A fair resource allocation method for cellular network users based on RIS-assisted edge computing

Abstract

The present invention proposes a method for fair resource allocation of users in a decellularized network with RIS-assisted edge computing, and the steps are as follows: first, build a decellularized network system with IRS-assisted edge computing, and calculate the channel state information of all relevant channels; second, by jointly designing the multi-user detection MUD matrix, the reflection beamforming vector of IRSs, the transmission power of WDs and the edge computing resource allocation, the objective optimization function of minimizing the maximum delay of the user is established; finally, the objective optimization function is jointly optimized and solved by alternating iterations to obtain the optimal values ​​of the amount of unloaded data, edge computing resources, the reflection beamforming vector of IRSs and the MUD matrix. The present invention proposes a decellularized network system with IRS-assisted edge technology, which is composed of multiple BSs and IRSs to improve the transmission environment. And the optimization algorithm adopted by the present invention has fast convergence, which is conducive to practical implementation.

Description

Technical Field

[0001] The present invention relates to the technical field of mobile edge computing, and in particular to a RIS-assisted edge computing method for allocating fair resources to de-cellular network users. Background Art

[0002] In recent years, the rapid development of Internet of Things (IoT) and Artificial Intelligence (AI) technologies has enabled a variety of new applications based on real-time communication (e.g., natural language processing, face / fingerprint recognition, autonomous driving, 3D media, etc.). Typically, these applications require lower latency and require more computing resources. However, this is challenging for IoT devices due to their limited computing power. To address this challenge, Mobile Edge Computing (MEC) has been proposed, where the computing tasks of IoT devices can be offloaded to edge servers that are usually equipped with huge computing resources. However, transmission delay needs to be considered in MEC systems, and the size of the transmission delay is determined by the transmission environment of the offload link. When wireless devices (WDs) are located at the edge of a cell or the communication link between base stations (BSs) and WDs is blocked, the offload link becomes worse, resulting in larger transmission delays. Therefore, studying how to improve the wireless communication environment is crucial to further develop the potential of MEC systems.

[0003] In order to provide better offloading links, an ultra-dense network (UDN) architecture with a large number of small BSs can be adopted to shorten the distance between BSs and WDs, or provide a direct link between them. However, as the number of BSs increases, inter-cell interference becomes a bottleneck for improving network throughput. Therefore, a user-centric decellularized network structure is proposed, in which BSs serve all WDs simultaneously to avoid multi-cell interference. On the other hand, due to the deployment of a large number of BSs, the energy consumption and hardware cost of cell-free networks are high. In recent years, a smart reflecting surface (IRS) composed of a large number of low-power passive reflecting elements has been proposed, which can focus the signal energy to the desired spatial direction by adjusting the phase shift of the reflecting surface, thereby expanding the wireless coverage. Summary of the invention

[0004] When WDs are located at the edge of the cell or the communication link between the base station BSs and WDs is blocked, the unloading delay will be very large. In order to solve this problem, the present invention proposes a fair resource allocation method for de-cellular network users of RIS-assisted edge computing. IRSs are used to replace some BSs, and the delay optimization problem in the cellular-free network system of IRS-assisted edge computing is studied.

[0005] The technical solution of the present invention is achieved in this way:

[0006] A RIS-assisted edge computing method for fair resource allocation to cellular network users, the steps of which are as follows:

[0007] S1. Build an IRS-assisted edge computing decellularized network system, including K single-antenna WDs, I IRSs, and B' BSs; and calculate the channel state information of all relevant channels;

[0008] S2, by jointly designing the multi-user detection MUD matrix, the reflection beamforming vector of IRSs, the transmission power of WDs and the edge computing resource allocation, an objective optimization function to minimize the maximum delay of users is established;

[0009] S3, introducing auxiliary variables t to transform the target optimization function into the objective function, and using the alternating optimization algorithm of block coordinate descent technology to divide the objective function into sub-objective function I and sub-objective function II;

[0010] S4. Sub-objective function I and sub-objective function II are jointly optimized and solved by alternating iterations to obtain the optimal values ​​of the offloaded data volume, edge computing resources, reflection beamforming vectors of IRSs, and MUD matrix.

[0011] Preferably, in step S1, the channel state information of the relevant channel is calculated by:

[0012] The direct link between the kth WD and the bth BS is expressed as The reflection link from the kth WD to the i-th IRS is expressed as The reflection link between the i-th IRS and the b-th BS is expressed as represents the space of m×n complex-valued matrices; the phase shift coefficient vector of the i-th IRS is denoted by θ i =[θ i,1 ,θ i,2 ,…,θ i,N ] T ,θ i,n ∈[0,2π); diagonal reflection matrix Θ of the i-th IRS i for:

[0013]

[0014] Among them, β i,n ∈[0,1] represents the reflection amplitude of the IRS element, represents the set of IRSs; the equivalent effective channel h from the kth WD to the bth BS b,k Defined as:

[0015]

[0016] Set all WDs to transmit at the same power; represents the multi-user detection MUD vector of the k-th WD on the b-th BS; the detection signal of the k-th WD at BSs It is expressed as:

[0017]

[0018] Among them, P t represents the unloading power of K WDs, s = [s 1 ,s 2 ,...,s j ,...,s K ] T represents K WDs signals; Indicates w b,k The conjugate transpose of Indicates w k The conjugate transpose of h d,b,j represents the direct link gain from the bth base station to the jth user, h r,i,j represents the reflection link gain from the i-th IRS to the j-th user, represents the noise vector received by the bth base station, h d,j represents the direct link gain of the jth user, is the MUD matrix The kth column of (a) Establishment by definition and (b) Established by definition Θ=diag(Θ 1 ,...,Θ I ), (c) It is established by defining h k =h d,k +GΘh r,k ; Therefore, the received SINR of the kth WD is:

[0019]

[0020] Among them, γ k (w k ,θ) is the received SINR of the kth WD; σ 2 represents the noise power at user k, θ is the reflection beamforming vector of IRSs;

[0021] The achievable rate for user k is

[0022] R k (w k ,θ)=Blog 2 (1+γk (w k ,θ)). (5);

[0023] Among them, R k (w k ,θ) represents the offload data rate of the kth user, and B represents the system bandwidth.

[0024] The RIS-assisted edge computing de-cellular network user fairness resource allocation method according to claim 2 is characterized in that, in step S2, a local computing delay model and an edge computing delay model are respectively constructed, which are respectively expressed as;

[0025]

[0026]

[0027] in, Calculate the delay locally, Delay for edge computing; represents the CPU cycle frequency of the kth WD, L k represents the total amount of data calculated for the kth WD, represents the amount of data unloaded by the kth WD, c k represents the computational complexity of the input data of the kth WD; Represents the total computing resources of the MEC server, Indicates the computing resources allocated by the MEC server to the kth WD, satisfying

[0028] Based on the local computing delay model and the edge computing delay model, the total delay of the kth WD is expressed as:

[0029]

[0030] Offloading data volume through joint optimization Edge computing resources The MUD matrix W and the reflected beamforming vector θ are used to minimize the maximum delay of WD. The objective optimization function is expressed as

[0031]

[0032] Wherein, formula (7a) is the IRS reflection coefficient constraint, and formula (7b) indicates that the amount of unloaded data of the kth WD is between 0 and the total input data volume L k The integer constraint between ; Formula (7c) indicates that the computing resources allocated to all WDs do not exceed the total edge computing resource constraint; Formula (7e) indicates the unit detection vector constraint of the kth WD.

[0033] Preferably, the objective function is:

[0034]

[0035] Preferably, the sub-objective function I is:

[0036]

[0037] Sub-objective function II is:

[0038]

[0039] Preferably, the method for jointly optimizing and solving the sub-objective function I and the sub-objective function II by alternating iteration is: firstly, given W and θ, the amount of unloaded data and edge computing resources e Optimize; then, based on the obtained and f e , optimize the MUD matrix W and the reflection beam forming vector θ; repeat the above process until convergence;

[0040] Uninstall data volume and edge computing resources e The optimization method is:

[0041] For a given W and θ, Expressed as

[0042] For a given f e , the optimal amount of unloaded data is:

[0043]

[0044] in, Indicates the operation of rounding down to an integer. Indicates the operation of rounding up to an integer, and selects The value of The values ​​are as follows:

[0045]

[0046] After obtaining the relationship between the offload data size and edge computing resources, substitute equation (11) into equation (9a) to obtain Rewrite it as:

[0047]

[0048] First, we reformulate (12a) as Then, by searching t equally, It is equivalent to the following feasibility problem:

[0049]

[0050] in, is t in the first 1 The value at iteration ; for a given target delay Through the CVX solver Solve it and get and f e The optimal solution of

[0051] The optimization method of the MUD matrix W and the reflected beamforming vector θ is:

[0052] According to the obtained and f e , can be simplified to

[0053] Optimize the MUD matrix W:

[0054] For a given reflected beamforming vector θ, can be rewritten as:

[0055]

[0056] By fixing t, we introduce the following feasibility problem

[0057]

[0058] in, The optimal solution is t * , for any given t≥t * , is feasible; if t≤t * , It is not feasible;

[0059] Rewrite the inequality in equation (15a) as:

[0060]

[0061] in, According to formula (17), It is still feasible after any phase rotation; based on this, a set of {w k},satisfy:

[0062]

[0063] Among them, Re(x) represents the real part operation, and Im(x) represents the imaginary part operation; The real and imaginary parts of are non-negative real numbers and zero, respectively, such as: Then, define a matrix A whose (j,k) elements are .|| 2 represents the 2-norm of a vector. Based on this, equation (17) can be re-expressed as:

[0064]

[0065] in, represents a vector, The kth element of is 1, and the other elements are zero; for a given tl at the lth iteration, It can be equivalently expressed as:

[0066]

[0067] Solve using CVX solver Get the optimal solution of the MUD matrix W;

[0068] Optimization of the reflected beamforming vector θ:

[0069] First define and Therefore, we have:

[0070]

[0071] in, and After getting W, can be restated as:

[0072]

[0073] Solving based on semidefinite relaxation SDR method

[0074] First, Rephrased as:

[0075]

[0076] in, R k,j and They are defined as:

[0077] and

[0078] definition And satisfy V ≥ 0, V ≥ 0 represents a semi-positive definite matrix, rank (V) = 1; can be re-expressed as:

[0079]

[0080] Among them, Tr(.) represents the trace operation; based on the binary search of t, by solving Solution to the feasibility problem

[0081]

[0082] in, is t in the first 2 The value of the iteration; through the CVX solver Solving, we can find the optimal solution; based on successive convex approximation SCA solution

[0083] For a specific iteration l ≥ 1, first v (l-1) is defined as the value of v obtained in the previous iteration; then, for a given The edge computing latency of the achievable maximum WD is expressed as

[0084] First, according to formula (22a), an auxiliary function is introduced It is defined as:

[0085]

[0086] If (v,{w k},t) is A set of feasible solutions for Each iteration solves After that, the maximum is equal to 0, that is, Therefore, the reflection beamforming vector can be updated by equivalently solving the following optimization problem:

[0087]

[0088] when therefore, It can be solved by To solve equivalently;

[0089] At a given t (l) , and local point v (l-1) In the case of The upper bound of is:

[0090]

[0091] Will Replace with And introduce another auxiliary variable z, It can be approximated as:

[0092]

[0093] Through the CVX solver The optimal solution of the reflected beam forming vector θ is obtained.

[0094] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention proposes a decellularized network system with intelligent reflection surface (IRS) assisted edge technology, which is composed of multiple BSs and IRSs to improve the transmission environment. The use of IRSs in the decellularized MEC system is superior to the traditional MEC system, and can reduce the delay by about 60% at most. The optimization algorithm of the IRSs reflection vector based on semidefinite relaxation (SDR) and successive convex approximation (SCA) technology adopted by the present invention has fast convergence, which is conducive to practical implementation. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0096] Figure 1 This is the IRS-assisted de-cellular network system proposed by the present invention.

[0097] Figure 2 This is the channel model in the IRS-assisted decellularized network system of the present invention.

[0098] Figure 3 Simulation scenario setup for offloading data to five BSs with the assistance of two WDs.

[0099] Figure 4 It is the curve of time delay varying with distance L.

[0100] Figure 5 This is the curve of latency changing with edge computing capability.

[0101] Figure 6 This is the curve of delay changing with the number of iterations. DETAILED DESCRIPTION

[0102] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0103] The embodiment of the present invention provides a RIS-assisted edge computing de-cellular network user fairness resource allocation method, under the edge computing capacity constraint and IRS phase shift constraint, by jointly optimizing the offloading data size Edge computing resources e , the reflection beamforming vector θ and the MUD matrix W to achieve the purpose of minimizing the maximum WD delay. In order to solve this non-convex problem, an algorithm based on block coordinate descent (BCD) is designed, in which the optimization variables related to the computation and communication settings are solved in an alternating iterative manner. The specific steps are as follows:

[0104] S1, such as Figure 1 As shown in the figure, a decellularized network system with IRS-assisted edge computing is built, in which multiple distributed BSs cooperate to serve multiple WDs with the help of IRSs. All IRSs and BSs are connected to a central processing unit via high-speed optical cables. The decellularized network system includes K single-antenna WDs, I IRSs and B' BSs; the number of units in the i-th IRS is denoted as N i , the number of antennas of the b-th base station is expressed as M b , let N i =N,M b =M, and represents the number of IRS units, represents the set of BSs, represents the set of IRSs, represents a set of WDs; Figure 2 As shown, a block fading channel model is adopted, in which the wireless channel remains unchanged in the current time block but changes in different time blocks, and it is assumed that the channel state information (CSI) of all relevant channels can be obtained using existing advanced channel estimation methods.

[0105] The direct link between the kth WD and the bth BS is expressed as The reflection link from the kth WD to the i-th IRS is expressed as The reflection link between the i-th IRS and the b-th BS is expressed as The phase shift coefficient vector of the i-th IRS is represented by θ i =[θ i,1 ,θ i,2 ,…,θ i,N ]T ,θ i,n ∈[0,2π); diagonal reflection matrix Θ of the i-th IRS i for:

[0106]

[0107] Among them, β i,n ∈[0,1] represents the reflection amplitude of the IRS element, represents the set of IRSs; assume that each element is fixed to 1 to maximize the reflected signal power. Therefore, the equivalent effective path h from the kth WD to the bth BS is b,k Defined as:

[0108]

[0109] P t represents the unloading power of K WDs, s = [s 1 ,s 2 ,...,s j ,...,s K ] T represents K WDs signals; for simplicity, all WDs are assumed to transmit with the same power; represents the multi-user detection MUD vector of the k-th WD on the b-th BS; the detection signal of the k-th WD at BSs It is expressed as:

[0110]

[0111] in, Indicates w b,k The conjugate transpose of Indicates w k The conjugate transpose of d,b,j represents the direct link gain from the bth base station to the jth user, h r,i,j represents the reflection link gain from the i-th IRS to the j-th user, represents the noise vector received by the bth base station, h d,j represents the direct link gain of the jth user, is the MUD matrix The kth column of (a) Establishment by definition and (b) Established by definition Θ=diag(Θ 1 ,...,Θ I ), (c) It is established by defining h k =hd,k +GΘh r,k ; Therefore, the received SINR of the kth WD is:

[0112]

[0113] Among them, γ k (w k ,θ) is the received SINR of the kth WD; σ 2 represents the noise power at the user end, θ is the reflection beamforming vector of IRSs;

[0114] The achievable rate for user k is

[0115] R k (w k ,θ)=Blog 2 (1+γ k (w k ,θ)). (5);

[0116] Among them, R k (w k ,θ) represents the offload data rate of user k, and B represents the system bandwidth.

[0117] S2, by jointly designing the multi-user detection MUD matrix, the reflection beamforming vector of IRSs, the transmission power of WDs and the edge computing resource allocation, the objective optimization function of minimizing the maximum delay of users is established;

[0118] In step S2, a local computing delay model and an edge computing delay model are constructed, which are represented as follows:

[0119]

[0120]

[0121] in, Calculate the delay locally, Delay for edge computing; represents the CPU cycle frequency of the kth WD, L k represents the total amount of data calculated for the kth WD, represents the amount of data unloaded by the kth WD, c k represents the computational complexity of the input data of the kth WD; the latency of edge computing usually includes three parts: a) the offloading latency of transmitting the computational data to the BS; b) the processing latency of executing the offloaded data on the MEC server; c) the latency of returning the computational results to the WDs. Represents the total computing resources of the MEC server, Indicates the computing resources allocated by the MEC server to the kth WD, satisfying The return latency is ignored here because the returned results are usually small.

[0122] Based on the local computing delay model and the edge computing delay model, the total delay of the kth WD is expressed as:

[0123]

[0124] Considering the fairness among WDs, the amount of data offloaded is optimized through joint optimization Edge computing resources The MUD matrix W and the reflected beamforming vector θ are used to minimize the maximum delay of WD. The objective optimization function is expressed as

[0125]

[0126] Wherein, formula (7a) is the IRS reflection coefficient constraint, and formula (7b) indicates that the amount of unloaded data of the kth WD is between 0 and the total input data volume L k The integer constraint between ; Formula (7c) indicates that the computing resources allocated to all WDs do not exceed the total edge computing resource constraint; Formula (7e) indicates the unit detection vector constraint of the kth WD. Obviously, It is difficult to solve directly.

[0127] S3, introducing auxiliary variables t to transform the target optimization function into the objective function, and using the alternating optimization algorithm of block coordinate descent technology to divide the objective function into sub-objective function I and sub-objective function II;

[0128] First, introduce an auxiliary variable t. Converts to the following

[0129]

[0130] Although The objective function (OF) and constraint (8b) are linear, and can be directly solved due to the following three aspects: Still challenging are: a) the piecewise form of (8a), b) the MUD matrix W and the reflected beamforming vector θ are coupled together, and c) (8) is non-convex with respect to θ. In general, there is no standard method to find the global optimal solution to such a non-convex optimization problem. To this end, an iterative algorithm is designed to obtain a local optimal solution. Specifically, the piecewise form of (8a) is reformulated into a linear form. Then, the computational settings are determined to alternately optimize the MUD matrix and the reflected beamforming vector. Finally, two effective algorithms based on SDR and SCA techniques are designed to obtain local optimal solutions for θ, respectively.

[0131] S4. Sub-objective function I and sub-objective function II are jointly optimized and solved by alternating iterations to obtain the optimal values ​​of the offloaded data volume, edge computing resources, reflection beamforming vectors of IRSs, and MUD matrix.

[0132] First, use BCD technology to It is divided into two independent sub-problems. Specifically, first, given W and θ, the amount of unloaded data and edge computing resources e Then, based on the obtained and f e , optimize the MUD matrix W and the reflected beamforming vector θ. Repeat the above process until convergence.

[0133] Uninstall data volume and edge computing resources e The optimization method is:

[0134] For a given W and θ, Expressed as

[0135]

[0136] For a given f e , the optimal amount of unloaded data is:

[0137]

[0138] in, Indicates the operation of rounding down to an integer. Indicates the operation of rounding up to an integer, and selects The value of The values ​​are as follows:

[0139]

[0140] let Represents integer values In addition, fix f e ,use represents the overall delay of the kth WD. Based on formula (6), can be restated as:

[0141]

[0142] From the above formula, it can be seen that when Increase from 0 to Delay decreases, however, when from Increase to Lk ,Delay Then, let The minimum delay of the kth WD is achieved. In addition, the amount of unloaded data must be a non-negative integer, so the optimal By performing the operation

[0143] After obtaining the relationship between the offload data size and edge computing resources, substitute equation (11) into equation (9a) to obtain Rewrite it as:

[0144]

[0145] is a non-convex problem; first, we reformulate (12a) as Then, by searching t equally, It is equivalent to the following feasibility problem:

[0146]

[0147] in, is t in the first 1 The value at iteration ; for a given target delay Through the CVX solver Solve it and get and f e The optimal solution of

[0148] if is feasible, then a given delay t can be achieved. Assume The optimal solution is It can be inferred that for any given t, if It is feasible and can be obtained And if Not feasible, yes Therefore, by searching for equal parts of t, we can check For a given t ≥ 0, we can equivalently solve

[0149] In summary, solving The process is shown in Algorithm 1.

[0150]

[0151] The optimization method of the MUD matrix W and the reflected beamforming vector θ is:

[0152] According to the obtained and f e , can be simplified to

[0153]

[0154] Solution It involves the joint optimization of the MUD matrix W, the beamforming vector {θ}, and the delay t, using an alternating iterative optimization algorithm to solve

[0155] Optimize the MUD matrix W:

[0156] For a given reflected beamforming vector θ, can be rewritten as:

[0157]

[0158] because It is still non-convex. By fixing t, we introduce the following feasibility problem:

[0159]

[0160] Hypothetical Question The optimal solution is t * , similar to the analysis in Section 3.1, for any given t ≥ t * , However, if t≤t * , is not feasible. Therefore, using binary search, Can be checked feasibility to solve it equivalently.

[0161] Rewrite the inequality in equation (15a) as:

[0162]

[0163] in, According to equation (17), it is obvious that for a feasible solution {w k}, It is still feasible after any phase rotation; based on this, a set of {w k},satisfy:

[0164]

[0165] Among them, Re(x) represents the real part operation, and Im(x) represents the imaginary part operation; The real and imaginary parts of are non-negative real numbers and zero, respectively, such as: Then, define a matrix A whose (j,k) elements are .|| 2 represents the 2-norm of a vector. Based on this, equation (17) can be re-expressed as:

[0166]

[0167] in, represents a vector, The kth element of is 1, and the other elements are zero; for a given tl at the lth iteration, It can be equivalently expressed as:

[0168]

[0169]

[0170] is a SOCP problem that can be solved using existing standard convex optimization techniques (CVX solver) Get the optimal solution of the MUD matrix W.

[0171] Optimization of the reflected beamforming vector θ:

[0172] Unlike solving W, since θ is common to all users, SOCP technology cannot find the optimal θ, making For all All are real numbers.

[0173] First define and Therefore, we have:

[0174]

[0175] in, and After getting W, can be restated as:

[0176]

[0177] Due to the existence of non-convex constraints (22a) and (22b), It is still difficult to solve directly. Next, two effective solutions based on SDR and SCA technology are designed to solve this problem.

[0178] Solving based on semidefinite relaxation SDR method

[0179] First, Rephrased as:

[0180]

[0181] in, R k,j and They are defined as:

[0182] and

[0183] definition And satisfy V ≥ 0, V ≥ 0 represents a semi-positive definite matrix, rank (V) = 1; can be re-expressed as:

[0184]

[0185] Where Tr(.) represents the trace operation; due to the rank 1 constraint, is non-convex. To continue solving, relax the rank 1 constraint and perform a binary search on t by solving Solution to the feasibility problem

[0186]

[0187] in, is t in the first 2 The value of the iteration; obviously, is a classic SDR problem, and the optimal solution can be found by the CVX solver. However, The SDR may not be tight. In this case, we can use Gaussian randomization technology based on The high-rank solution obtained in A feasible solution of .

[0188] In summary, by alternating and To find out The specific steps are shown in Algorithm 2. For each iteration, we first solve the problem based on θ obtained in the previous iteration. Then solve according to W obtained in step 3 From the solution Start, don’t solve because is feasible at any given θ, but the converse may not be true.

[0189] In addition, based on the proposed algorithm 2, OF is monotonically non-increasing.

[0190]

[0191] According to a set of solutions (W,θ) The OF value in is defined as In the (l 2 ) iterations, if is feasible, then the solution ) is also a problem A feasible solution of . and Representing the problem In the (l 2 ) and (l 2 +1) times the optimal solution. yes The optimal solution of , then, Therefore, the following inequality can be obtained

[0192] when When the solution of is not rank 1, a Gaussian randomization process is needed to reconstruct a rank 1 solution. Therefore, the performance of the reconstructed solution depends heavily on the generated Gaussian random numbers. For example, due to the uncertainty of randomization, it may be found This results in highly suboptimal solutions, which will lead to performance degradation. In addition, in order to find a better solution, a large number of Gaussian random numbers need to be generated. And solving the SDR problem is time-consuming, especially when the matrix dimension is large. Therefore, in order to reduce the computational complexity and ensure performance, a more efficient algorithm needs to be further designed.

[0193] SCA solution based on successive convex approximation

[0194] In order to overcome the shortcomings of SDR technology, an effective scheme based on SCA technology is proposed to update the reflection beamforming vector v. Instead, we try to find a feasible solution v that reduces the maximum edge computing latency. In particular, for a specific iteration l≥1, we first convert v( l-1 ) is defined as the value of v obtained in the previous iteration; then, for a given The edge computing latency of the achievable maximum WD is expressed as

[0195] First, according to formula (22a), an auxiliary function is introduced It is defined as:

[0196]

[0197] If (v,{w k},t) is A set of feasible solutions for Each iteration solves After that, the maximum is equal to 0, that is, Therefore, the reflection beamforming vector can be updated by equivalently solving the following optimization problem:

[0198]

[0199] when That is, the maximum edge computing latency is reduced. It can be solved by To solve equivalently;

[0200] because The OF of is non-convex, so it is difficult to solve directly. Inspired by the SCA technique, we first use the first-order Taylor expansion of the second convex term to obtain A convex upper bound on . At a given t (l) , and local point v (l-1) In the case of The upper bound of is:

[0201]

[0202] Will Replace with And introduce another auxiliary variable z, It can be approximated as:

[0203]

[0204] So far, is converted into a convex form, which can be solved by existing convex optimization solvers such as CVX. Assume that v * yes The optimal solution of Substitution It can be found The feasible solution of It is still feasible, so the solution is We can get a better solution than Smaller value. Algorithm 3 gives the specific steps based on the SCA algorithm.

[0205]

[0206] In Algorithm 4, a solution based on BCD is provided The specific steps of the algorithm. It is worth noting that the auxiliary variable t is also OF is continuously updated as steps 2 and 3 are implemented. and Indicates that in (l 4-1) iteration, the value of t after step 3 is achieved, and the value of t after step 1 is achieved 4 In the iteration, the value of t after step 2 is achieved. This is because in step 2, can be regarded as the overall maximum delay of WD. However, in step 3, is the maximum edge computing delay of WD. However, since the overall delay of WD and the edge processing delay of WD are reduced in different iterations, the convergence of Algorithm 4 can be guaranteed. Therefore, we can get

[0207]

[0208] Simulation Analysis

[0209] The performance of the method of the present invention is evaluated by simulation. Consider a three-dimensional system model such as Figure 3 As shown in Figure 1, 5 BSs provide services to two WDs at the same time. WDs can choose to offload part of the computational data to the MEC node for remote computation with the assistance of two IRSs. The detailed location settings of BS and IRS are provided in the “Location Model” module in Table 1.

[0210] Table 1 Simulation default parameter settings

[0211]

[0212] The distance-dependent path loss model is:

[0213]

[0214] Here C 0 =-30dB is the reference distance d 0 =1m, d is the corresponding channel distance, and κ is the path loss exponent. The specific settings are shown in the "Communication Model" module in Table 1. Then, for small-scale fading, all relevant channels use the Rician fading channel model. Therefore, the channel model H is:

[0215]

[0216] Here β UB Refers to the Rayleigh factor, H LoS and H NLoS denote the LoS deterministic component and the non-LOS Rayleigh fading component respectively. H is equivalent to the Rayleigh fading channel when β UB = 0 and LoS channel when β UB→∞. Note that for the WD-BS channel model, the square root of the large-scale fading coefficient needs to be multiplied by the element of the small-scale fading coefficient. Similarly, the WD-IRS and IRS-BS channels can also be generated according to the above steps, using β UI and β IB represents their Rician factors. In addition, set β IB →∞,β UI = 0, and β UB = 0. The default settings for these parameters are given in the “Communication Model” module of Table 1. In addition, the calculation settings are specified in the “Calculation Model” module of Table 1. The simulation results are given below to evaluate the maximum WD delay achieved by the proposed BCD-based algorithm in various simulation environments and compared with the following benchmark algorithms:

[0217] No IRS: Set the reflection matrix Θ to the zero matrix and optimize other optimization variables using Algorithm 4.

[0218] No direct links: Assume that all direct links between WDs and BSs are completely blocked by some mobile or static objects, i.e., H = 0, and all variables are optimized using Algorithm 4.

[0219] Random phase shift: The IRS phase shift is set to a uniformly distributed random value in the range [0, 2π), while the other optimization variables are optimized using Algorithm 4.

[0220] Figure 4-6 The delays for different parameter settings are given.

[0221] 1) Influence of WDs position: Figure 4 The effect of WDs location on latency under different algorithms / schemes is shown. It is observed that the two algorithms proposed in the present invention can achieve lower latency compared to the baseline algorithm, especially when WDs are close to IRSs. In addition, for all IRS-added schemes, there are two obvious troughs at L=60m and L=100m. This is because when WDs are close to either of the two IRSs, the IRSs can receive stronger signals transmitted from WDs. In addition, under the “no IRS” scheme, the latency increases when the WD is far away from the BSs. Compared with the “no IRS” scheme, the latency reduction of the “random phase shift” scheme is very limited. In addition, it is observed that the latency of the “no direct link” scheme is the highest, and when the WD is close to one of the two IRSs, the latency gap is larger than that of the proposed scheme. Therefore, deploying an IRS with an optimized phase shift design can expand signal coverage, improve the signal transmission environment, and reduce latency.

[0222] 2) Impact of edge computing capabilities: Figure 5 The relationship between latency and edge computing capabilities under different schemes is shown. It can be observed that for all schemes, when When it is small, the delay increases with decreases significantly with the increase of Reach a certain value, that is, 30×10 9 cycle / s, the delay starts to decrease slowly. This is because when When is small, edge processing delay plays a dominant role, while when When,becomes larger, the offloading latency dominates. This shows that it is cost-effective to equip edge servers with appropriate computing power in order to minimize latency.

[0223] 3) Convergence: In order to demonstrate the convergence of the method of the present invention, Figure 6 The delay is given by the number of iterations I o The results show that all the considered algorithms have fast convergence, which verifies the practicality of the algorithms.

[0224] The present invention combines the edge computing capacity constraint and the IRS phase shift constraint to optimize the unloaded data size. Edge computing resources e , the reflection beamforming vector θ and the MUD matrix W to achieve the purpose of minimizing the maximum WD delay. In order to solve this non-convex problem, a BCD-based algorithm is designed, in which the optimization variables related to the computation and communication settings are solved in an alternating iterative manner. A large number of simulation results verify the benefits of deploying IRS in MEC systems. In particular, compared with traditional MEC systems, the delay can be reduced from 160ms to 100ms for distances L = 60m and 100m. In addition, the simulation results show that the method of the present invention has fast convergence, verifying its engineering feasibility.

[0225] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A fair resource allocation method for RIS-assisted edge computing in cellular network users. It is characterized in that The steps are as follows: S1. Build an IRS-assisted edge computing decellularized network system, including K single-antenna WDs, I IRSs, and B' BSs; and calculating channel state information of all relevant channels; In step S1, the channel state information of the relevant channel is calculated as follows: The direct link between the kth WD and the bth BS is expressed as The reflection link from the kth WD to the i-th IRS is expressed as The reflection link between the i-th IRS and the b-th BS is expressed as represents the space of m×n complex-valued matrices; the phase shift coefficient vector of the i-th IRS is denoted by θ i =[θ i,1 ,θ i,2 ,…,θ i,N ] T ,θ i,n ∈[0,2π); diagonal reflection matrix Θ of the i-th IRS i for: Among them, β i,n ∈[0,1] represents the reflection amplitude of the IRS element, represents the set of IRSs; the equivalent effective channel h from the kth WD to the bth BS b,k Defined as: Set all WDs to transmit at the same power; represents the multi-user detection MUD vector of the k-th WD on the b-th BS; the detection signal of the k-th WD at BSs It is expressed as: Among them, P t represents the unloading power of K WDs, s = [s 1 ,s 2 ,...,s j ,...,s K ] T represents K WDs signals; s j represents the uninstall signal of the jth user; h j =h d，j +Gh r，j represents the combined channel from the jth user to the BS; Indicates w b,k The conjugate transpose of Indicates w k The conjugate transpose of h d,b,j represents the direct link gain from the bth base station to the jth user, h r,i,j represents the reflection link gain from the i-th IRS to the j-th user, represents the noise vector received by the bth base station, h d,j represents the direct link gain of the jth user, is the MUD matrix The kth column of (a) Establishment by definition and (b) Established by definition Θ=diag(Θ 1 ,...,Θ I ), (c) It is established by defining h k =h d,k +GΘh r,k ; Therefore, the received SINR of the kth WD is: Among them, γ k (w k ,θ) is the received SINR of the kth WD; σ 2 represents the noise power at user k, θ is the reflection beamforming vector of IRSs; The achievable rate for user k is R k (w k ,i)=Blog 2 (1+c k (w k (5); Among them, R k (w k ,θ) represents the offload data rate of the kth user, and B represents the system bandwidth; S2, by jointly designing the multi-user detection MUD matrix, the reflection beamforming vector of IRSs, the transmission power of WDs and the edge computing resource allocation, an objective optimization function to minimize the maximum delay of users is established; In step S2, a local computing delay model and an edge computing delay model are constructed, which are represented as follows: in, Calculate the delay locally, Delay for edge computing; represents the CPU cycle frequency of the kth WD, L k represents the total amount of data calculated for the kth WD, l k represents the amount of data unloaded by the kth WD, c k represents the computational complexity of the input data of the kth WD; Represents the total computing resources of the MEC server, Indicates the computing resources allocated by the MEC server to the kth WD, satisfying Based on the local computing delay model and the edge computing delay model, the total delay of the kth WD is expressed as: The amount of data unloaded by joint optimization is l = [l 1 ,l 2 ,...,l K ] T , edge computing resources The MUD matrix W and the reflected beamforming vector θ are used to minimize the maximum delay of WD. The objective optimization function is expressed as in, represents the user index set, K represents the total number of users; Formula (7a) is the IRS reflection coefficient constraint, and Formula (7b) represents the kth WD’s unloaded data volume between 0 and the total input data volume L k The integer constraint between ; Formula (7c) indicates that the computing resources allocated to all WDs do not exceed the total edge computing resource constraint; Formula (7e) indicates the unit detection vector constraint of the kth WD; S3, introducing auxiliary variables t to transform the target optimization function into the objective function, and using the alternating optimization algorithm of block coordinate descent technology to divide the objective function into sub-objective function I and sub-objective function II; The objective function is: (7a),(7b),(7c),(7d),(7e).(8b) in, represents the total computation delay of the kth user, and the variable is The sub-objective function I is: Sub-objective function II is: S4. The sub-objective function I and the sub-objective function II are jointly optimized and solved by alternating iterations to obtain the optimal values ​​of the offloaded data volume, edge computing resources, the reflection beamforming vector of IRSs, and the MUD matrix. The joint optimization solution method is as follows: first, given W and θ, the offloaded data volume l and the edge computing resources f e Optimize; then, based on the obtained l and f e , optimize the MUD matrix W and the reflection beam forming vector θ; repeat the above process until convergence; Offload data volume l and edge computing resources f e The optimization method is: For a given W and θ, Expressed as For a given f e , the optimal amount of unloaded data is: in, Indicates the operation of rounding down to an integer. Indicates the operation of rounding up to an integer, and selects The value of The values ​​are as follows: After obtaining the relationship between the offload data size and edge computing resources, substitute equation (11) into equation (9a) to obtain Rewrite it as: First, we reformulate (12a) as Then, by searching t equally, It is equivalent to the following feasibility problem: in, is t in the first 1 The value at iterations; for a given target delay Through the CVX solver Solve and get l and f e The optimal solution of The optimization method of the MUD matrix W and the reflected beamforming vector θ is: According to the obtained l and f e , can be simplified to Optimize the MUD matrix W: For a given reflected beamforming vector θ, can be rewritten as: By fixing t, we introduce the following feasibility problem in, The optimal solution is t * , for any given t≥t * , is feasible; if t≤t * , It is not feasible; Rewrite the inequality in equation (15a) as: in, B represents the channel bandwidth, p t represents the user unloading power; according to formula (17), It is still feasible after any phase rotation; based on this, a set of {w k },satisfy: Among them, Re(x) represents the real part operation, and Im(x) represents the imaginary part operation; The real and imaginary parts of are non-negative real numbers and zero, respectively, such as: Then, define a matrix A whose (j,k) elements are ||.|| 2 represents the 2-norm of a vector. Based on this, equation (17) can be re-expressed as: in, represents a vector, The kth element of is 1, and the other elements are zero; for a given t at the lth iteration l , It can be equivalently expressed as: Solve using CVX solver Get the optimal solution of the MUD matrix W; Optimization of the reflected beamforming vector θ: First define and Therefore, we have: in, and After getting W, can be restated as: Solving based on semidefinite relaxation SDR method First, Rephrased as: in, R k,j and They are defined as: and definition And satisfy V ≥ 0, V ≥ 0 represents a semi-positive definite matrix, rank (V) = 1; can be re-expressed as: Among them, Tr(.) represents the trace operation; based on the binary search of t, by solving Solution to the feasibility problem in, is t in the first 2 The value of the iteration; through the CVX solver Solving, we can find the optimal solution; based on successive convex approximation SCA solution For a specific iteration l ≥ 1, first v (l-1) is defined as the value of v obtained in the previous iteration; then, for a given The edge computing latency of the achievable maximum WD is expressed as represents the edge computing latency of the kth user; First, according to formula (22a), an auxiliary function is introduced It is defined as: If (v,{w k },t) is a set of feasible solutions to P3.4, Each iteration solves After that, the maximum is equal to 0, that is, Therefore, the reflection beamforming vector can be updated by equivalently solving the following optimization problem: st(22b). when therefore, It can be solved by To solve equivalently; At a given t (l) , and local point v (l-1) In the case of The upper bound of is: Will Replace with And introduce another auxiliary variable z, It can be approximated as: Through the CVX solver The optimal solution of the reflected beam forming vector θ is obtained.

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