation, the integer constraints and fraction constraints of the original problem are converted into a tractable form; S4. Solve the variable coupling problem by alternating optimization method, convert the non-convex problem into a convex optimization problem by using SCA iterative algorithm and SDR technology, and solve the convex optimization problem by BCD algorithm, wherein the BCD algorithm divides the multi-variable coupled resource blocks and optimizes the corresponding resource blocks while fixing other resource blocks; S5, based on the iterative optimization variable values ​​generated in S4 and using the BCD iterative algorithm to obtain the suboptimal solution of the multi-input single-output URLLC system parameters, in the process of obtaining the suboptimal solution, the maximum energy efficiency of the single antenna user and the optimal solution of the reliability constraint are obtained through iteration; Wherein, the multi-input single-output URLLC system includes single-antenna users, N antenna base stations and M reflection units IRS, step S1 specifically includes: definition For user collection, It is a collection of IRS units; the data transmission link from the antenna base station to the single antenna user through the IRS Reflection link from IRS to base station and IRS user reflection link The data transmission link from the antenna base station to the single antenna user is: ;in, The dimension is N A complex vector with 1 row and 1 column; The dimension is M A complex vector with 1 row and 1 column; The dimension is M OK N A complex matrix of columns; Assume that the base station uses linear precoding and define the precoding vector of the base station for a single-antenna user as , the phase shift matrix at the IRS is defined as , the phase shift variable at the IRS is defined as , the passive beamforming at the IRS is defined as ;in , represents a diagonal matrix function, represents the phase shift of the mth unit of IRS, , T represents transpose; The phase shift of the mth reflection unit IRS is converted into a complex function, that is, the Euler transformation formula , It represents the phase shift of the first reflection unit IRS converted into a complex function, Indicates M The phase shift of each reflection unit IRS is converted into a complex function, represents an imaginary unit; The actual power consumption of the IRS unit is defined as ,in, Indicates the code of the IRS unit; Indicates encoding The number of Indicates that the code is Power consumption when It represents the accumulation of all IRS units. The actual power consumption of the IRS unit is determined by the working state of the PIN diode pin; Single antenna user The signal-to-noise ratio is defined as , ;in, represents the intensity of received Gaussian white noise; H represents conjugate transpose; Represents a user collection Except for single antenna users All other single-antenna users except Indicates a single antenna user The precoding vector of According to the finite block length coding theory, a single antenna user The achievable transmission rate is expressed as ;in, represents channel dispersion; Indicates a single antenna user The block length is Indicates a single antenna user The probability of packet transmission error; Gauss The inverse function of a function is defined as ;when hour, , single antenna user The achievable transmission rate is further expressed as ;in ; Use imperfect CSI to build a system covariance uncertain channel model; for a single antenna user The covariance matrix of is defined as ;in, represents the expectation operator; When the system considers the impact of imperfect CSI, the channel gain is constant in each coherent block, and the expectation operator is ignored. The true covariance channel matrix is ;in, represents the channel covariance uncertainty matrix, and its dimension is N OK N A complex matrix with columns; and , represents the maximum norm value of the corresponding covariance channel estimation error, Single antenna user The signal-to-noise ratio can be rewritten as ; The total power consumption of the downlink URLLC system is defined as , and satisfy the formula ;in, It represents the power amplification factor; Indicates the circuit power introduced by deploying an antenna in a base station; Indicates the power of a single user under a single antenna; Indicates static circuit power consumption; The step S2 of constructing a mathematical model for maximizing system energy efficiency specifically includes: ;in, Indicates the number of phase shift levels, represents the quantization resolution, Represents quantization interval; constraints represents the minimum transmission rate of the user, represents the required transmission rate threshold; constraint Indicates the maximum transmit power of the system. Indicates the actual maximum transmit power threshold; constraint Indicates the maximum transmission block length of the user, Indicates the maximum threshold value for limited block length transmission; constraint Indicates the reliability of the user, represents the maximum reliability threshold of a finite block length transmission system; constraint Represents the discrete phase shift of the IRS unit supporting phase shift encoding; constraint Represents the IRS unit discrete beam constraint vector; constraint represents the channel uncertainty level; Represents maximization P1 The objective function and the optimization variables are single antenna users The precoding vector , discrete phase shift of IRS unit , the discrete beam vector of the IRS unit , Single antenna user The probability of packet transmission error , Single antenna user The block length , represents the square of the matrix norm; Wherein, the step S3 comprises: By replacing parameters and transforming the problem, the integer constraints and fractional constraints of the original problem are transformed into a tractable form for solving the non-convex optimization problem P1. First, the constraints are proved by contradiction. At the optimal solution, the equation holds true, satisfying ; Then by proving the constraint Equivalent to its corresponding signal-to-noise ratio constraint, satisfying ;in Represents the signal-to-noise ratio threshold and satisfies ; ; ; Finally, the function Defined as ,in, , and Respectively The internal parameters of the function, Indicates the range A positive integer, Indicates the range A positive integer of ; When considering the impact of imperfect CSI, a single-antenna user Signal-to-noise ratio Re-expressed as: ;in, Indicates a single antenna user The precoding vector The active beamforming matrix composed of The dimension is N OK N The identity matrix of columns; Introduction To solve discrete constraints ;in, represents the selection variable of the reflection unit IRS; Represents a reflection set, the range is ; The selection variable of the reflection unit IRS can only select binary numbers 0 or 1; Converts to: in, Representing a collection The elements; at this time the constraint There are still discrete variables, and the following transformation is used to constrain Convert to a continuous constraint: Then, the Dinkelbach method was used to P1 Fractional objective function Convert to subtractive form of parameters; introduce new auxiliary variables , defined as the fraction at the corresponding number of iterations ; The objective function is rewritten as ; At this point, the original optimization problem P1 Equivalently transformed into the following optimization problem: ;in, The function represents the rank of the matrix; Represents maximization P2 The objective function and the optimization variables are the user's active beamforming matrix , discrete phase shift of IRS unit , the discrete beam vector of the IRS unit , single antenna user The block length and the selection variables of the IRS unit ; Wherein, the step S4 comprises: The alternating optimization method is used to solve the variable coupling problem. Then, for each sub-problem, the SCA iterative algorithm and SDR technology are used to convert the non-convex optimization problem into a convex optimization problem, and the BCD algorithm is used to solve the optimal solution of each sub-problem to solve the non-convex optimization problem. P2 ; Given parameters Optimization parameters , a non-convex optimization problem P2 Convert to ;in, Represents maximization P3 The objective function and the optimization variable is a single antenna user The block length , using the first-order Taylor series expansion P3 The non-convex objective function is converted to a convex objective function: , in, express The nth iteration value; then, using the BCD algorithm, the problem P3 Convert to ;in Represents maximization P4 The objective function and the optimization variable is a single antenna user The block length ; P4 It is a LP subproblem; Given parameters Optimization parameters , a non-convex optimization problem P2 Convert to ;in Represents maximization P5 The objective function and the optimization variable is a single antenna user The precoding vector , Represents the trace of a matrix; introduces the symbol , and are defined as Using a first-order Taylor series expansion And find its convex lower bound: in, express The nth iteration value, express Approximation of Indicates about A derivation of Representation function About variables A derivation of The value at ,in, Represents a user collection Except for single antenna users All other single-antenna users except Represents a user collection Except for single antenna users For all other single-antenna users except express; Will P5 Constraints in Transform and rewrite as: Then the BCD algorithm is used, the problem P5 The equivalent conversion is: ; Represents maximization P6 The objective function and the optimization variable is a single antenna user The precoding vector At this time, the SDR algorithm is used to relax the constraint C7. P6 Convert to the first SDP question; Given parameters Optimization parameters , a non-convex optimization problem P2 Converts to: ;in Represents maximization P7 The objective function and the optimization variables are the discrete phase shifts of the IRS unit , the discrete beam vector of the IRS unit and the selection variables of the IRS unit ; The expected signal of a single-antenna user can be expressed as ;in, ; It indicates the deformation of the user-base station channel including direct link and reflection link. represents the passive beamforming vector of the IRS reflector unit after the direct link and the reflection link deformation; at this time, the single antenna user The signal-to-noise ratio at is reformulated as: ; Importing symbols and , and are defined as: The actual power consumption of IRS is a complex function of quantization resolution and discrete phase shift encoding, which can be expressed by the following approximate function: ; Discrete Phase Shift Variables of IRS Converted to discrete beam constraints, Further expressed as: in, Represents the newly introduced slack variable, which represents the new matrix when IRS discrete phase shift adopts encoding, and its dimension is M OK M List, express M A row vector with 1 row and 1 column and all internal elements are 1. Represents real part operations of complex numbers; The approximate expression of is: ; Using a first-order Taylor series expansion And find its convex lower bound: in, express The nth iteration value, express Approximation of Indicates about A derivation of Representation function About variables A derivation of The value at in, represents the single antenna user set Except for single antenna users For all other single-antenna users except express; Will P7 Constraints in Transform and rewrite as: constraint This also equivalently converts to: , in, express The nth iteration value; question P7 The equivalent conversion is: ; Represents maximization P8 The objective function and the optimization variables are the discrete beamforming vector matrices of the IRS unit. , discrete phase shift coding matrix of IRS unit and the selection variables of the IRS unit At the same time, P8 Non-convex constraints in Replace it with the following constraints: represents a new matrix composed of the passive beamforming matrix and the passive beamforming vector of the reflection unit IRS, with a dimension of M+2 OK M+2 Column; Use the first-order Taylor series to expand the non-convex constraint C9b to convert it into the following convex constraint: in, represents the nuclear norm of matrix Y, represents the norm of matrix Y, represents the eigenvector corresponding to the largest eigenvalue of matrix Y, Represents the nth iteration value of matrix Y; Using a first-order Taylor series to expand the non-convex constraint C8, it is equivalent to the following convex constraint: in, represents the nuclear norm of matrix X, represents the norm of the matrix X, represents the eigenvector corresponding to the largest eigenvalue of matrix X, Represents the nth iteration value of matrix X; Then the BCD algorithm is used, the problem P8 The equivalent conversion is: ; Represents maximization P9 The objective function and the optimization variables are the discrete beamforming vector matrices of the IRS unit. , discrete phase shift coding matrix of IRS unit , and the selection variables of the IRS unit ;at this time, P9 It is the second SDP question; Wherein, the step S5 comprises: Initialization parameters , set n=0; Obtaining the optimal parameters by proof by contradiction ; pass Calculate and update ; Given parameters , solve P4 and update the parameters ; Given parameters , solve P6 and update the parameters ; Given parameters , solve P9 and update the parameters ; By parameters ,renew ; Until convergence.

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