RIS-assisted millimeter wave URLLC communication system hybrid precoding design method

Abstract

The invention discloses an RIS-assisted millimeter wave URLLC communication system hybrid precoding design method. Establishing an RIS-assisted downlink millimeter wave URLLC communication system model, and defining a user reachable rate; establishing an optimization problem which takes maximization of a user reachable rate weighted sum as a target and takes digital precoding, analog precoding and an RIS phase shift matrix of a transmitter as variables; introducing an auxiliary variable to simplify a target function, and adding a corresponding constraint condition to ensure the equivalence of an optimization problem; decomposing the equivalent optimization problem into three sub-problems, and calculating optimization variables by using a first-order Taylor expansion technology, a minimum Euclidean distance method and a continuous convex approximation algorithm; and iteratively calculating the absolute value of the difference of the weighted sums of the reachable rates of the corresponding users before and after the optimization variables are updated until a preset termination condition is met. According to the method, the hardware cost of wireless transmission is reduced, and the system performance of URLLC millimeter wave communication is remarkably improved by optimizing the sending direction and phase of the beam.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a RIS-assisted millimeter wave URLLC communication system hybrid precoding design method. Background Art

[0002] High reliability and low latency communication (URLLC) is one of the representative application scenarios in the fifth generation (5G) communication technology. URLLC has the characteristics of high reliability and low latency, which makes it widely used in smart medical care, industrial production and other fields. With the continuous development of 5G technology, the problem of spectrum resource shortage has become more and more prominent, and millimeter wave (mmWave) in the high frequency band provides a feasible solution for expanding the communication frequency band with its abundant spectrum resources. Therefore, URLLC communication based on the millimeter wave band has been applied, which also provides a new solution for high-speed access services. However, the millimeter wave wavelength is short, and the signal will produce large attenuation during the transmission process, which leads to the limited transmission distance of millimeter wave communication. In order to solve this problem, the path loss in millimeter wave communication is compensated by introducing precoding technology in the system. In addition, although the design of all-digital precoding in URLLC communication scenarios has achieved certain results, in millimeter wave communication, the research on hybrid precoding for URLLC communication is relatively limited. Considering the advantages of rich spectrum resources of millimeter wave communication and low cost and high energy efficiency of hybrid precoding hardware design, it is of great theoretical and application value to design an efficient hybrid precoding scheme for millimeter wave URLLC scenarios.

[0003] In order to solve the problem that signals in millimeter wave channels are easily blocked, traditional solutions usually expand the transmission range of millimeter wave communications by deploying ordinary relays. However, deploying a large number of ordinary relays will greatly increase the energy consumption and hardware cost of the system, and active relays may also cause greater signal interference. As a passive relay, reconfigurable intelligent surface (RIS) can not only reconstruct the communication environment, but also has low deployment cost and high flexibility, and has received widespread attention in academia and industry. Combining RIS with precoding technology can not only improve the performance of millimeter wave communications, but also optimize the transmission direction and phase of the beam. At present, traditional communications have fully studied key technologies such as millimeter waves, digital precoding, and intelligent reflective surfaces, but the research on these technologies in 5G URLLC scenarios is still relatively limited, and there is a lack of joint optimization of several technologies. By fully considering and jointly optimizing these technologies, the frequency efficiency performance and long-distance transmission performance of the communication system can be further improved, and the business needs of 5G URLLC scenarios can be better met. Summary of the invention

[0004] The object of the present invention is to provide a RIS-assisted millimeter wave URLLC communication system hybrid precoding design method with low hardware cost.

[0005] The technical solution to achieve the purpose of the present invention is: a RIS-assisted millimeter wave URLLC communication system hybrid precoding design method, comprising the following steps:

[0006] Step S1, establishing a RIS-assisted downlink millimeter wave URLLC communication system model, defining the achievable rate of users in the URLLC system, and establishing an optimization problem with the goal of maximizing the weighted sum of user achievable rates and with transmitter digital precoding, analog precoding and RIS phase shift matrix as variables;

[0007] Step S2, introducing auxiliary variables to simplify the objective function, and adding corresponding constraints to ensure the equivalence of the optimization problem, and then using the first-order Taylor expansion technique to transform the non-convex objective function into a convex objective function;

[0008] Step S3, fixing the RIS phase shift matrix and the transmitter analog precoding, and optimizing the transmitter digital precoding by using a continuous convex approximation technique algorithm based on first-order Taylor expansion;

[0009] Step S4, fixing the RIS phase shift matrix and the transmitter digital precoding, and optimizing the transmitter analog precoding using the minimum Euclidean distance method;

[0010] Step S5, fixing the transmitter digital precoding and analog precoding, and optimizing the RIS phase shift matrix using matrix equivalent transformation technology and continuous convex approximation algorithm;

[0011] Step S6, calculate the absolute value of the difference between the weighted sum of user achievable rates corresponding to transmitter digital precoding, transmitter analog precoding and RIS phase shift matrix before and after updating, and determine whether the absolute value is less than the set threshold: if not, return to step S3; if less, terminate the calculation and output the maximum value of the weighted sum of system user achievable rates.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) by using the first-order Taylor expansion technology, the minimum Euclidean distance method and the continuous convex approximation algorithm to update the transmitter digital precoding, the transmitter analog precoding and the RIS phase shift matrix, and calculating the corresponding user achievable rate weighted sum, a higher system achievable rate can be obtained, thereby improving the system transmission performance; (2) the calculation process is simple, the solution complexity is low, and the convergence speed is fast; (3) no new equipment is required, thereby reducing the hardware cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The present invention is a flow chart of the RIS-assisted millimeter wave URLLC communication system hybrid precoding design method. DETAILED DESCRIPTION

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0015] Combination Figure 1 The present invention provides a RIS-assisted millimeter wave URLLC communication system hybrid precoding design method, comprising the following steps:

[0016] Step S1: Establish a RIS-assisted downlink millimeter wave URLLC communication system model, define the achievable rate of users in the URLLC system, and establish an optimization problem with the goal of maximizing the weighted sum of user achievable rates and with transmitter digital precoding, analog precoding and RIS phase shift matrix as variables, as follows:

[0017] Step S1.1: Establish a RIS-assisted millimeter wave URLLC communication system model. The transmitter adopts a fully connected hybrid structure, in which the base station is configured with N t Transmit antennas, the number of RF chains is N RF , the system contains K single-antenna users, and the smart reflective surface has N reflective units;

[0018] After channel transmission, the signal received by the kth user is

[0019]

[0020] in, represents the digital precoding sent by the base station to the kth user; represents analog precoding; since the system adopts a fully connected hybrid structure, F RF Each item in satisfies the constant modulus constraint s k represents the kth modulation data symbol; n k~CN(0,σ k 2 ) means the mean is zero and the variance is σ k 2 Additive Gaussian white noise; represents the reflection coefficient matrix of RIS, θ n ∈[0,2π) and β n ∈[0,1] represent the phase shift and amplitude coefficient of the nth reflection unit of RIS respectively; in order to ensure the ability of the reflection signal, all elements of RIS are designed to maximize the reflection signal, and the amplitude of all reflection elements is set to 1, that is, β n =1; represents the reflection link channel from RIS to the kth user, represents the direct link channel from the base station to the kth user, G represents the direct link channel from the base station to the RIS;

[0021] The signal-to-noise ratio of the kth user can be expressed as

[0022]

[0023] in, represents the equivalent channel from the base station to the kth user. Therefore, the achievable rate of the kth user in the URLLC system can be expressed as

[0024]

[0025] Among them, V(γ k )=1-(1+γ k ) -2 represents the channel dispersion value from the base station to user k, and its value is related to the signal-to-noise ratio γ of user k k ε represents the decoding error probability of the user, Q -1 It represents the inverse function of Gaussian Q function, and M is used to represent the length of URLLC data block.

[0026] Step S1.2: Define the weighted sum of the achievable rates of system users as

[0027]

[0028] Among them, α k represents the weight of the achievable rate of the kth user, α k The larger the value, the higher the priority of the k-th user.

[0029] Step S1.3: Establish an optimization problem with the goal of maximizing the weighted sum of user achievable rates and with transmitter analog precoding, transmitter digital precoding and RIS phase shift matrix as variables, as follows:

[0030]

[0031] Among them, P t is the maximum transmission power of the base station, |Θ nn |=1 means that each element in the diagonal phase shift matrix of RIS must satisfy the constraint of modulus 1, |F RF (i,j)|=1 is the constant modulus constraint of the transmitter analog precoding.

[0032] Step S2: introduce auxiliary variables to simplify the objective function, add corresponding constraints to ensure the equivalence of the optimization problem, and then use the first-order Taylor expansion technique to transform the non-convex objective function into a convex objective function, as follows:

[0033] Since the unknown optimization variables Θ, F RF and f BB,k In the signal-to-noise ratio γ kIn the RIS, each unit and the transmitter analog precoding are constant modulus constraints, which makes it difficult to directly solve the optimization problem (P1). Therefore, an auxiliary variable ρ is introduced. k represents the lower limit of the signal-to-noise ratio, that is

[0034]

[0035] At this time, the reachable rate of user k in the objective function can be rewritten as

[0036]

[0037] in, is a constant term, V(ρ k )=1-(1+ρ k ) -2 is about the auxiliary variable ρ k Although the auxiliary variable ρ k Instead of the signal-to-noise ratio γ k , but the dispersion function The existence of R k It is still a non-convex and non-concave function. Considering ρ k > 0, then there must exist 1-(1+ρ k ) -2 <1, at this time V(ρ k )=1-(1+ρ k ) -2 >0, therefore, V(ρ k ) is a concave function. For the non-convex expression Using the first-order Taylor expansion technique, we can obtain The upper bound of

[0038]

[0039] in, and is a constant term, represents the last iteration ρ k The value of

[0040] Substituting (8) into (7), the achievable rate of the kth user can be re-expressed as k The relevant expression is denoted as

[0041]

[0042] The first term is about ρ k The second term is about ρ k is a linear function of is a convex function.

[0043] Based on this, the original problem (P1) can be transformed into the following optimization problem

[0044]

[0045] At this time, the objective function is a convex function. However, under the newly added constraint ρ k ≤γ k In the optimization variable F RF 、f BB,k and Θ are coupled together, and the right side of the constraint is about the optimization variable F RF 、f BB,k and Θ are not jointly concave. Furthermore, the power constraint Both the constant modulus constraint and the constant modulus constraint are not convex constraints, so the problem is still not a convex optimization problem and needs further processing. Problem (P2) is decomposed into three sub-problems and optimized alternately.

[0046] Step S3, fixing the RIS phase shift matrix and the transmitter analog precoding, and optimizing the transmitter digital precoding using a continuous convex approximation algorithm based on first-order Taylor expansion, as follows:

[0047] When the phase shift matrix Θ of RIS and the transmitter digital precoding F RF Given, with respect to the variable f BB,k The weighted sum optimization problem of the achievable rate of system users (P2) can be simplified to

[0048]

[0049] The constraints in this optimization subproblem are is a non-convex constraint. Furthermore, the non-convex constraint ρ k ≤γ k can be equivalently converted into

[0050]

[0051] Using matrix operations, the optimization variable f BB,k After extraction, formula (12) can be equivalently expressed as

[0052]

[0053] in, and is the optimization variable f BB,k Irrelevant constant matrix; the right side of the inequality in formula (13) is about the optimization variable f BB,k and ρ k It is neither convex nor concave;

[0054] To solve this problem, first define

[0055]

[0056] Where A is a semi-positive definite matrix, r>0.

[0057] For formula (14), Performing a first-order Taylor expansion at the point, we can obtain

[0058]

[0059] The inequality holds because f A (x,r) is convex with respect to x and r. Therefore, the constraint ρ k ≤γ k can be rewritten as

[0060]

[0061] At this time, the non-convex constraint (13) is converted to a convex constraint (16), and the optimization problem (P2-1) can be converted to

[0062]

[0063] The optimization problem (P2-1') is a convex optimization problem. For a given feasible The optimization problem (P2-1') can be solved by convex optimization tools (such as CVX).

[0064] Step S4, fixing the RIS phase shift matrix and the transmitter digital precoding, and optimizing the transmitter analog precoding using the minimum Euclidean distance method, as follows:

[0065] Since each unit in analog precoding is constant modulus, solving analog precoding directly from the optimization problem (P2) is a complex process. Therefore, the present invention adopts the idea of ​​minimizing the Euclidean distance between hybrid precoding and full digital precoding to design analog precoding. The optimization problem is:

[0066]

[0067] in, is a matrix composed of K transmitter digital precoding, W is full digital precoding, which can be used with F BB After expanding the objective function in problem (P3) and removing the constant term, we get the following optimization problem:

[0068]

[0069] Definition, μ = [vec(F RF );1] is the matrix variable F RFAfter column vectorization, the column vector composed of 1 is and X = F BB W H is the variable F RF After matrix operations, problem (P4) can be reformulated as

[0070]

[0071] in, is a constant matrix independent of the variable μ, ν max is the maximum eigenvalue corresponding to the matrix Ψ. At this point, the objective function of problem (P5) is convex with respect to the variable μ, but the max convex function is still a non-convex problem. Therefore, it is necessary to transform the objective function into a linear function. Using the first-order Taylor expansion, the objective function of problem (P5) can be further expressed as

[0072]

[0073] in, is the result of the previous iteration. Removing the constant term on the right side of equation (21), the optimization problem (P5) is simplified to

[0074]

[0075] The optimal solution to problem (P6) is

[0076]

[0077] According to the result μ, the transmitter simulation precoding F can be obtained RF .

[0078] Step S5: fix the transmitter digital precoding and analog precoding, and optimize the RIS phase shift using a continuous convex approximation algorithm, as follows:

[0079] Given the transmitter digital precoding f BB,k and simulated precoding F RF After that, the optimization problem (P2) can be simplified to

[0080]

[0081] definition, is the vector composed of the diagonal elements of the RIS phase shift matrix, u=[v;1] is the row vector composed of the vector v and 1, is the equivalent channel of the kth user. Based on this, the non-convex constraint ρ in problem (P2-2) k ≤γ k can be equivalently converted into

[0082]

[0083] By performing an equivalent transformation on formula (25), we can obtain

[0084]

[0085] in, and is a constant matrix independent of the optimization variable u. At this time, the right side of the inequality in equation (26) is still non-convex and non-concave. According to the transformation of equations (14) and (15), equation (26) is further expressed as

[0086]

[0087] At this time, equation (27) is a convex constraint on the optimization variable u. Since the RIS phase shift constraint is a non-convex constant modulus constraint, after relaxing this constraint, the optimization problem (P2-2) can be re-expressed as

[0088]

[0089] The optimization problem (P2-2') is a convex optimization problem, which can be solved efficiently by convex optimization tools (such as CVX). Finally, in order to recover the constant modulus constraint, the RIS phase shift can be expressed as

[0090]

[0091] Among them, ∠(.) represents the radian value of the complex phase angle, and the phase shift matrix Θ of RIS can be obtained according to u.

[0092] Step S6, calculating the absolute value of the difference between the weighted sum of the user achievable rates corresponding to the transmitter digital precoding, the transmitter analog precoding and the RIS phase shift matrix before and after updating, until the termination condition is met, as follows:

[0093] Step S6.1, calculating the absolute value of the difference between the weighted sum of user achievable rates corresponding to transmitter digital precoding, transmitter analog precoding and RIS phase shift matrix before and after updating;

[0094] Step S6.2: Compare the absolute value of the difference between the weighted sums of the user achievable rates and the set value. If it is greater than the set value, return to step 3; if it is less than the set value, terminate the calculation and output the maximum value of the weighted sum of the system user achievable rates.

Claims

1. A RIS-assisted millimeter wave URLLC communication system hybrid precoding design method, characterized in that: The following steps are involved: Step S1, establishing a RIS-assisted downlink millimeter wave URLLC communication system model, defining the achievable rate of users in the URLLC system, and establishing an optimization problem with the goal of maximizing the weighted sum of user achievable rates and with transmitter digital precoding, analog precoding and RIS phase shift matrix as variables; Step S2, introducing auxiliary variables to simplify the objective function, and adding corresponding constraints to ensure the equivalence of the optimization problem, and then using the first-order Taylor expansion technique to transform the non-convex objective function into a convex objective function; Step S3, fixing the RIS phase shift matrix and transmitter analog precoding, and optimizing the transmitter digital precoding by using a continuous convex approximation technique based on first-order Taylor expansion; Step S4, fixing the RIS phase shift matrix and the transmitter digital precoding, and optimizing the transmitter analog precoding using the minimum Euclidean distance method; Step S5, fixing the transmitter digital precoding and analog precoding, and optimizing the RIS phase shift matrix using matrix equivalent transformation technology and continuous convex approximation algorithm; Step S6, calculate the absolute value of the difference between the weighted sum of user achievable rates corresponding to transmitter digital precoding, transmitter analog precoding and RIS phase shift matrix before and after updating, and determine whether the absolute value is less than the set threshold: if not, return to step S3; if less, terminate the calculation and output the maximum value of the weighted sum of system user achievable rates.

2. The RIS-assisted millimeter wave URLLC communication system hybrid precoding design method according to claim 1, characterized in that: The RIS-assisted downlink millimeter wave URLLC communication system model described in step S1 is established, the achievable rate of the user in the URLLC system is defined, and an optimization problem is established with the goal of maximizing the weighted sum of the user's achievable rate and with the transmitter digital precoding, analog precoding and RIS phase shift matrix as variables, as follows: Step S1.1: Establish a RIS-assisted millimeter wave URLLC communication system model. The transmitter adopts a fully connected hybrid structure, in which the base station is configured with N t Transmit antennas, the number of RF chains is N RF , the system contains K single-antenna users, and the smart reflective surface has N reflective units; After channel transmission, the signal received by the kth user is in, represents the reflection link channel from RIS to the kth user; represents the reflection coefficient matrix of RIS, θ n ∈[0,2π) and β n ∈[0,1] represent the phase shift and amplitude coefficient of the nth reflection unit of RIS respectively; in order to ensure the ability of the reflection signal, all elements of RIS are designed to maximize the reflection signal, and the amplitude of all reflection elements is set to 1, that is, β n =1; G represents the direct link channel from the base station to the RIS; represents the direct link channel from the base station to the kth user; represents analog precoding; since the system adopts a fully connected hybrid structure, F RF Each item in satisfies the constant modulus constraint s k represents the kth modulation data symbol; n k ~CN(0,σ k 2 ) means the mean is zero and the variance is σ k 2 Additive Gaussian white noise; represents the digital precoding sent by the base station to the kth user; The signal-to-noise ratio of the kth user is expressed as in, represents the equivalent channel from the base station to the kth user; the achievable rate of the kth user in the URLLC system is expressed as Among them, V(γ k )=1-(1+γ k ) -2 represents the channel dispersion value from the base station to user k. The channel dispersion value is related to the signal-to-noise ratio γ of user k. k ε represents the decoding error probability of the user, Q -1 represents the inverse function of the Gaussian Q function, and M is used to characterize the length of the URLLC data block; Step S1.2: Define the weighted sum of the achievable rates of system users as Among them, α k represents the weight of the achievable rate of the kth user, α k The larger the value, the higher the priority of the k-th user; Step S1.3: Establish an optimization problem with the goal of maximizing the weighted sum of user achievable rates and with transmitter analog precoding, transmitter digital precoding and RIS phase shift matrix as variables, as follows: Among them, P t is the maximum transmission power of the base station, |Θ nn |=1 means that each element in the diagonal phase shift matrix of RIS must satisfy the constraint of modulus 1, |F RF (i,j)|=1 is the constant modulus constraint of the transmitter analog precoding.

3. The RIS-assisted millimeter wave URLLC communication system hybrid precoding design method according to claim 2, characterized in that: The introduction of auxiliary variables in step S2 simplifies the objective function, and adds corresponding constraints to ensure the equivalence of the optimization problem. Then, the first-order Taylor expansion technique is used to transform the non-convex objective function into a convex objective function, as follows: Since the unknown optimization variables Θ, F RF and f BB,k In the signal-to-noise ratio γ k In the RIS, each unit and the transmitter analog precoding are constant modulus constraints, which makes it difficult to directly solve the optimization problem (P1). Therefore, an auxiliary variable ρ is introduced. k Represents the lower limit of the signal-to-noise ratio, that is: At this time, the achievable rate of user k in the objective function is rewritten as: in, is a constant term, V(ρ k )=1-(1+ρ k ) -2 is about the auxiliary variable ρ k function; although the auxiliary variable ρ k Instead of the signal-to-noise ratio γ k , but the dispersion function The existence of R k It is still a non-convex and non-concave function; considering ρ k > 0, then there must exist 1-(1+ρ k ) -2 <1, at this time V(ρ k )=1-(1+ρ k ) -2 >0, therefore, V(ρ k ) is a concave function; for the non-convex expression Using the first-order Taylor expansion, we can obtain The upper bound of is: in, and is a constant term, represents the last iteration ρ k The value of Substituting (8) into (7), the achievable rate of the kth user is re-expressed as k The relevant expression is denoted as The first term is about ρ k The second term is about ρ k is a linear function of is a convex function Based on this, the original problem (P1) is transformed into the following optimization problem At this time, the objective function is a convex function; but under the newly added constraint ρ k ≤γ k In the optimization variable F RF 、f BB,k and Θ are coupled together, and the right side of the constraint is about the optimization variable F RF 、f BB,k and Θ are not jointly concave. Furthermore, the power constraint Both the constant modulus constraint and the constant modulus constraint are not convex constraints, so the problem is still not a convex optimization problem. Problem (P2) is decomposed into three sub-problems and optimized alternately.

4. The RIS-assisted millimeter wave URLLC communication system hybrid precoding design method according to claim 3, characterized in that: The fixed RIS phase shift matrix and transmitter analog precoding described in step S3 optimize the transmitter digital precoding using a continuous convex approximation technique algorithm based on first-order Taylor expansion, as follows: When the phase shift matrix Θ of RIS and the transmitter digital precoding F RF Given, with respect to the variable f BB,k The weighted sum optimization problem of the achievable rate of system users (P2) is simplified to Constraints in optimization problems is a non-convex constraint; further, the non-convex constraint ρ k ≤γ k The equivalent transformation is: Using matrix operations, the optimization variable f BB,k After extraction, formula (12) is equivalent to: in, and is the optimization variable f BB,k Irrelevant constant matrix; the right side of the inequality in formula (13) is about the optimization variable f BB,k and ρ k It is neither convex nor concave; To solve this problem, first define Where A is a semi-positive definite matrix, r>0; For formula (14), Performing a first-order Taylor expansion at the point, we get The inequality holds because f A (x,r) is convex with respect to x and r; therefore, the constraint ρ k ≤γ k is rewritten as At this time, the non-convex constraint (13) is converted to a convex constraint (16), and the optimization problem (P2-1) is converted to The optimization problem (P2-1') is a convex optimization problem. For a given feasible The optimization problem (P2-1') is solved by convex optimization tools (such as CVX).

5. The RIS-assisted millimeter wave URLLC communication system hybrid precoding design method according to claim 4, characterized in that: The fixed RIS phase shift matrix and transmitter digital precoding described in step S4 are optimized using the minimum Euclidean distance method for transmitter analog precoding, as follows: The idea of ​​minimizing the Euclidean distance between hybrid precoding and full digital precoding is used to design analog precoding. The optimization problem is: in, is a matrix composed of K transmitter digital precoding, W is the full digital precoding; after expanding the objective function in problem (P3) and removing the constant term, the following optimization problem is obtained Definition, μ = [vec(F RF );1] is the matrix variable F RF After column vectorization, the column vector composed of 1 is and X = F BB W H is the variable F RF After matrix operations, the problem (P4) is reformulated as follows: in, is a constant matrix independent of the variable μ, ν max is the maximum eigenvalue corresponding to the matrix Ψ; at this time, the objective function of problem (P5) is convex with respect to the variable μ, but the max convex function is still a non-convex problem, and the objective function needs to be converted into a linear function. Using the first-order Taylor expansion, the objective function of problem (P5) is further expressed as: in, is the result of the previous iteration. By removing the constant term on the right side of equation (21), the optimization problem (P5) is simplified to: The optimal solution to problem (P6) is According to the result μ, the transmitter simulated precoding F is obtained RF .

6. The RIS-assisted millimeter wave URLLC communication system hybrid precoding design method according to claim 5, characterized in that: The fixed transmitter digital precoding and analog precoding described in step S5 utilize a continuous convex approximation algorithm to optimize the RIS phase shift, as follows: Given the transmitter digital precoding f BB,k and simulated precoding F RF After that, the optimization problem (P2) is simplified to: definition, is the vector composed of the diagonal elements of the RIS phase shift matrix, u=[v;1] is the row vector composed of the vector v and 1, is the equivalent channel of the kth user; based on this, the non-convex constraint ρ in problem (P2-2) k ≤γ k The equivalent transformation is: By performing equivalent transformation on formula (25), we can obtain: in, and is a constant matrix independent of the optimization variable u. At this time, the right side of the inequality in equation (26) is still non-convex and non-concave. According to the transformation of equations (14) and (15), equation (26) is further expressed as: At this time, equation (27) is a convex constraint on the optimization variable u. Since the RIS phase shift constraint is a non-convex constant modulus constraint, after relaxing the constraint, the optimization problem (P2-2) is reformulated as: The optimization problem (P2-2') is a convex optimization problem, which can be solved efficiently by convex optimization tools. In order to restore the constant modulus constraint, the RIS phase shift is expressed as Among them, ∠(.) represents the radian value of the complex phase angle, and the phase shift matrix Θ of RIS is obtained according to u.

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