A group construction method of a distributed adjustable intelligent metasurface

Abstract

The application provides a distributed adjustable intelligent metasurface group construction method, specifically, IRS is arranged around a base station as a supplement of a 6G network, a deployment area of the IRS is determined according to a position of the base station and a service user range; information of the user is acquired, and the number of the IRS is determined according to the number of the users in the service range of the base station; then a beamforming and phase optimization algorithm is introduced, the single-face orientation restriction of the IRS is considered, coordinate parameters of the user are acquired, distribution characteristics of the user are obtained through statistical analysis, and whether the distribution position of the user is at an edge position of the service range of the base station is determined to determine whether a distributed deployment or a centralized deployment is adopted; the coordinates of the IRS are initialized, initial deployment is carried out, the optimal coordinates of each IRS are obtained through continuous iteration optimization, distributed IRS group construction is completed, and different IRS groups exist for each user due to different position information, so that the user is provided with service.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a distributed group construction method for tunable smart metasurfaces in future sixth-generation (6G) mobile communications. Background Technology

[0002] Currently, intelligent metasurfaces, also known as intelligent reflective surfaces (IRS), have become one of the hot research technologies in 6G. They have the following advantages: low cost, as IRS does not need to have receiving and transmitting capabilities compared to traditional relay equipment, only the ability to reflect signals; reconfigurable channels, as IRS actively controls the reflected signals by controlling the reflective units on it, thus reconfiguring the channel between the user and the base station; and flexible deployment, as IRS is a flat thin plate that does not require other additional equipment such as power amplifiers or processors, and can be deployed on the exterior surface of buildings.

[0003] When configuring an IRS, the factors that are usually considered are: the number of IRSs, the number of reflective units on the IRS, and the location of the IRS. Common deployment methods include centralized deployment, where multiple reflective units are concentrated on a single IRS, and distributed deployment, where multiple reflective units are distributed across multiple IRS panels.

[0004] While centralized deployment, which is typically considered, can bring better capacity or overall speed improvements, it widens the service gap between central and edge users, making it difficult to guarantee the service quality of edge users and compromising fairness for all users in the system. In contrast, distributed deployment, although requiring fewer reflection units per IRS, can increase the probability of connection between the IRS and users, thereby increasing the channel capacity for users.

[0005] The flexible deployment and reflection characteristics of IRS bring richer network resources and ubiquitous access opportunities. Adjusting the distribution of IRS in the network according to user needs can robustly guarantee the quality of service for network users. However, the addition of IRS makes the interference topology more complex. At the same time, the cascaded channel of base station-IRS-user will also make the signal processing of joint base station and IRS more complex. The intelligent metasurface introduces cascaded channels into the original channel, which changes the mathematical structure of the original beamforming algorithm. Joint beamforming design and phase optimization are required. Therefore, it is necessary to construct groups of IRS and optimize the algorithm.

[0006] Based on this, the present invention establishes an adjustable distribution model according to the user distribution parameters and considering the total system throughput, and constructs groups considering the orientation of IRS, so as to serve users with multiple IRS, ensure the overall service quality of users, and improve system performance. Summary of the Invention

[0007] This invention proposes a method for constructing a distributed tunable smart metasurface group. Specifically, firstly, the deployment area of ​​the IRS is determined based on the location of the base station; then, the number of IRSs is determined based on the number of users; next, a beamforming and phase optimization algorithm is introduced, considering the single-face orientation limitation of the IRS, and the deployment method is determined based on the distribution location of the users; finally, the deployment location of the IRS is determined by iterative optimization based on the user's coordinate information, thus completing the construction of the distributed IRS group. For each user, due to different location information, there are different IRS groups providing services to them.

[0008] The IRS configuration method of the present invention includes the following steps:

[0009] Step 200: Determine the deployment area of ​​the IRS based on the location of the base station.

[0010] Let the service range of the base station be a circle with radius r0, with the base station at the center. Users are randomly distributed on an inner circle with radius λ2r0 (0 < λ2 < 1) and outer circle with radius r0. The deployment area of ​​the IRS is within this circle with radius r0 centered on the base station. Within this circle, this invention further introduces the parameter λ1 (0 < λ1 < 1) to make the IRS evenly distributed on a circle with radius λ1r0.

[0011] Step 210: Determine the number of IRSs based on the number of users.

[0012] An IRS, through beamforming design, can serve multiple users. Assuming a single IRS can serve a maximum of K0 users, the number of users K within the area is obtained based on... Determine the number of IRS, N. Where N represents... Round up.

[0013] Considering the one-sided reflection characteristic of IRS, meaning it can only serve users on the same side as the base station, a service cluster of IRS is introduced. The criteria for determining this user cluster are:

[0014]

[0015] Where D(i,o) represents the distance between user i and the base station, cos(θ) i,j )=(λ1 2 r0 2 +D 2 (i,j)-D 2 (i,o)) / (2λ1r0D(i,j)), where D(i,j) represents the distance between user i and smart metasurface j.

[0016] if The number of IRSs is then N. If this condition is not met, let N = N + 1 and re-evaluate the condition. Until this condition is met.

[0017] Step 220: Next, a beamforming and phase optimization algorithm is introduced, taking into account the single-face orientation limitation of the IRS, and the deployment method is determined according to the distribution location of the users.

[0018] This invention proposes an algorithm to determine the deployment method of an IRS, specifically, to decide whether to adopt a centralized or distributed deployment based on user distribution characteristics. The following problem is constructed and solved, with the overall network throughput as the optimization objective and the beamforming matrix V and phase matrix Φ as the optimization variables:

[0019]

[0020] st

[0021]

[0022] In the objective function of this optimization problem, α i Characterizing user fairness, R i It is the user's speed, V i This is the phase matrix of the IRS. The optimization objective function is the total network throughput, assuming fairness for all users, i.e., α. i All are equal to 1, and the constraint P is the total power of the base station, that is, the total power transmitted to users must be lower than the total power of the base station.

[0023] Note that the objective function in the optimization problem is non-convex, making it an NP-hard problem. Therefore, an auxiliary weight matrix W associated with user i is introduced. i The optimization problem can be equivalent to the following problem:

[0024]

[0025] st

[0026]

[0027] 0≤θ j,n ≤2π,n=1,...,N,j=1,...,J

[0028] The optimization problem is solved by iteratively employing an alternating optimization algorithm until convergence. This optimization problem is divided into two subproblems: optimizing the beamforming matrix with a fixed phase matrix and optimizing the phase matrix with a fixed beamforming matrix. Let D be the number of iterations of the alternating optimization algorithm, d1 be the number of iterations of the beamforming matrix with a fixed phase matrix, and d2 be the number of iterations of the phase matrix with a fixed beamforming matrix.

[0029] By adjusting different λ1 and λ2 parameters and different values ​​of J and N, user sum rate diagrams can be obtained under different scenarios. From the results of these simulation diagrams, corresponding conclusions can be drawn to guide the deployment of IRS. If users are randomly distributed, they should be deployed near the base station using a centralized deployment method; if users are distributed at the edge of the base station's service range, they should be deployed far away from the base station using a distributed deployment method.

[0030] Step 230: Based on the user's coordinate information, continuously iterate and optimize to determine the deployment location of the IRS, and complete the construction of the distributed IRS group.

[0031] Obtain the coordinate information of each user. Each user has an IRS that serves them, and the user clusters of the IRS... It is possible to obtain the IRS service cluster J of user i. i Find the minimum sum of distances between user i and smart metasurface j, i.e. At this point, the IRS is closest to the users it serves, resulting in the best performance. Therefore, it is necessary to iteratively update the coordinates of the j-th IRS until the optimal solution to this problem is obtained. At this point, the sum of distances between all users i and the smart metasurface j is minimized, the user sum and rate are maximized, and the user experience is best. Finally, the deployment locations of the IRSs are determined, and the IRS group construction is completed. For each user, due to different location information, there are different IRS groups providing services to them.

[0032] Beneficial effects

[0033] This invention proposes a group construction method for IRS from the perspective of user experience fairness. Firstly, it proposes a method for determining the regional deployment of IRS based on user distribution range, and then proposes a method for determining the number of IRS and a deployment strategy.

[0034] This invention takes into account the function of an IRS that can serve multiple users through beamforming design, and also considers the single-sided reflection characteristics of the IRS. Therefore, it proposes the concept of user cluster to characterize the set of users that the IRS can serve.

[0035] Regarding the choice of deployment method, simulation results show that when users are distributed at the edge, distributed IRS deployment has a higher total system throughput than centralized IRS deployment. Adding reflection units increases the number of independent sub-channels in the IRS cascaded channel under the distributed IRS deployment method, which already has a high connection probability, resulting in higher channel diversity gain and faster channel capacity growth. However, for randomly distributed users, since distributed deployment makes it difficult to guarantee proximity to users, while centralized IRS deployment can guarantee proximity to the base station, resulting in lower cascaded link path loss, centralized IRS deployment inherently has a higher total system throughput than distributed IRS deployment. Adding reflection units improves the channel link conditions for each served user, increases channel gain, and leads to faster growth in the total system throughput of centralized IRS deployment. Attached Figure Description

[0036] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings:

[0037] Figure 1 This is a schematic diagram of the network model using an IRS-assisted base station according to the present invention;

[0038] Figure 2 This is a flowchart illustrating the algorithm implementation of the present invention;

[0039] Figure 3 This is a comparison chart of the effects of centralized and distributed deployments when the user is at the edge;

[0040] Figure 4 This is a comparison chart of the effects of centralized and distributed deployments when users are randomly distributed. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings.

[0042] A schematic diagram of the network model using an IRS-assisted base station of the present invention is attached. Figure 1 As shown in the diagram, the base station is located at the center of the circle, and the service range of the base station is a circle with radius r0. Users are randomly distributed on an inner circle with radius λ2r0 (0<λ2<1) and outer circle with radius r0.

[0043] The algorithm flow for this case is attached. Figure 2 As shown, the specific implementation steps are as follows:

[0044] Step 300: Determine the deployment area of ​​the IRS based on the location of the base station.

[0045] After obtaining the location information of the base station, it can be determined that the deployment area of ​​the IRS is within this circle with the base station as the center and a radius of r0. Within this circle, the parameter λ1 (0 < λ1 < 1) is further introduced to make the IRS evenly distributed on the circle with a radius of λ1r0.

[0046] Step 310: Determine the number of IRSs based on the number of users.

[0047] An IRS, through beamforming design, can serve multiple users. Assuming a single IRS can serve a maximum of K0 users, the number of users K within the area is obtained based on... Determine the number of IRS, N. Where N represents... up Rounding

[0048] Considering the one-sided reflection characteristic of IRS, which means it can only serve users on the same side as the base station, a service cluster of IRS is introduced. The criteria for determining this user cluster are:

[0049]

[0050] Where D(i,o) represents the distance between user i and the base station, cos(θ) i,j )=(λ1 2 r0 2 +D 2 (i,j)-D 2 (i,o)) / (2λ1r0D(i,j)), where D(i,j) represents the distance between the user and the smart metasurface j.

[0051] Considering deployment costs, we need to know the minimum number of IRSs required. Therefore, if the requirements are met... The number of IRSs is then N. If this condition is not met, let N = N + 1 and re-evaluate the condition. Until this condition is met.

[0052] Step 320: Next, a beamforming and phase optimization algorithm is introduced, taking into account the single-face orientation limitation of the IRS, and the deployment method is determined according to the distribution location of the users.

[0053] First, let's explain the concepts of centralized and distributed deployment. There are J IRSs in total, and each IRS has N reflection units. Let J*N = C0, where C0 is a fixed constant, which can be set to 100 here. Then, J = 1, N = 100 is a centralized deployment, and J = 100, N = 1 or J = 500, N = 2 is a distributed deployment.

[0054] The distribution location of users reveals their distribution characteristics, such as whether they are located at the edge of the base station. This invention proposes an algorithm to determine the deployment method of the IRS. Using the total network throughput as the optimization objective, and the optimization variables being the beamforming matrix V at the base station and the phase matrix Φ of the IRS, the following optimization problem is established and solved to determine the IRS deployment method. Let the channel state information between the base station and user i be... The channel state information between the base station and the smart metasurface j is And the channel state information between the smart metasurface j and user i is The phase of the N reflective units of the intelligent metasurface j is The beamforming matrix of the base station for user i is expressed in the form of: And transmit data vector S i Then user i receives signal y i It can be represented as

[0055]

[0056] in Let i be the noise vector at user i, satisfying This represents the noise variance.

[0057] Consider the received signal at user i passing through a linear receiver filter. The estimated signal vector after that is Due to the received signal y i and noise n i They are independent of each other, and the mean squared error (MSE) at user i can be expressed as:

[0058]

[0059] in The covariance matrix of the signal received at user i:

[0060]

[0061] Where N i Let be the covariance matrix of the interference and noise signal received at user i.

[0062] Minimize the mathematical representation as Tr(E) i The receiving filter for the MSE matrix is ​​MMSE receiver:

[0063]

[0064] Therefore, use The MSE matrix is

[0065]

[0066] Then the achievable rate for user i can be expressed as:

[0067]

[0068] With the total network throughput as the optimization objective, and the optimization variables being the beamforming matrix V and the phase matrix Φ, the optimization problem is as follows:

[0069]

[0070] st

[0071]

[0072] In the objective function of this optimization problem, α i To characterize user fairness, when the optimization objective function in this chapter is the network throughput formula, all users are fair, i.e., α. i All are equal to 1, and the constraint P is the total power of the base station, that is, the total power transmitted to users must be lower than the total power of the base station.

[0073] Note that the objective function in the optimization problem is non-convex, making it an NP-hard problem. Therefore, an auxiliary weight matrix W associated with user i is introduced. i The optimization problem can be equivalent to the following problem:

[0074]

[0075] st

[0076]

[0077] 0≤θ j,n ≤2π,n=1,...,N,j=1,...,J

[0078] The optimization problem is solved by iteratively employing an alternating optimization algorithm until convergence. This optimization problem is divided into two subproblems: optimizing the beamforming matrix with a fixed phase matrix and optimizing the phase matrix with a fixed beamforming matrix. Let D be the number of iterations for the alternating optimization algorithm, d1 be the number of iterations for the beamforming matrix with a fixed phase matrix, and d2 be the number of iterations for the phase matrix with a fixed beamforming matrix.

[0079] Given a phase matrix Φ, for a variable U i W i V i When the matrix sets of any two variables are fixed, if the objective function of the subproblem is concave with respect to the other variable, the optimal solution for the other variable can be obtained based on the first-order condition for a convex function. Given a beamforming matrix... Obtain the receiver matrix and auxiliary weight matrix The optimal solution is found where d2 = 0 in the subproblem of optimizing the beamforming matrix with fixed phase. Then... and And the mathematical symbols within it can be represented as

[0080]

[0081]

[0082]

[0083]

[0084] Then fix and Calculate the optimal weight matrix The objective function is rewritten as a function of V for optimization.

[0085]

[0086] st

[0087]

[0088] Since the objective function in this problem is related to V i Since it is convex, V can be obtained by differentiating the Lagrange function. i The optimal solution. Decoupling the Lagrange function, the equation with respect to V... i The function can be written as

[0089]

[0090] Based on Lagrange's first-order optimization conditions, V i By taking the derivative, we can obtain the result for Beamforming matrix V i Mathematically represented as

[0091]

[0092]

[0093] Additionally, for users Where 0 satisfies the complementary relaxation condition of the power constraint, and the beamforming matrix V i For a function of λ, to maximize the satisfaction of the power constraint, it needs to satisfy...

[0094]

[0095] Furthermore, the above equation is equivalent to (Λ+λ).-2 Θ = P, that is

[0096] Where Λ and Θ are respectively represented as

[0097]

[0098]

[0099] The above equation shows that the problem of solving Lagrange multipliers using power constraints can be solved. Since it is a decreasing function of λ, the optimal value of λ can be obtained using the bisection method. The maximum number of iterations for this beamforming optimization algorithm is... At this point, it can be calculated that... and

[0100] Optimize the phase matrix with a fixed beamforming matrix, when given and Then the objective function of the optimization problem can be transformed into a function with the phase matrix Φ as the variable. Note that... Ignoring terms in the objective function that are independent of the phase matrix, we can obtain its simplified form and formulate the optimization problem as follows:

[0101]

[0102] st0≤θ j,n ≤2π,n=1,...,N,j=1,...,J

[0103] The objective function can be transformed and decoupled into phase Φ. j The function can be obtained

[0104]

[0105] in, This demonstrates the influence of the IRS user service cluster on the algorithm, and some of its parameters can be expressed as follows:

[0106]

[0107]

[0108]

[0109] definition That is, the phase matrix Φ j By vectorizing the objective function, the objective function can be transformed into...

[0110]

[0111] in definition It is possible to obtain a simplified objective function form and establish the optimization problem as follows:

[0112]

[0113]

[0114] Where F and K are positive semi-definite matrices, Ξ is also a positive semi-definite matrix. Due to the constraints, this problem is non-convex, and the Riemann conjugate gradient method is used to solve it.

[0115] Note that the search space of the problem to be solved is the product of N circles in the complex plane. The Riemannian manifold, mathematically represented as

[0116]

[0117] Then the tangent space of a point φ on the manifold is

[0118]

[0119] Among all the tangent vectors, similar to Euclidean space, one vector associated with the negative Riemann gradient represents the direction of maximum decrease of a function. The Riemann gradient at point φ on this manifold... It is based on the Euclidean gradient In tangent space The tangent vector is given by the orthogonal projection onto the surface.

[0120]

[0121] After obtaining the Riemann gradient, it is necessary to know the search method for gradient descent. And the step size β. The update criterion for the search direction of the conjugate gradient in Euclidean space is given. Furthermore, note that each point in a Riemannian manifold corresponds to its own tangent space, thus involving different tangent spaces. and Operations between two vectors cannot be directly combined between these two spaces; a mapping between two tangent vectors in different tangent spaces is required, called a transformation factor. In this manifold space, the transformation factor between two tangent vectors in different tangent spaces is...

[0122]

[0123] Obtain the direction vector

[0124]

[0125] in To achieve faster convergence, the Polak-Ribiere parameter can be used.

[0126] Finally, the vector is mapped from the tangent space to the manifold itself.

[0127]

[0128] The optimized vector is obtained as

[0129]

[0130] in The Armijo backtracking step size is used to search for the target function, which eventually converges to the point where the Riemann gradient is zero. This algorithm utilizes the well-known Armijo backtracking step size and Polak-Ribiere parameters to ensure that the objective function does not increase in each iteration.

[0131] The beamforming design algorithm process is summarized as follows:

[0132] Step 1: Obtain user distribution parameters I, λ2, and the specific distribution location of each user; obtain IRS distribution parameters J and λ1; and based on the users and IRS distribution parameters, establish the service user cluster of IRSj as follows:

[0133] Step 2: Based on the above input parameters and formulas, establish an adjustable IRS distribution model and obtain the channel model.

[0134] Step 3: First, initialize the alternation iteration count D = 0, the beamforming matrix iteration count d1 = 0, and the maximum convergence count. The number of iterations of the phase matrix d2 = 0 and the maximum number of convergences Beamforming matrix And make it satisfy Phase Matrix Then the beamforming matrix and phase matrix are iterated alternately at D = 0, 1, 2, ..., D max Fixed phase matrix Beamforming matrix iteration Substitution Computational optimization Substitution Computational optimization renew

[0135] Step 4: d1←d1+1, if Then return to step three; otherwise, stop the iteration; fix the beamforming matrix. Phase matrix iteration Substitution D i,j F j,l,i and K j,l Furthermore, solve for the Euclidean gradient. The Riemann gradient is then obtained, and η0 is initialized to -gradf(φ). (D,0) Select Armijo backtracking search step size. Seeking Solving the Euclidean gradient Further obtain the Riemann gradient Find the transformation factor between tangent vectors in different tangent spaces. Choose the Polak-Ribiere parameters. And obtain the direction vector

[0136] Step 5: d2←d2+1, if If the iteration fails, return to step four; otherwise, stop the iteration.

[0137] Step Six: If D≤D max If the value is -1, return to step two; otherwise, stop iterating.

[0138] By adjusting different λ1r0 parameters and different values ​​of J and N, user sum-rate diagrams under different scenarios can be obtained, as shown in the attached figure. Figure 3 As shown, users are distributed at the edge of the base station's service range. A distributed deployment, with the IRS also deployed at the edge of the base station, can achieve maximum user speed. (See attached image.) Figure 4 As shown, users are distributed within the service area of ​​the base station. By adopting a centralized deployment and placing the IRS around the base station, the maximum user rate can be achieved.

[0139] Step 330: Based on the user's coordinate information, continuously iterate and optimize to determine the deployment location of the IRS, and complete the construction of the distributed IRS group.

[0140] Obtain the coordinate information of each user. Each user has an IRS that serves them, and the user clusters of the IRS... It is possible to obtain the IRS service cluster J of user i. i Find the minimum sum of distances between user i and smart metasurface j, i.e. At this point, the IRS is closest to the user it serves, resulting in the best performance. Therefore, it is necessary to continuously iterate and update the coordinates of the j-th IRS until the optimal solution to this problem is obtained. At this point, the coordinates of each IRS represent its optimal deployment location. This completes the construction of the optimized group of distributed, adjustable IRSs. For each user, due to different location information, a different IRS group provides services to them.

Claims

1. A group construction method of a distributed adjustable intelligent metasurface, characterized in that, Comprise: Inter-Reference Servers (IRS) are deployed around base stations as a supplement to 6G networks. The deployment area of ​​the IRS is determined based on the base station's location, the IRS's orientation, and the range of users it serves. User information and IRS user clusters are obtained. The number of IRSs is determined based on the number of users (K) within the base station's service range. The specific method for obtaining IRS user clusters is to consider the one-sided reflection characteristic of the IRS, meaning it can only serve users on the same side as the base station. The angular characteristics of the IRS and users are then introduced to obtain the IRS user clusters. The criteria for determining this user cluster are: ,in, Indicates user Distance to base station , This represents the distance between the metasurface and the base station. , Indicates user and intelligent reflective surface The distance between them; obtaining the user's coordinate information, and using beamforming and phase optimization algorithms to determine the IRS deployment method, specifically, taking the total network throughput as the optimization objective, and the optimization variables as the beamforming matrix V and the phase matrix Φ, yields the following optimization problem: ,in Characterizes user fairness, It is the user's speed. It is the beamforming matrix of the base station for user i, which is fair to all users, i.e. All values ​​are equal to 1, and the constraint P is the total power of the base station, meaning the total power transmitted to users must be lower than the total power of the base station. An alternating optimization algorithm is used iteratively until convergence is achieved, solving this optimization problem. This optimization problem is divided into two subproblems: optimizing the beamforming matrix with a fixed phase matrix and optimizing the phase matrix with a fixed beamforming matrix. Let D be the number of iterations for the alternating optimization algorithm, and let the number of iterations for optimizing the beamforming matrix with a fixed phase matrix be... The number of iterations for optimizing the phase matrix with a fixed beamforming matrix is: By adjusting different parameters The values ​​of the number of IRS J and the number of reflection units N per IRS can be used to obtain the sum rate map of users in different scenarios. If the sum rate map shows that users are randomly distributed, then the IRS should be deployed in a centralized manner near the base station. If the user is distributed at the edge of the base station service range, far away from the base station, the IRS distributed deployment is adopted; according to the determined IRS deployment mode, the coordinates of the IRS are initialized, initial deployment is carried out, and the optimal position of each IRS is obtained through continuous iteration optimization of related parameters, and the distributed IRS group construction is completed.

2. The method of claim 1, wherein, Considering the circular service range of the base station, the deployment area of the IRS is determined according to the position of the base station and the service range of the base station, assuming that the service range of the base station is a circle with a radius of , and the base station is located at the center of the circle, and the users are randomly distributed on the annulus with an inner circle radius of and an outer circle radius of .

3. The method of claim 1, wherein, The number of IRSs is determined according to the number of users, assuming that a single IRS can serve users at most, the number of users in the area is obtained , and the number of IRSs is determined as , where represents the ceiling.

4. The method of claim 1, wherein, The optimal position of each IRS is obtained through continuous iteration optimization, that is, the coordinate information of each user is obtained, each user has an IRS serving it, and the user cluster of the IRS The IRS service cluster of user i can be obtained The minimum distance sum between user i and intelligent reflecting surface j is calculated, that is, At this time, the IRS is closest to the user it serves, the communication effect is best, and the service quality is best, therefore, the coordinates of the jth IRS need to be continuously iterated and updated until the optimal solution of this problem is obtained, and the distributed IRS group construction is completed.

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