A resource allocation method for IRS-MEC system

Abstract

This invention relates to the fields of mobile edge computing and wireless communication technology, specifically disclosing a resource allocation method for an IRS-MEC system. The method aims to minimize the maximum weighted computational energy consumption of user tasks in an IRS-assisted MEC system. It employs a local CPU operating frequency optimization algorithm based on closed-form solutions and a migration decision threshold optimization algorithm based on binary search to optimize user migration decisions. Based on an alternating optimization feasibility judgment algorithm, it jointly optimizes the migrating user's transmit power, the reflection coefficient of the smart reflective surface, the access point's receive beamforming, and the MEC server's CPU operating frequency. This allows users to make reasonable migration decisions and ensures that system resources are allocated rationally, thereby minimizing the maximum weighted computational energy consumption (WCE) of user tasks. This method has fast convergence speed, low complexity, and is easy to implement.

Description

Technical Field

[0001] This invention relates to the fields of mobile edge computing and wireless communication technology, and in particular to a resource allocation method for an IRS-MEC system. Background Technology

[0002] In recent years, with the popularization of smart users and the surge in demand for wireless multimedia applications, mobile edge computing (MEC) has emerged as a new computing paradigm. Its core idea is to offload user-generated computationally intensive tasks from the cloud to the network edge, thereby meeting the low-latency requirements of computing tasks. Simultaneously, to achieve customized wireless propagation environments, a wireless communication enabling technology called intelligent reflecting surface (IRS) has been proposed. Essentially, IRS introduces unit control capabilities based on the special structural design of microscopic electromagnetic units to intelligently control the reflection behavior of electromagnetic wave signals incident on its surface, thus obtaining a customizable wireless propagation environment. Given that IRS can achieve signal enhancement at specified spatial locations on demand, its introduction into MEC systems can improve user computation offloading and transmission performance.

[0003] IRS-MEC systems involve joint decision-making and allocation of resources across multiple dimensions, requiring solutions to problems such as migration decisions, communication resource allocation, and computing resource allocation for edge computing servers. Existing resource allocation mechanisms often utilize optimization theory for modeling, which typically results in non-convex problems with high solution complexity. Furthermore, current research on migration decisions and resource allocation in IRS-MEC systems primarily focuses on latency, energy consumption, or the weighted sum of latency and energy consumption, neglecting the minimum-maximum weighted energy consumption. Summary of the Invention

[0004] This invention provides a resource allocation method for an IRS-MEC system, which solves the technical problem of how to reduce the requirements for user computing power, reduce the energy consumption caused by user computing-intensive task execution, and at the same time improve user computing offloading and transmission performance.

[0005] To address the above technical problems, this invention provides a resource allocation method for an IRS-MEC system. The IRS-MEC system includes an intelligent reflective surface (IRS) with multiple reflective elements, a multi-antenna access point, K single-antenna users, and an MEC server. The intelligent reflective surface is installed adjacent to the K users, and the MEC server is installed adjacent to the access point. Each user has a transmission channel with the access point and the intelligent reflective surface, and the access point also has a transmission channel with the intelligent reflective surface. The key aspect is that this resource allocation method specifically includes the following steps:

[0006] S1. Calculate the local CPU operating frequency f of user k. k,loc Local task computing power consumption The formula for calculating the migration decision threshold ξ is given, where k = 1, 2, ..., K;

[0007] S2. Based on the calculation formula of the migration decision threshold ξ, determine the set of migration calculation users to be used as input for step S3. and migration decision threshold ξ;

[0008] S3, within a defined set of migration computing users Under the migration decision threshold ξ, an optimization model is constructed with the objective of minimizing the maximum user task computational energy consumption.

[0009] S4. Solve the optimization model to obtain the transmit power of the migrating user, the reflection coefficient of the smart reflective surface, the receiving beamforming of the access point, and the CPU operating frequency of the MEC server.

[0010] Furthermore, in step S1, the operating frequency of user k's local CPU... Local task computing power consumption The migration decision threshold ξ is calculated by the following formula:

[0011]

[0012]

[0013] ξ=(ξ max +ξ min ) / 2

[0014]

[0015] Where T represents the maximum delay tolerance; b k c represents the size of the computation task data for user k; k This represents the number of CPU clock cycles required for user k to compute a 1-bit task; a k Let a represent the migration decision variable for user k. k =0 indicates that the user has migrated, a k =1 indicates that the user will not migrate; ρ is the CPU energy consumption coefficient for each user; ξ max ξ represents the maximum migration decision threshold; min μ represents the minimum migration decision threshold; k Let k be the energy consumption weighting coefficient. This represents the energy consumption for user k's task migration. Describes a set of K users. Let k represent any value, indicating that the same formula is used for calculation for each user.

[0016] Furthermore, step S2 specifically includes the following steps:

[0017] S21. Initialization: All users choose local computation, meaning the migration decision variable for all users is 1, denoted as a. k =1, energy consumption for user k's migration Minimum migration decision threshold ξ min =0; First convergence precision ε>0;

[0018] S22. Perform iterative calculations: In each iteration, for the current user k, determine... If the value is greater than the migration decision threshold ξ, then set the migration decision variable a. k =0 indicates that the user has migrated, and the set of users who chose to migrate is calculated. And determine whether the first convergence condition |ξ is met. max -ξ min If |≤ε, all iterations end; otherwise, the migration decision threshold ξ is updated and the next iteration for the next migration user begins.

[0019] S23. Output the current set of migrated users at the end of the iteration. And migration decision threshold ξ.

[0020] Further, in step S3, the optimization model is constructed as follows:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] Where p represents the transmit power of all migrated users, φ represents the reflection coefficient vector of the smart reflective surface, W represents the receive beamforming matrix of the access point, and f c This indicates the CPU operating frequency of the MEC server; find{} represents the process of finding a feasible point that makes the problem feasible; r k p represents the achievable transmission rate for migrating user k;k This represents the transmit power of the migrating user k. This represents the maximum transmit power of the migrating user k; it is used to simplify custom parameters. F represents the CPU operating frequency allocated to migrating user k by the MEC server. c This represents the maximum computing power of the MEC server; φ m The reflection coefficient of the m-th reflective unit on the intelligent reflective surface is given by m = 1, 2, ..., M, where M is the number of reflective units on the intelligent reflective surface.

[0028] Furthermore, step S4 specifically includes the following steps:

[0029] S41. Initialize the number of iterations and the second error precision ε1, and randomly generate the transmit power p of the migrating user. (0) The reflection coefficient vector φ of the intelligent reflective surface (0) The CPU operating frequency f of the MEC server c(0) and the received beamforming matrix W of the access point (0) ;

[0030] S42. Given a set of φ, f c W, based on the initialization parameters in step S41, and the set of migrating users given in step S2. Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution of p;

[0031] S43, Given a set of f c W, p, based on the initialization parameters in step S41, and the set of migrating users given in step S2. Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution of φ;

[0032] S44. Given a set of φ and p, based on the initialization parameters in step S41, and the set of migrating users given in step S2... Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution of W;

[0033] S45. Given a set of W, φ, and p, based on the initialization parameters in step S41, and the set of migrating users given in step S2... Under the migration decision threshold ξ, the optimization model is solved to obtain f. c Intermediate solution;

[0034] S46, based on f c Find the intermediate solutions of W, φ, and p, solve the optimization model, and determine whether the second convergence condition ||p is satisfied.(n) -p (n-1) || 2 +||f c(n) -f c(n-1) || 2 +||φ (n) -φ (n-1) || 2 +||vec(W (n) -W (n-1) ) 2 ≤ε1, where |||| represents the Euclidean norm of the complex vector, vec() represents vectorization, n represents the number of iterations n, and n-1 represents the number of iterations n-1. If the optimization model has a feasible solution and satisfies the second convergence condition, then the migration computation energy consumption of the migrating user is calculated based on the feasible solution. And update the upper bound of the migration decision threshold to ξ. max =ξ, if the optimization model has no feasible solution, i.e., cannot satisfy the second convergence condition, then update the lower bound of the migration decision threshold to ξ. min =ξ;

[0035] S47. Repeat steps S42 to S46 until the first convergence condition |ξ is satisfied. max -ξ min If |≤ε, output f at this time. c The solutions to W, φ, and p are used as the solutions to the optimization model.

[0036] Further, step S42 specifically includes the following steps:

[0037] S421. Given a set of φ and f obtained in the (n-1)th iteration. c The values ​​of W are denoted as φ. (n-1) f c(n-1) W (n-1) The set of migrated users given in step S2 Under the migration decision threshold ξ, the optimization model is transformed into a power optimization model:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] Where, ω k Let represent the auxiliary variable introduced to approximate the signal-to-interference-plus-noise ratio (SIR) of the k-th user, and δ represent the auxiliary variables introduced to approximate the interference power and noise power. This represents the auxiliary variable introduced to transform the feasibility determination problem regarding transmit power into an optimization problem; B represents the channel bandwidth; σ represents the channel bandwidth. 2 Indicates background noise; w k This represents the received beamforming vector of the access point for user k; Indicates to w k Take the conjugate transpose; intermediate variable G i =H AP Φh r,i H represents the cascaded channel from the smart reflective surface to the access point for the i-th migrating user. AP h represents the baseband equivalent channel from the smart reflective surface to the access point. r,i Let represent the baseband equivalent channel of the i-th migrating user to the smart reflective surface, and Φ represent the reflection coefficient matrix of the smart reflective surface; h d,i h d,k Let p represent the baseband equivalent channels from the i-th migrating user and the k-th migrating user to the access point, respectively, where i is in the set of migrating users excluding k. i δ represents the transmit power of the i-th migrating user; [n] Let δ be the value obtained in the nth iteration. ω represents the value obtained in the nth iteration. k G k This represents the cascaded channel from the k-th user to the smart reflective surface and then to the access point;

[0046] S422. Based on the initialization parameters obtained in step S41, the power optimization model is solved using an optimization method based on continuous convex approximation to obtain an intermediate solution p of the transmit power p. (n) .

[0047] Further, step S43 specifically includes the following steps:

[0048] S431, Given f c(n-1) W (n-1) p (n) The set of migrated users given in step S2 Under the migration decision threshold ξ, the optimization model is transformed into a reflection coefficient optimization model:

[0049]

[0050]

[0051]

[0052] Ψ m,m =1, m=1,2,...,M+1,

[0053]

[0054] Among them, among them, This indicates the auxiliary variable introduced to transform the feasibility determination problem regarding the reflection coefficient vector of the intelligent reflective surface into an optimization problem. Indicates about a positive semidefinite matrix, Represents a vector with respect to φ. Let M denote the complex matrix space of dimension (M+1)×(M+1); Ψ represents the upper bound of the uplink reachable rate for user k; m,m Represents the element in the m-th row and m-th column of Ψ; rank(Ψ) represents the rank of Ψ;

[0055] S432. Solve the reflection coefficient optimization model to obtain the intermediate solution φ of the reflection coefficient vector of the intelligent reflective surface. (n) .

[0056] Further, in step S431, the approximate achievable rate of migrating user k is determined. We obtain the following formula:

[0057]

[0058] in, Represents Tr(V) k,i Ψ) in Ψ (n) Jacobian matrix of a point, Tr(V) k,i Ψ) represents V k,i Ψ trace, Ψ (n) The value of Ψ obtained in the nth iteration is represented by <>, where <> represents the inner product, and h d,k,i , V k,i D1, k (Ψ), D 2,k (Ψ (n) ) are intermediate variables that simplify the formula, and are given by the following formulas:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] in, Represents Tr(V) k,i Ψ) in Ψ (n) Jacobian matrix of a point, Tr(V) k,i Ψ) represents the relationship between V and V k,i Ψ trace, Ψ (n) The value of Ψ obtained in the nth iteration is represented by <>, where <> represents the inner product, and |h d,k,j | 2 Indicates the relationship with h d,k,j Take the modulus and square it. Indicates to Find the norm and its square; h d,k,i , V k,i D 1,k (Ψ), D 2,k (Ψ (n) ) are intermediate variables that simplify the formula, and are given by the following formulas:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] Among them, diag(h r,i ) indicates that for h r,i Take the diagonal matrix; Indicates to Take the conjugate transpose; Indicates the relationship between h d,k,i Take the conjugate transpose; j indicates that in The j-th user, p j V represents the transmit power of the j-th user. k,j V coming soon k,i Replace the subscript i with j in V. k,i The result can be obtained through calculation; Tr(V) k,j Ψ) represents the relationship between V and V k,j Ψ trace; h d,k,j That is, h d,k,i Replace the subscript i with j in h. d,k,i The answer can be obtained through calculation; This indicates that the set of migrated users will be traversed sequentially. For pj (Tr(V k,j Ψ)+|h d,k,j | 2 Summation is performed using Tr(V). k,i Ψ (n) ) indicates that for V k,i Ψ (n) Tracing, This indicates that the set of migrated users will be traversed sequentially. For p i (Tr(V k,i Ψ (n) )+|h d,k,i | 2 After summing, subtract p when i=k i (Tr(V k,i Ψ (n) )+|h d,k,i | 2 The value of ).

[0071] Further, step S44 specifically includes:

[0072] Given φ (n) p (n) f c(n-1) Solving the optimization model yields an intermediate solution W for the receiving beamforming matrix of the access point. (n) In calculating the intermediate solution W (n) First, let's give the optimal access point receive beamforming vector for the k-th user in the nth iteration:

[0073]

[0074] in, intermediate variable h k =H AP Φh r,k +h d,k intermediate variable h i =H AP Φh r,i +h d,i , I N This represents an N×N identity matrix. h represents a complex matrix space of dimension N×N. r,k Let eig{} represent the baseband equivalent channel of the kth migrated user to the smart reflective surface, eig{} represent taking the eigenvalue, max{} represent taking the maximum value, eigvec{} represent taking the eigenvector, and N represent the number of antennas of the access point;

[0075] Therefore, the intermediate solution W for the receiving beamforming of the access point can be obtained. (n) for

[0076] Further, step S45 specifically includes:

[0077] Given φ (n) W (n) p (n) The set of migrated users given in step S2 Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution f of the CPU operating frequency of the MEC server. c(n) In calculating the intermediate solution f c(n) First, let's give the formula for calculating the optimal CPU operating frequency of the MEC server for the k-th user in the nth iteration:

[0078]

[0079] Therefore, the intermediate solution f of the CPU operating frequency of the MEC server can be obtained. c(n) for

[0080] This invention relates to the fields of mobile edge computing and wireless communication technology, specifically disclosing a resource allocation method for an IRS-MEC system. The method aims to minimize the maximum weighted computational energy consumption of user tasks in an IRS-assisted MEC system. It employs a local CPU operating frequency optimization algorithm based on closed-form solutions and a migration decision threshold optimization algorithm based on binary search to optimize user migration decisions. Based on an alternating optimization feasibility judgment algorithm, it jointly optimizes the migrating user's transmit power, the reflection coefficient of the smart reflective surface, the access point's receive beamforming, and the MEC server's CPU operating frequency. This allows users to make reasonable migration decisions and ensures that system resources are allocated rationally, thereby minimizing the maximum weighted computational energy consumption (WCE) of user tasks. This method has fast convergence speed, low complexity, and is easy to implement. Attached Figure Description

[0081] Figure 1 This is a network topology diagram of an IRS-MEC system provided in an embodiment of the present invention;

[0082] Figure 2 This is a flowchart illustrating the steps of a resource allocation method for an IRS-MEC system provided in an embodiment of the present invention.

[0083] Figure 3 This is a comparison chart of the minimum-maximum weighted energy consumption of the optimization method provided in the embodiments of the present invention and scenarios with and without IRS and with random IRS. Detailed Implementation

[0084] The embodiments of the present invention are described in detail below with reference to the accompanying drawings. The embodiments are given for illustrative purposes only and should not be construed as limiting the present invention. The accompanying drawings are for reference and illustration only and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0085] like Figure 1 As shown in the network topology diagram, a typical IRS-MEC system includes an Intelligent Reflecting Surface (IRS) with M (M≥2) reflective elements, a multi-antenna Access Point (AP), K single-antenna users, and an MEC server. The IRS is installed near the K users, and the MEC server is installed near the Access Point. Each user has a transmission channel between itself and the Access Point and the IRS, and there is also a transmission channel between the Access Point and the IRS. The number of antennas in the AP is N (N≥2).

[0086] Users have intensive tasks that need to be migrated to the MEC for processing, meaning there is a communication requirement between the AP and the user. The IRS is connected to an IRS controller, which has two operating modes: a receive mode for environmental awareness (CSI estimation) and a reflection mode for scattering incident signals. The AP is responsible for collecting data, including channel state information, and controlling the phase change of the IRS reflection coefficient through a dedicated AP-IRS link (AP—IRS controller—IRS).

[0087] Metamaterials are artificial structural materials built upon subwavelength structures (also known as meta-atoms). They utilize the exotic electromagnetic responses of these designed subwavelength structures to achieve electromagnetic parameters or properties that do not exist in nature. Metasurfaces are a subfield of metamaterials research; essentially, they are ultrathin two-dimensional arrays of planar materials. They are designed by systematically arranging subwavelength-sized artificial electromagnetic materials into a planar array to achieve flexible and effective control over the direction, polarization, and propagation mode of electromagnetic waves. Based on the flexible electromagnetic wave manipulation characteristics of metasurfaces, not only can reconfigurable cavity metasurface antennas be designed to increase the capacity of cluster MIMO channel spatial multiplexing systems, but metasurfaces can also be used to design novel wireless communication systems based on metasurface waveform modulation.

[0088] This system constructs an intelligent reflective surface based on a programmable metasurface and applies it to mobile edge computing networks. It enables programmability in wireless environments, thereby improving user computing offload transmission performance and alleviating local computing pressure without significantly increasing system deployment costs.

[0089] exist Figure 1Based on the system shown, this embodiment provides a resource allocation method based on the IRS-MEC system, aiming to minimize the maximum WCE of the IRS-MEC system, such as... Figure 2 As shown, the steps include:

[0090] S1. Calculate the local CPU operating frequency f of user k. k,loc Local task computing power consumption The formula for calculating the migration decision threshold ξ is given, where k = 1, 2, ..., K;

[0091] S2. Based on the calculation formula of the migration decision threshold ξ, determine the set of migration calculation users to be used as input for step S3. and migration decision threshold ξ;

[0092] S3, within a defined set of migration computing users Under the migration decision threshold ξ, an optimization model is constructed with the objective of minimizing the maximum user task computational energy consumption.

[0093] S4. Solve the optimization model to obtain the user's transmit power, the reflection coefficient of the smart reflective surface, the receiving beamforming of the access point, and the CPU operating frequency of the MEC server.

[0094] Furthermore, step S1 specifically includes

[0095] In step S1, the operating frequency of user k's local CPU... Local task computing power consumption The migration decision threshold ξ is calculated by the following formula:

[0096]

[0097]

[0098] ξ=(ξ max +ξ min ) / 2

[0099]

[0100] Where T represents the maximum delay tolerance; b k c represents the size of the computation task data for user k; k This represents the number of CPU clock cycles required for user k to compute a 1-bit task; a k Let a represent the migration decision variable for user k. k =0 indicates that the user has migrated, a k =1 indicates that the user will not migrate; ρ is the CPU energy consumption coefficient for each user; ξ max ξ represents the maximum migration decision threshold; minμ represents the minimum migration decision threshold; k Let k be the energy consumption weighting coefficient. This represents the energy consumption for user k's task migration. Describes a set of K users. Let k represent any value, indicating that the same formula is used for calculation for each user.

[0101] Furthermore, step S2 specifically includes the following steps:

[0102] S21. Initialization: All users choose local computation, meaning the migration decision variable for all users is 1, denoted as a. k =1, energy consumption for user k's migration Minimum migration decision threshold ξ min =0; First convergence precision ε>0;

[0103] S22. Perform iterative calculations: In each iteration, for the current user k, determine... If the value is greater than the migration decision threshold ξ, then set the migration decision variable a. k =0 indicates that the user has migrated, and the set of users who chose to migrate is calculated. And determine whether the first convergence condition |ξ is met. max -ξ min If |≤ε, all iterations end; otherwise, the migration decision threshold ξ is updated and the next iteration begins for the next migrating user. If |≤ε, the user will not migrate.

[0104] S23. Output the current set of migrated users at the end of the iteration. And migration decision threshold ξ.

[0105] Furthermore, step S3 specifically includes the following steps:

[0106] In step S3, the optimization model is constructed as follows:

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] Where p represents the transmit power of all migrated users, φ represents the reflection coefficient vector of the smart reflector, W represents the receive beamforming matrix of the access point, and f c This indicates the CPU operating frequency of the MEC server; `find{}` represents the process of finding feasible points that make the problem feasible; `r` k p represents the achievable transmission rate for migrating user k; k This represents the transmit power of the migrating user k. This represents the maximum transmit power of the migrating user k; it is used to simplify custom parameters. F represents the CPU operating frequency allocated to migrating user k by the MEC server. c Indicates the maximum computing power of the MEC server; φ m Let m represent the reflection coefficient of the m-th reflective element of the intelligent reflective surface, where m = 1, 2, ..., M, and M is the number of reflective elements provided on the intelligent reflective surface.

[0114] Step S4 specifically includes the following steps:

[0115] S41. Initialize the number of iterations and the second error precision ε1, and randomly generate the transmit power p of the migrating user. (0) The reflection coefficient vector φ of the intelligent reflective surface (0) The CPU operating frequency f of the MEC server c(0) and the receiving beamforming matrix W of the access point (0) ;

[0116] S42. Given a set of φ, f c W, based on the initialization parameters in step S41, and the set of migrating users given in step S2. Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution of p;

[0117] S43, Given a set of f c W, p, based on the initialization parameters in step S41, and the set of migrating users given in step S2. Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution of φ;

[0118] S44. Given a set of φ and p, based on the initialization parameters in step S41, and the set of migrating users given in step S2... Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution of W;

[0119] S45. Given a set of W, φ, and p, based on the initialization parameters in step S41, and the set of migrating users given in step S2... Under the migration decision threshold ξ, the optimization model is solved to obtain f. c Intermediate solution;

[0120] S46, based on f c Find the intermediate solutions of W, φ, and p, solve the optimization model, and determine whether the second convergence condition ||p is satisfied. (n) -p (n-1) || 2 +||f c(n) -f c(n-1) || 2 +||φ (n) -φ (n-1) || 2 +||vec(W (n) -W (n-1) )|| 2 ≤ε1, where |||| represents the Euclidean norm of the complex vector, vec() represents vectorization, n represents the number of iterations, and n-1 represents the number of iterations (n-1). If the optimization model has a feasible solution and satisfies the second convergence condition, then the migration computation energy consumption of the migrating users is calculated based on the feasible solution. And update the upper bound of the migration decision threshold to ξ. max =ξ, if the optimization model has no feasible solution, i.e., cannot satisfy the second convergence condition, then update the lower bound of the transition decision threshold to ξ. min =ξ;

[0121] S47. Repeat steps S42 to S46 until the first convergence condition |ξ is met. max -ξ min If |≤ε, output f at this time. c The solutions for W, φ, and p are used as the solutions to the optimization model.

[0122] Step S42 specifically includes the following steps:

[0123] S421. Given a set of φ and f obtained in the (n-1)th iteration. c The values ​​of W are denoted as φ. (n-1) f c(n-1) W (n-1) The set of migrated users given in step S2 Under the migration decision threshold ξ, the optimization model is transformed into a power optimization model:

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] Where, ω k Let represent the auxiliary variable introduced to approximate the signal-to-interference-plus-noise ratio (SIR) of the k-th user, and δ represent the auxiliary variables introduced to approximate the interference power and noise power. This represents the auxiliary variable introduced to transform the feasibility determination problem regarding transmit power into an optimization problem; B represents the channel bandwidth; σ represents the channel bandwidth. 2 Indicates background noise; w k This represents the received beamforming vector of the access point for user k; Indicates to w k Take the conjugate transpose; intermediate variable G i =H AP Φh r,i H represents the cascaded channel from the i-th migrating user to the smart reflector surface to the access point. AP h represents the baseband equivalent channel from the smart reflector surface to the access point. r,i Let represent the baseband equivalent channel of the i-th migrating user to the smart reflective surface, and Φ represent the reflection coefficient matrix of the smart reflective surface; h d,i h d,k Let p represent the baseband equivalent channels from the i-th migrating user and the k-th migrating user to the access point, respectively, where i is in the set of migrating users excluding k. i δ represents the transmit power of the i-th migrating user; [n] Let δ be the value obtained in the nth iteration. ω represents the value obtained in the nth iteration. k G k This represents the cascaded channel from the k-th user to the smart reflective surface and then to the access point;

[0132] S422. Based on the initialization parameters obtained in step S41, the power optimization model is solved using an optimization method based on continuous convex approximation to obtain the intermediate solution p of the transmit power p. (n) .

[0133] Step S43 specifically includes the following steps:

[0134] S431, Given f c(n-1) W (n-1) p (n) The set of migrated users given in step S2 Under the migration decision threshold ξ, the optimization model is transformed into a reflection coefficient optimization model:

[0135]

[0136]

[0137]

[0138] Ψ m,m =1, m=1,2,...,M+1,

[0139]

[0140] in, This indicates the auxiliary variable introduced to transform the feasibility determination problem regarding the reflection coefficient vector of the intelligent reflective surface into an optimization problem. Indicates about a positive semidefinite matrix, Represents a vector with respect to φ. Let M denote the complex matrix space of dimension (M+1)×(M+1); Ψ represents the upper bound of the uplink reachable rate for user k; m,m Represents the element in the m-th row and m-th column of Ψ; rank(Ψ) represents the rank of Ψ;

[0141] S432. Solve the reflection coefficient optimization model to obtain the intermediate solution φ of the reflection coefficient vector of the intelligent reflective surface. (n) .

[0142] In step S431, the approximate reachability rate of the migrating user k is determined. We obtain the following formula:

[0143]

[0144] in, Represents Tr(V) k,i Ψ) in Ψ (n) Jacobian matrix of a point, Tr(V) k,i Ψ) represents the relationship between V and V k,i Ψ trace, Ψ (n) The value of Ψ obtained in the nth iteration is represented by <>, where <> represents the inner product, and |h d,k,j | 2 Indicates the relationship between h d,k,j Take the modulus and square it. Indicates to Find the norm and its square; h d,k,i , V k,i D 1,k (Ψ), D 2,k (Ψ (n) ) are intermediate variables that simplify the formula, and are given by the following formulas:

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] Among them, diag(h r,i ) indicates that for h r,i Take the diagonal matrix; Indicates to Take the conjugate transpose; Indicates the relationship between h d,k,i Take the conjugate transpose; j indicates that in The j-th user, p j V represents the transmit power of the j-th user. k,j V coming soon k,i Replace the subscript i with j in V. k,i The result can be obtained through calculation; Tr(V) k,j Ψ) represents the relationship between V and V k,j Ψ trace; h d,k,j That is, h d,k,i Replace the subscript i with j in h. d,k,i The answer can be obtained through calculation; This indicates that the set of migrated users will be traversed sequentially. For p j (Tr(V k,j Ψ)+|h d,k,j | 2 Summation is performed using Tr(V). k,i Ψ (n) ) indicates that for V k,i Ψ (n) Tracing, This indicates that the set of migrated users will be traversed sequentially. For p i (Tr(V k,i Ψ (n) )+|h d,k,i | 2 After summing, subtract p when i=k i (Tr(V k,i Ψ (n) )+|h d,k,i | 2 The value of ).

[0151] Step S44 is as follows:

[0152] Given φ(n) p (n) f c(n-1) Solving the optimization model yields the intermediate solution W of the receiving beamforming matrix at the access point. (n) In calculating the intermediate solution W (n) First, let's give the optimal access point receive beamforming vector for the k-th user in the nth iteration:

[0153]

[0154] in, intermediate variable h k =H AP Φh r,k +h d,k intermediate variable h i =H AP Φh r,i +h d,i , I N This represents an N×N identity matrix. h represents a complex matrix space of dimension N×N. r,k Let eig{} represent the baseband equivalent channel of the k-th migrating user to the smart reflective surface, eig{} represent taking the eigenvalue, max{} represent taking the maximum value, eigvec{} represent taking the eigenvector, and N represent the number of antennas at the access point.

[0155] Therefore, the intermediate solution W for the receiving beamforming at the access point can be obtained. (n) for

[0156] Step S45 is as follows:

[0157] Given φ (n) W (n) p (n) The set of migrated users given in step S2 Under the migration decision threshold ξ, the optimization model is solved to obtain the intermediate solution f of the CPU operating frequency of the MEC server. c(n) In calculating the intermediate solution f c(n) First, let's give the formula for calculating the optimal CPU operating frequency of the MEC server for the k-th user in the nth iteration:

[0158]

[0159] Therefore, the intermediate solution f for the CPU operating frequency of the MEC server can be obtained. c(n) for

[0160] This invention provides a resource allocation method for an IRS-MEC system. The method aims to minimize the maximum weighted computational energy consumption (WCE) of user tasks in the IRS-assisted MEC system. It employs a local CPU operating frequency optimization algorithm based on closed-form solutions and a migration decision threshold optimization algorithm based on binary search to optimize user migration decisions. A feasibility judgment algorithm based on alternating optimization is used to jointly optimize the migrating user's transmit power, the reflection coefficient of the smart reflector, the access point receiving beamforming, and the MEC server CPU operating frequency. This allows users to make reasonable migration decisions and ensures that system resources are allocated appropriately, thereby minimizing the maximum weighted computational energy consumption (WCE) of user tasks. This method has fast convergence speed, low complexity, and is easy to implement.

[0161] The proposed method is compared with the random IRS reflection coefficient algorithm and the IRS-free optimization algorithm in terms of performance. The proposed method simultaneously optimizes user migration decisions, local and MEC server CPU operating frequencies, user transmit power, IRS phase shift matrix, and access point receive beamforming vector. In contrast, the random IRS reflection coefficient algorithm only optimizes user migration decisions, local and MEC server CPU operating frequencies, user transmit power, and access point receive beamforming vector, with the IRS reflection coefficient phase being a random value. The IRS-free algorithm refers to applications where there is no IRS; accordingly, it only optimizes user migration decisions, local and MEC server CPU operating frequencies, user transmit power, and access point receive beamforming vector.

[0162] To verify the optimization performance of the proposed method, this embodiment uses minimizing maximum user task computational energy consumption (WCE) as the metric, and conducts experimental simulations. The simulation settings are as follows: the access point and IRS coordinates are (0,0) and (5m,5m) respectively; users are randomly distributed within a circular area centered at (55m,0) with a radius of 5m. The number of users and access point antennas are set to 4, the channel bandwidth is set to 5MHz, the background noise is set to -80dBm, the maximum user transmit power is set to 1W, and the energy consumption factor is set to 10. -28 Task data volume b k Let [800, 1200] Kb be the number of CPU clock cycles required for the task computation, c. k Set to [800, 900] cycles / bit, maximum latency tolerance T is set to 1s, and local maximum computing power is [not specified]. Set to 1GHz, the maximum computing power F of the MEC server c Set to 40GHz, weighting coefficient μ k Set it to 1.

[0163] Furthermore, the system fading model considers both large-scale and small-scale fading, i.e. Specifically, large-scale fading adopts a distance-dependent path loss model L(d)=C0(l / D0). -α Where C0 = -30dB represents the path loss at a reference distance D0 = 1, l represents the distance between the two nodes, and α represents the path loss exponent. The path loss exponent of the channel is set to α. UB =3.5,α IB =α UI =2.2, where α UB ,α IB and α UI These represent the path loss exponents from user to access point, from IRS to access point, and from user to IRS, respectively; small-scale fading uses the Ricean fading model, where all Ricean factors are set to β. UB =β IB =β UI =1.

[0164] Figure 3 This is a comparison of the optimization performance of the proposed optimization method (①), the random IRS reflection coefficient algorithm (②), and the optimization algorithm without IRS (③) as the number of IRS reflection units changes. In the simulation, the number of IRSs varied from 8 to 128. It can be seen that as the number of IRS reflection units gradually increases, the minimum-maximum WCE of the IRS optimization algorithm and the random IRS optimization algorithm decreases, while the optimization algorithm without IRS remains unchanged. In this case, the performance gap between the optimization algorithm without IRS and the random IRS optimization algorithm becomes increasingly larger. This result shows that even without optimizing the phase shift of the IRS, deploying an IRS can still provide a certain system performance gain. Specifically, when the number of IRS reflection units is 64, the proposed optimization algorithm (①) saves 16 mJ of minimum-maximum WCE compared to the random IRS reflection coefficient algorithm (②), and 36 mJ of minimum-maximum WCE compared to the random IRS reflection coefficient algorithm (③). The rationale for this phenomenon is that the IRS can provide an additional signal path from the user to the access point for offloading transmission, thereby improving the signal-to-noise ratio of the received signal.

[0165] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A resource allocation method for an IRS-MEC system, the IRS-MEC system comprising an intelligent reflective surface (IRS) with multiple reflective elements, a multi-antenna access point, K single-antenna users, and an MEC server, wherein the intelligent reflective surface is installed adjacent to the K users, the MEC server is installed adjacent to the access point, each user has a transmission channel with the access point and the intelligent reflective surface, and the access point has a transmission channel with the intelligent reflective surface, characterized in that... The resource allocation method specifically includes the following steps: S1. Calculate the operating frequency of user k's local CPU. Local task computing power consumption Provide migration decision thresholds The calculation formula, k=1,2,…,K; the operating frequency of the local CPU of user k. Local task computing power consumption and migration decision threshold Calculated by the following formula: ， ， ， ， Where T represents the maximum delay tolerance; This indicates the size of the computation task data for user k; This represents the number of CPU clock cycles required for user k to compute a 1-bit task; Let the migration decision variable for user k be represented. This indicates that the user has migrated. This indicates that the user will not migrate; It is the CPU energy consumption coefficient for each user; Indicates the maximum migration decision threshold; This represents the minimum migration decision threshold; The energy consumption weighting coefficient for user k; This represents the energy consumption for task migration by user k. Represents a set of K users; Let k represent any value, indicating that the same formula is used for calculation for each user; S2, Based on migration decision threshold The calculation formula determines the set of migration calculation users used as input for step S3. and migration decision threshold ; S3, within a defined set of migration computing users and migration decision threshold The following optimization model is constructed with the objective of minimizing the maximum user task computational energy consumption; the optimization model is constructed as follows: ， ， ， ， ， ， in, This represents the transmit power of all migrated users. This represents the reflection coefficient vector of the intelligent reflective surface. This represents the receive beamforming matrix of the access point. This indicates the CPU operating frequency of the MEC server; This refers to the process of finding feasible points that make the optimization model viable. This represents the achievable transmission rate for the migrating user k; This represents the transmit power of the migrating user k. This represents the maximum transmit power of the migrating user k; it is used to simplify custom parameters. , ; This indicates the CPU operating frequency allocated to the migrating user k by the MEC server. This indicates the maximum computing power of the MEC server; The reflection coefficient of the m-th reflective unit on the intelligent reflective surface is given by m = 1, 2, ..., M, where M is the number of reflective units on the intelligent reflective surface. S4. Solve the optimization model to obtain the transmit power of the migrating user, the reflection coefficient of the smart reflective surface, the receiving beamforming of the access point, and the CPU operating frequency of the MEC server.

2. The resource allocation method for an IRS-MEC system according to claim 1, characterized in that, Step S2 specifically includes the following steps: S21. Initialization: All users choose local computation, meaning the migration decision variable for all users is 1, represented as... , energy consumption for user k's migration ; Minimum migration decision threshold First convergence accuracy ; S22. Perform iterative calculations: In each iteration, for the current user k, determine... Is it greater than the migration decision threshold? If it is greater than, then let the migration decision variable... This indicates that the user has migrated, and the set of users who chose to migrate is calculated. And determine whether the first convergence condition is met. If the condition is met, all iterations end; otherwise, the transition decision threshold is updated. And proceed to the next iteration targeting the next migrating user; S23. Output the current set of migrated users at the end of the iteration. and migration decision threshold .

3. The resource allocation method for an IRS-MEC system according to claim 2, characterized in that, Step S4 specifically includes the following steps: S41, Initialize the number of iterations and the second error precision Randomly generate the transmit power of the migrating user The reflection coefficient vector of the intelligent reflective surface The CPU operating frequency of the MEC server and the receiving beamforming matrix of the access point ; S42, Given a set , , Based on the initialization parameters in step S41, the set of migrating users given in step S2 and migration decision threshold Next, the optimization model is solved to obtain... Intermediate solution; S43, Given a set , , Based on the initialization parameters in step S41, the set of migrating users given in step S2 and migration decision threshold Next, the optimization model is solved to obtain... Intermediate solution; S44, Given a set , Based on the initialization parameters in step S41, the set of migrating users given in step S2 and migration decision threshold Next, the optimization model is solved to obtain... Intermediate solution; S45, Given a set , , Based on the initialization parameters in step S41, the set of migrating users given in step S2 and migration decision threshold Next, the optimization model is solved to obtain... Intermediate solution; S46, based on , , , The intermediate solutions are used to solve the optimization model and determine whether the second convergence condition is satisfied. Where || represents the Euclidean norm of the complex vector, vec() denotes vectorization, n represents the number of iterations, and n-1 represents the number of iterations (n-1). If the optimization model has a feasible solution and satisfies the second convergence condition, then the migration computation energy consumption of the migrating users is calculated based on the feasible solution. And update the upper bound of the migration decision threshold to If the optimization model has no feasible solution, i.e., cannot satisfy the second convergence condition, then the lower bound of the migration decision threshold is updated to be... ; S47. Repeat steps S42 to S46 until the first convergence condition is met. Output at this time , , , The solution is taken as the solution of the optimization model.

4. The resource allocation method for an IRS-MEC system according to claim 3, characterized in that, Step S42 specifically includes the following steps: S421. Given a set of results obtained in the (n-1)th iteration , , The values ​​are denoted as follows: , , The set of migrated users given in step S2 and migration decision threshold Next, the optimization model is transformed into a power optimization model: ， ， ， ， ， ， ， in, This represents the auxiliary variable introduced to approximate the signal-to-interference-plus-noise ratio (SIR) of the k-th user. This represents the auxiliary variables introduced to approximate the interference power and noise power. B represents the auxiliary variable introduced to transform the feasibility determination problem regarding transmit power into an optimization problem. Indicates background noise; This represents the received beamforming vector of the access point for user k; Indicates to Take the conjugate transpose; intermediate variable This represents the cascaded channel from the smart reflective surface to the access point for the i-th migrating user. This represents the baseband equivalent channel from the intelligent reflective surface to the access point. This represents the baseband equivalent channel for the i-th migrated user to the smart reflective surface. This represents the reflection coefficient matrix of the intelligent reflective surface; , Let i and k represent the baseband equivalent channels from the i-th migrating user and the k-th migrating user to the access point, respectively, where i is in the set of migrating users excluding k. This represents the transmit power of the i-th migrating user; This represents the result obtained in the nth iteration. , This represents the result obtained in the nth iteration. , This represents the cascaded channel from the k-th user to the smart reflective surface and then to the access point; S422. Based on the initialization parameters obtained in step S41, the power optimization model is solved using an optimization method based on continuous convex approximation to obtain the transmit power. intermediate solution .

5. The resource allocation method for an IRS-MEC system according to claim 3, characterized in that, Step S43 specifically includes the following steps: S431, Given , , The set of migrated users given in step S2 and migration decision threshold Next, the optimization model is transformed into a reflection coefficient optimization model: ， ， ， ， ， in, This indicates the auxiliary variable introduced to transform the feasibility determination problem regarding the reflection coefficient vector of the intelligent reflective surface into an optimization problem. Indicates about a positive semidefinite matrix, Indicates about vector, Indicates dimension as The space of complex matrices; This represents the upper bound of the uplink reachable rate for user k; express The element in the m-th row and m-th column; express rank; S432. Solve the reflection coefficient optimization model to obtain an intermediate solution for the reflection coefficient vector of the intelligent reflective surface. .

6. A resource allocation method for an IRS-MEC system according to claim 5, characterized in that, In step S431, the approximate reachability of the migrating user k is determined. We obtain the following formula: ， in, express exist Jacobian matrix of a point Indicates to Tracing, This represents the result obtained in the nth iteration. value, This indicates the inner product. Indicates to Take the modulus and square it. Indicates to Find the norm and its square; , , , These are intermediate variables that make the formula simpler, and are given by the following formulas: ， ， ， ， ， in, Indicates to Take the diagonal matrix; Indicates to Take the conjugate transpose; Indicates to Take the conjugate transpose; j indicates that in The j-th user in the list, This represents the transmit power of the j-th user. Soon Replace the subscript i with j in the table, according to The answer can be obtained through calculation; Indicates to Tracking; Right now Replace the subscript i with j in the table, according to The answer can be obtained through calculation; This indicates that the set of migrated users will be traversed sequentially. ,right Perform summation; Indicates to Tracing, This indicates that the set of migrated users will be traversed sequentially. ,right Subtract after summing time The value of .

7. A resource allocation method for an IRS-MEC system according to claim 5, characterized in that, Step S44 specifically involves: Given , , Solving the optimization model yields an intermediate solution for the receiving beamforming matrix of the access point. In calculating intermediate solutions First, let's give the optimal access point receive beamforming vector for the k-th user in the nth iteration: ， in, , intermediate variables intermediate variables , , The dimension is The identity matrix, The dimension is The space of complex matrices, This represents the baseband equivalent channel for the k-th migrating user to the smart reflective surface. Indicates taking eigenvalues, Indicates taking the maximum value. This indicates the extraction of feature vectors, and N represents the number of antennas at the access point; Therefore, the intermediate solution for the receiving beamforming of the access point can be obtained. for .

8. A resource allocation method for an IRS-MEC system according to claim 6, characterized in that, Step S45 specifically involves: Given , , The set of migrated users given in step S2 and migration decision threshold Next, the optimization model is solved to obtain an intermediate solution for the CPU operating frequency of the MEC server. In calculating intermediate solutions First, let's give the formula for calculating the optimal CPU operating frequency of the MEC server for the k-th user in the nth iteration: ， Therefore, an intermediate solution for the CPU operating frequency of the MEC server can be obtained. for .

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