Time delay optimization method in non-ideal intelligent metasurface assisted broadband edge calculation

Abstract

The invention provides a time delay optimization method in non-ideal intelligent metasurface-assisted broadband edge calculation. The time delay optimization method is used for solving the technical problem that an IRS of an existing ideal reflection model cannot reflect a real reflection model. The method comprises the following steps of: unloading data from a base station equipped with an edge server by a user under the assistance of an IRS to construct a non-ideal IRS model; according to a phase shift model, a communication model and a calculation model of the non-ideal IRS model, constructing an optimization problem for jointly optimizing user unloading data volume, edge calculation resources, MUD vectors and reference phase shift of the IRS to minimize weighting and time delay of all users; a block coordinate descent algorithm is adopted to jointly optimize computing resources and communication resources. According to the method, the non-convex IRS reflection constraint problem can be effectively simplified by alternately optimizing calculation and communication resources, the solving efficiency is improved, and better resource allocation and performance optimization are realized. By optimizing the resource allocation of the IRS-assisted broadband mobile edge computing system, the user time delay can be remarkably reduced, the system performance and the resource utilization efficiency are improved, and meanwhile, the importance and the performance gain of the non-ideal IRS reflection model are verified.

Description

Technical Field

[0001] The present invention relates to the technical field of mobile edge computing, and in particular to a delay optimization method in non-ideal intelligent metasurface-assisted broadband edge computing. Background Art

[0002] The ultra-high communication rate requirements of 5G and B5G networks have promoted the development of many enabling technologies, including MIMO (multiple input multiple output), ultra-dense networks, and the use of millimeter wave bandwidth. However, the related energy consumption and hardware costs are still bottlenecks for their large-scale deployment. Intelligent reflecting surfaces (IRS), composed of a large number of ultra-low power and nearly passive reflecting elements, have entered the wireless communication research community as a revolutionary technology. It can combat the randomness of wireless transmission and achieve a controllable wireless propagation environment. Adaptive adjustment of IRS reflective units can collaboratively realize reflection beamforming and use beamforming gain to improve communication quality. Since it does not include RF chains, large-scale IRS can be deployed in different communication scenarios, greatly reducing power consumption and costs.

[0003] It is worth noting that most of the existing research on IRS-assisted wireless communication systems is limited to narrowband channels. When considering more general broadband frequency-selective channels, the problem will be very different and more difficult to solve, because a universal IRS reflection pattern needs to be designed for all subcarriers, while traditional digital beamformers are only optimized for each subcarrier separately. Most of the existing work on IRS assumes an ideal IRS reflection model, that is, each reflection unit has a constant reflection amplitude, a variable phase shift, and the same broadband signal response. The IRS design under the ideal reflection model can be easily implemented using classical optimization tools such as semidefinite relaxation, manifold optimization, and maximum minimization (MM). However, due to the limitations of hardware circuits, this ideal reflection model of IRS is difficult to implement. This design that does not reflect the real reflection model will inevitably cause non-negligible performance loss in actual systems.

[0004] The invention patent with application number 202410261244.9 relates to the field of communication technology, and in particular, provides a delay optimization method for a millimeter wave mobile edge computing system based on an intelligent reflective surface. The above method includes constructing a millimeter wave mobile edge computing system with an intelligent reflective surface, the system includes K single-antenna IoT devices, two intelligent reflective surfaces, an edge server, and a millimeter wave base station; channel modeling is performed based on the intelligent reflective surface and the millimeter wave base station to construct a 3D millimeter wave Saleh-Valenzuela channel model; according to the channel model, the uplink transmission rate of the IoT device during the calculation offloading process is determined; according to the uplink transmission rate, the optimal calculation offloading amount and the optimized uplink transmission rate are determined. The above method improves the transmission quality of the wireless channel through the intelligent reflective surface, and improves the performance of the system calculation offloading through the partial offloading strategy. However, the above invention does not fully consider dynamic environmental changes and real-time performance requirements. Summary of the invention

[0005] In view of the technical problem that the IRS of the existing ideal reflection model cannot reflect the real reflection model, the present invention proposes a delay optimization method in non-ideal intelligent metasurface assisted broadband edge computing, which uses a three-dimensional amplitude-frequency-phase shift relationship to accurately describe the non-ideal IRS reflection model in the broadband system.

[0006] In order to achieve the above object, the technical solution of the present invention is implemented as follows: a delay optimization method in non-ideal intelligent metasurface assisted broadband edge computing, the steps of which are as follows:

[0007] Step 1: A non-ideal IRS model is constructed based on the data unloading of users to a base station equipped with an edge server under the assistance of IRS. Based on the phase shift model, communication model and calculation model of the non-ideal IRS model, an optimization problem of jointly optimizing the amount of user unloaded data, edge computing resources, MUD vector and the reference phase shift of IRS to minimize the weighted sum delay of all users is constructed;

[0008] Step 2: Use the block coordinate descent algorithm to jointly optimize computing resources and communication resources.

[0009] Preferably, the non-ideal IRS model considers a broadband multi-user orthogonal frequency division multiplexing system with I subcarriers, K single-antenna users unload a certain ratio of computing data to a BS equipped with an edge server with the assistance of IRS, and each user is equipped with a wireless device; the edge server and BS are deployed together and connected by wired optical fiber; it is assumed that the antenna spacing at the BS and the element spacing of the IRS are large enough so that the small-scale fading of different antennas and reflective elements are independent of each other.

[0010] Preferably, in the communication model, let represents the transmission distance from the base station BS to the kth wireless device on the i-th subcarrier, Indicates the frequency domain channel from the base station to the IRS, represents the frequency domain channel from IRS to the kth wireless device; represents the reflection matrix of the i-th subcarrier, φ i,m It represents the phase shift coefficient of the i-th subcarrier on the m-th reflection unit and satisfies the following functional relationship:

[0011] Among them, θ m represents the reference phase shift of the mth IRS, θ=[θ1,…,θ M ] T represents the reference phase shift vector, F(θ m ,f i ) represents the reference phase shift and center frequency f at the mth IRS i The reflection amplitude function, G(θ m ,f i ) is the reference phase shift and center frequency f at the mth IRS i The phase shift function of represents the transmission signal of K wireless devices on the i-th subcarrier, s k,i Indicates the information symbol to be transmitted, [·] T represents transpose; and satisfies Let P t represents the transmission power of the wireless device, then the received signal on the i-th subcarrier at the BS is expressed as

[0012]

[0013] in, represents the noise vector, satisfying n t represents the number of antennas of the nth base station, represents complex Gaussian distribution, σ 2 represents the noise power;

[0014] Let w k,i represents the multi-user detection MUD vector of the kth user on the i-th subcarrier, then the signal of the kth user on the i-th subcarrier recovered at the BS is Expressed as

[0015]

[0016] The signal-to-interference-to-noise ratio of the kth user on the i-th subcarrier is

[0017]

[0018] Correspondingly, the offloading rate of the kth user on the i-th subcarrier is

[0019] R k,i (w k,i ,Φ i )=Blog[1+r k,i (w k,i ,Φ i )];

[0020] The total transmission rate of the kth user is:

[0021]

[0022] in,

[0023] Preferably, the computing model adopts a partial offloading application model in which computing data can be arbitrarily divided: the wireless device offloads part of the computing data to the edge server for remote processing, and performs local computing on the other part of the data; wherein the local computing is: let L k , l k and c k denote the total input data volume, unloaded data volume and number of CPU cycles required to calculate each bit of input data of the kth wireless device respectively; then the local calculation delay is expressed as in, is the local computing capacity of the kth wireless device; in edge computing: and They represent the total computing power of the edge server and the edge computing resources allocated to the kth wireless device, respectively, satisfying Edge computing latency usually includes the offloading latency of computing data and the computing latency on the edge server. The edge computing latency is expressed as

[0024] The total delay of the kth wireless device is

[0025]

[0026] Preferably, by optimizing the amount of data offloaded by the wireless device l = [l1, ..., l k ,…,l K ] T , edge computing resources Multi-user detection MUD vector of base station The reference phase shift θ of the IRS minimizes the weighted sum delay of all wireless devices, and the resulting optimization problem is:

[0027]

[0028] in, represents the weight of the kth wireless device, D k (w k,θ,e k ,f k e ) represents the total delay of the kth wireless device, φ i,m represents the phase shift coefficient of the ith subcarrier on the mth reflection unit, F(θ m ,f i ) represents the reference phase shift θ at the mth IRS m and the center frequency f i The reflection amplitude function, G(θ m ,f i ) is the reference phase shift θ at the mth IRS m and the center frequency f i The phase shift function of the wireless device; the amount of data offloaded by the wireless device e k Should be a value between 0 and the total input data size L k integer; represents the total computing power of the edge server; the multi-user detection MUD vector of the kth user w k,i represents the multi-user detection MUD vector of the k-th user on the i-th subcarrier, represents the edge computing resources of the kth wireless device.

[0029] Preferably, the method of jointly optimizing computing resources and communication resources using a block coordinate descent algorithm is as follows: first, the communication resources are fixed, and the amount of unloaded data and edge computing resources are optimized; then, the computing resources are fixed, and the receiving vector of the base station BS and the reference phase shift of the IRS are optimized until convergence; the segmented objective function is converted into a form that is easier to solve, and the equivalence between sum rate maximization and MSE minimization is utilized. The sub-problem of communication resources is converted into a multivariable problem, which is solved using a block coordinate descent algorithm to solve the reference phase shift of each IRS, and then the reference phase shift θ is iteratively updated until convergence.

[0030] Preferably, when the communication resources are fixed, the method for optimizing the amount of offloaded data and edge computing resources is: for a given base station's received MUD vector W and a reference phase shift θ, the optimization problem is simplified to:

[0031]

[0032] 1) Optimizing the amount of unloaded data: Given a set of solutions {W,θ,f e}, you can set Get the optimal amount of unloaded data

[0033] in, represents the local computing delay corresponding to the optimal offloaded data volume, represents the edge computing latency corresponding to the optimal amount of unloaded data when other optimization variables are given, Indicates the optimized amount of unloaded data;

[0034] Since the amount of data to be unloaded must be a positive integer, the optimal amount of data to be unloaded is for

[0035]

[0036] in, and Respectively represent rounding down and rounding up;

[0037] 2) Optimize edge computing resources e :First, given a set of solutions for {W,θ,l}, we can solve the problem of optimal unloading data volume by Substituted into the objective function, the optimization problem is reformulated as

[0038]

[0039] The above optimization problem is a strictly convex problem, and the optimal solution satisfies the KKT condition; the corresponding Lagrangian function is expressed as

[0040]

[0041] Among them, μ ≥ 0 is a non-negative Lagrange multiplier; the optimal edge computing resource and the Lagrange multiplier μ* satisfies the following KKT conditions:

[0042]

[0043] For a given Lagrange multiplier μ, the optimal edge computing resource is

[0044]

[0045] In order to meet the constraints Need to meet Right now Since the Lagrange multiplier μ≠0 and The Lagrange multiplier μ is monotonically decreasing. Using the binary search method, Find the optimal Lagrange multiplier μ* in the range of .

[0046] Preferably, the method for fixing the computing resources and optimizing the receiving vector of the base station BS and the reference phase shift of the IRS is:

[0047] Given the offloaded data volume e and edge computing resources f e When , the optimization problem is simplified to

[0048]

[0049] When the above optimization problem is solved optimally, there must be a total delay D k Equal to the local computing latency And equal to the edge computing latency The total delay D k Replaced with edge computing latency And removing the constant term, the optimization problem is reformulated as

[0050]

[0051] By introducing the auxiliary variable β, the optimization problem is transformed into:

[0052]

[0053] Among them, auxiliary variables β=[β1,…,β k ,…,β K ] T ; The Lagrangian form of the above optimization problem is:

[0054]

[0055] Among them, {λ k}≥0 represents the Lagrangian multiplier; therefore, the augmented Lagrangian form of the optimization problem is expressed as:

[0056]

[0057] Assume that the solution to the optimization problem is (W*,θ*,β*), then there must be a set of Lagrange multipliers λ* that satisfy the following KKT conditions:

[0058]

[0059] The superscript * indicates the optimal solution. represents the derivative symbol;

[0060] according to get

[0061]

[0062] The solution to the above augmented Lagrangian problem includes two steps: (1) for a given Lagrangian multiplier λ and auxiliary variable β, jointly optimize the MUD vector W and the reference phase shift θ; (2) use the modified Newton method to update the Lagrangian multiplier λ and auxiliary variable β until convergence.

[0063] Preferably, given a set of solutions for {λ,β,l}, the augmented Lagrangian form of the optimization problem reduces to a weighted sum rate maximization problem:

[0064]

[0065] Using the equivalence between the sum rate maximization problem and the MSE minimization problem, the weighted sum rate maximization problem is transformed into a modified MSE minimization problem; when other optimization variables are fixed, the MSE minimization problem is convex for each optimization variable. By introducing auxiliary variables The modified MSE function of the kth wireless device on the ith subcarrier is:

[0066]

[0067] The superscript * indicates conjugation. Indicates taking real value;

[0068] By introducing the weighting parameter The weighted sum rate maximization problem is equivalently converted to the optimization problem P1:

[0069]

[0070] Among them, ρ k,i is the weighting parameter, the auxiliary variable Υ and the weighting parameter ρ represent the variable Υ k,i and ρ k,i The optimization problem P1 is decoupled into four sub-problems, and the optimal solution of each sub-problem is given respectively:

[0071] 1) With the MUD vector W, the reference phase shift θ and the auxiliary variable Υ fixed, the subproblem about the weight parameter ρ is expressed as

[0072]

[0073] By letting the objective function be about the weight parameter ρ k,i The first-order partial derivative of is equal to 0, and the optimal solution of the weighted parameter is:

[0074] Among them, r k,i represents the signal-to-noise ratio of the kth user on the i-th subcarrier;

[0075] 2) With the MUD vector W, the reference phase shift θ and the weighting parameter ρ fixed, the subproblem about the auxiliary variable Υ is expressed as

[0076]

[0077] By letting the objective function be about the auxiliary variable Υ k,i The first-order partial derivative of is equal to 0, and the auxiliary variable Υ is obtained k,i The optimal value is

[0078]

[0079] 3) With the reference phase shift θ, weighting parameter ρ and auxiliary variable Υ fixed, the subproblem about the MUD vector W is formulated as the optimization problem P2

[0080]

[0081] Defining Equivalent Channels The objective function of the optimization problem P2 is simplified to the function

[0082]

[0083] Define intermediate variables:

[0084]

[0085] Function g1 can be reformulated as

[0086]

[0087] The optimization problem P2 is simplified to

[0088]

[0089] Among them, the intermediate variable O k,i is a K×I matrix with the (k,i)th element being 1 and the other elements being 0; since matrices A and D k,i They are all semi-positive definite matrices and are solved using the existing convex optimization toolbox to obtain the optimized MUD vector W.

[0090] 4) With the MUD vector W, weight parameter ρ and auxiliary variable Υ fixed, the subproblem about the reference phase shift θ is simplified to

[0091]

[0092] Define the intermediate variable φ i =[φ i,1 ,…,φ i,M ] T , and The above subproblem is reformulated as optimization problem P3

[0093]

[0094] Among them, the matrix Λ i , vector υ i and scalar ζ i They are

[0095]

[0096] The reference phase shift θ to be optimized is embedded in N complex functions. The optimization problem P3 is split into M sub-problems. Each element of the reference phase shift θ is optimized separately, and the other M-1 elements are fixed. θ is updated iteratively until convergence. The objective function is divided into

[0097]

[0098] Fix other elements and only consider the mth element. The objective function is expressed as

[0099]

[0100] The reference phase shift θ of the mth RIS unit m The sub-problem of is expressed as optimization problem P3:

[0101]

[0102] Defining intermediate variables Substituting constraints (b) and (c) into the objective function of optimization problem P3, optimization problem P3 can be reformulated as optimization problem P4:

[0103]

[0104] Among them, the objective function

[0105]

[0106] The three-step search method is used to find the optimal solution of the optimization problem P4:

[0107] Step 1: Narrow the search range: Initialize the starting point and search step h>0 in the range of [-π,π]; if the target function g3(θ0+h)<g3(θ0), continue to search forward; otherwise, search backward until the target function g3(θ m ) value increases;

[0108] Step 2: Find the minimum point by continuously splitting the search range until a predefined threshold is reached;

[0109] Step 3: Compare the minimum points The objective function g3(θ m ) value, determine the minimum value and the corresponding phase shift.

[0110] Preferably, let the reference phase shift θ of IRS be m Controlled by b bits and evenly distributed in the range of [-π,π), then:

[0111]

[0112] The IRS optimization design subproblem under the discrete phase model is expressed as

[0113]

[0114] Alternately optimize each element of the reference phase shift θ and fix the other elements until convergence. In order to find the optimal BPS Check the feasible set one by one All feasible solutions in the above equation are used, and the non-ideal IRS reflection model is used to calculate the relevant reflection coefficient of each subcarrier, and the reference phase shift θ that can minimize the objective function is selected. m as the optimal value.

[0115] Compared with the prior art, the invention has the following beneficial effects: Based on the amplitude-phase shift-frequency three-dimensional reflection model, the invention considers the resource optimization problem of the intelligent reflection surface (IRS) assisted broadband mobile edge computing (MEC) system; under the conditions of satisfying multiple practical constraints, including limited edge computing capabilities, unit norm multi-user detection (MUD) vectors and non-ideal IRS reflection models, by jointly optimizing the amount of data unloaded by wireless devices (WD), edge computing resources, MUD vectors and reference phase shifts to minimize the weighted and delayed values ​​of all users, the weighted and delayed values ​​of users can be effectively reduced, and the overall performance and resource utilization efficiency of the system can be improved. Since the problem formed introduces non-convex IRS reflection constraints and there are multiple coupled variables and segmented objective function forms, it is difficult to solve directly; the invention proposes an algorithm based on block coordinate descent (BCD), which alternately optimizes computing and communication resources, can effectively simplify the non-convex IRS reflection constraint problem, improve the solution efficiency, and thus achieve better resource allocation and performance optimization. Among them, in the communication resource optimization subproblem, the Lagrangian dual reconstruction (LDR) technology and KKT conditions are used to transform the original problem into a weighted sum rate maximization problem, which can simplify the optimization process, ensure the effectiveness and optimality of the solution, and improve the utilization efficiency of communication resources. Then, the equivalent relationship between sum rate maximization and mean square error (MSE) minimization is used to convert the communication resource optimization subproblem into a multivariable problem, and the BCD algorithm is used to effectively solve it, which can achieve a balance between rate maximization and mean square error (MSE) minimization, thereby improving the overall performance and stability of the system. The simulation results verify the performance gain of deploying IRS in different environments and the necessity of considering non-ideal IRS reflection models in passive beamforming design. On the whole, the present invention can significantly reduce user delays, improve system performance and resource utilization efficiency by optimizing the resource allocation of the IRS-assisted broadband mobile edge computing system, and at the same time verify the importance and performance gain of the non-ideal IRS reflection model. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] 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.

[0117] Figure 1 It is a schematic diagram of the model of the IRS-assisted MEC system of the present invention.

[0118] Figure 2 Graphs showing changes in amplitude and phase shift according to the present invention, including (a) changes in amplitude with phase shift at a specific carrier frequency, and (b) changes in phase shift with frequency.

[0119] Figure 3 is the objective function g3(θ m ) changes with the fundamental phase shift in [-π,π], where (a)-(c) are three examples obtained under different initial values.

[0120] Figure 4 It is the simulation scene setting of the present invention.

[0121] Figure 5 Schematic diagram of the convergence of the present invention, where (a) is Algorithm 4, (b) is Algorithm 2, and (c) is Algorithm 3.

[0122] Figure 6 This is a curve diagram showing the influence of the resolution b on the WD weighting and delay of the present invention.

[0123] Figure 7 is the number of BS antennas N in the present invention t Schematic diagram of the impact of WD weighting and delay on different schemes.

[0124] Figure 8 Schematic diagram of the effect of the number of IRS units M on the WD weights and delays of different schemes of the present invention.

[0125] Fig. 9 The edge computing capability of the present invention is f total Schematic diagram of the impact of WD weighting and delay on different schemes.

[0126] Fig.10 Schematic diagram of the influence of the user location L on the weighting and delay of different schemes WD in the present invention.

[0127] Fig.11 Schematic diagram of the effect of the WD number K on the WD weighting and delay of different schemes according to the present invention. DETAILED DESCRIPTION

[0128] 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.

[0129] like Figure 1 As shown, a delay optimization method in non-ideal intelligent metasurface-assisted broadband edge computing, the steps of which are as follows:

[0130] Step 1: A non-ideal IRS model is constructed based on the user unloading data to a base station equipped with an edge server with the assistance of IRS. Based on the phase shift model, communication model and computing model of the non-ideal IRS model, an optimization problem is constructed to jointly optimize the amount of user unloading data, edge computing resources, MUD vector and the baseline phase shift of IRS to minimize the weighted sum delay of all users.

[0131] The present invention considers a broadband multi-user orthogonal frequency division multiplexing (OFDM) system with I subcarriers. K single-antenna users unload a certain ratio of computational data to a base station (BS) equipped with an edge server with the assistance of IRS. t and M represent the number of base station antennas and the number of IRS units, respectively. and Denote the subcarrier set, user set, BS antenna set, and IRS reflector set, respectively. The edge server and BS are deployed together and connected by a high-speed, low-latency wired optical fiber. Therefore, the data transmission delay between the BS and the edge server is ignored. In addition, it is assumed that the antenna spacing at the BS and the element spacing of the IRS are large enough so that the small-scale fading of different antennas and reflector elements are independent of each other.

[0132] The present invention studies a more practical broadband scenario: the relative bandwidth, that is, the bandwidth and carrier frequency ratio is less than 5%. c =2.4GHz and bandwidth B = 100MHz, the phase shift model is modeled. Some articles propose the relationship between the amplitude and phase shift of the IRS unit and the relationship between the phase shift and frequency. Figure 2 As shown in (a), from Figure 2 As can be seen from (a), the relationship between the amplitude and phase shift of the IRS unit at different frequencies can be regarded as a quadratic function. In addition, within the bandwidth B = 100MHz, there is no obvious difference in the amplitude-phase shift curves of different frequencies, which means that a unified fitting function can be used for different frequencies. In addition, it can be obtained from Figure 2(b) shows that the phase shift as a function of frequency can be approximately fitted as a straight line. m When the frequency of the incident signal changes, the slope and intercept of the phase shift-frequency line will also change. The reflected amplitude F(θ,f) and phase shift G(θ,f) of the IRS unit related to the frequency of the incident signal can be modeled as

[0133]

[0134] Among them, the functions K(θ) and B(θ) represent the slope and intercept of the phase shift-frequency line respectively. The center frequency f of each subcarrier (obtained based on OFDM technology) i Defined as N is the number of IRS reflective elements. is a parameter related to the specific circuit implementation. Figure 2 The actual example shown, the specific parameter values ​​are shown in Table 1. Figure 2 The dotted lines in the figure are fitting results, and the solid lines are non-ideal amplitude-phase shift and phase shift-frequency relationship curves.

[0135] Table 1 Simulation parameter settings

[0136]

[0137] In the communication model, let and They respectively represent the frequency domain channels from the base station BS to the kth wireless device WD (each user is equipped with a wireless device) on the i-th subcarrier, from the base station BS to the IRS unit, and from the IRS unit to the k-th wireless device WD. represents the reflection matrix of the i-th subcarrier, where φ i,m It represents the phase shift coefficient of the ith subcarrier on the mth reflection unit, satisfying the following functional relationship

[0138]

[0139] Among them, θ m represents the BPS of the mth IRS unit, θ=[θ1,…,θ M ] T represents the BPS vector. represents the transmission signal of K wireless devices WDs on the i-th subcarrier, s k,i Indicates the information symbol to be transmitted, [·] T represents transpose. And satisfies The superscript H denotes the conjugate transpose. t represents the transmission power of the wireless device WD, then the received signal on the i-th subcarrier at the base station BS can be expressed as

[0140]

[0141] in, represents the noise vector, satisfying n t , σ 2 represent the number of antennas, complex Gaussian distribution and noise power of the nth base station respectively.

[0142] Let w k,i represents the multi-user detection MUD vector of the kth user on the i-th subcarrier, then the signal of the kth user on the i-th subcarrier recovered at the BS is It can be expressed as

[0143]

[0144] The signal-to-interference-plus-noise ratio (SINR) of the kth user on the i-th subcarrier is

[0145]

[0146] Correspondingly, the offloading rate of the kth user on the i-th subcarrier is

[0147] R k,i (w k,i ,Φ i )=Blog[1+r k,i (w k,i ,Φ i )] (6)

[0148] The total transmission rate of the kth user is

[0149]

[0150] in,

[0151] The computing model of the present invention adopts a partial offloading application model in which computing data can be arbitrarily divided. The wireless device WD can offload part of the computing data to the edge server for remote processing, and perform local computing on the other part of the data. The local computing is: Let L k , l k and c k They represent the total input data volume, unloaded data volume, and the number of CPU cycles required to calculate each bit of input data of the k-th wireless device WD respectively; the local computing capacity of the k-th wireless device WD, that is, the number of CPU operation cycles per second is Then the local computation delay can be expressed as In edge computing: and They represent the total computing power of the edge server (cycles / second) and the edge computing resources allocated to the kth wireless device WD, satisfying Edge computing latency usually consists of three parts: (1) computing data offloading latency; (2) computing latency on edge servers; and (3) computing result return latency. Usually, since the amount of computing result data is small, the last part of the computing result return latency is negligible. Therefore, edge computing latency can be expressed as

[0152] The total delay of the kth wireless device WD is

[0153]

[0154] The present invention optimizes the unloaded data volume l=[l1,…,l K ] T , edge computing resources Multi-user detection MUD vector of base station BS The reference phase shift θ of the IRS minimizes the weighted sum delay of all wireless devices WD. The resulting optimization problem is formulated as

[0155]

[0156] in, represents the weight of the kth wireless device WD. (9b) and (9c) are the amplitude and phase shift constraints of the non-ideal IRS model, respectively. (9d) is the phase shift constraint of IRS; (9e) is the unit mode MUD vector constraint of the wireless device WD; (9f) represents the amount of unloaded data l of the wireless device WD k Should be a value between 0 and L k integer; represents the total computing power of the edge server; (9g) and (9h) represent the computing power constraints of the edge server.

[0157] Step 2: Use the block coordinate descent algorithm to jointly optimize computing resources and communication resources.

[0158] In the optimization variables of problem (9), {l,f e} are variables related to computational design; {W,θ} are variables related to communication design. The difficulties in solving problem (9) mainly exist in the following aspects: (1) the piecewise form of the objective function; (2) the coupling influence of W and θ; (3) the objective function is non-convex with respect to θ. Therefore, the present invention utilizes the BCD technique to decouple computation and communication design to provide a local optimal solution to the problem. Then, the piecewise objective function is converted into a form that is easier to solve. Utilizing the equivalence between sum rate maximization and MSE minimization, the communication design subproblem is converted into a multivariable problem that can be effectively solved using the BCD technique. In order to solve the non-convexity problem of θ, the reference phase shift of each IRS unit can be solved separately, and then θ is iteratively updated until convergence.

[0159] The present invention adopts BCD technology to jointly optimize computing and communication resources. Specifically, firstly, the communication resources are fixed to optimize the amount of unloaded data and edge computing resources; then, the computing resources are fixed to optimize the receiving vector of the base station BS and the BPS of the IRS. The ultimate goal is to jointly optimize computing and communication resources until convergence.

[0160] When jointly optimizing computing resources, the communication resources are fixed. Given the received MUD vector W of the base station BS and the BPS reference phase shift θ, the original optimization problem (9) can be simplified to

[0161]

[0162] 3) Optimizing the amount of unloaded data l: Given a set of solutions {W,θ,f e}, you can set Get the optimal amount of unloaded data

[0163]

[0164] in, represents the local computing delay corresponding to the optimal offloaded data volume, represents the edge computing latency corresponding to the optimal amount of unloaded data when other optimization variables are given, Indicates the amount of optimized offload data.

[0165] In addition, since the amount of data to be unloaded must be a positive integer, the optimal amount of data to be unloaded is for

[0166]

[0167] in, and Indicates rounding down and rounding up respectively.

[0168] Proof: For the convenience of representation, let Indicates the amount of data unloaded after rounding operation lk ∈{0,1,…,L k According to formula (8), the overall delay of the kth wireless device WD is can be restated as follows

[0169]

[0170] From formula (13), we can see that when the amount of unloaded data Increase from 0 to Overall delay Reduce the amount of data when offloading from Increase to the total input data volume L k Overall delay Therefore, in order to minimize the overall delay, the amount of unloaded data should be Due to the amount of uninstalled data The optimal value should be a non-negative integer, which can be used to calculate the amount of data to be unloaded. After rounding, the optimal amount of unloaded data is obtained Its expression is

[0171] 4) Optimize edge computing resources e :Next, first given a set of solutions for {W,θ,l}, we then explore the edge computing resources f e By substituting formula (11) into the objective function (10a), the computational design subproblem can be reformulated as

[0172]

[0173] The following will prove that problem (14) is a convex optimization problem. Then, according to the KKT condition, we get the edge computing resource f k e The optimal solution of .

[0174] Objective function (14a) about edge computing resources The second-order derivative f″ is expressed as

[0175]

[0176] Due to the parameters 、c k , R k and are all positive, and L k ≥0 and The second-order derivative f″≥0 can be obtained. In addition, constraints (9g) and (9h) are both edge computing resources The linear form of . Therefore, it can be concluded that problem (14) is a strictly convex problem, and its optimal solution satisfies the KKT condition. The corresponding Lagrangian function can be expressed as

[0177]

[0178] Where μ ≥ 0 is a non-negative Lagrange multiplier. Optimal edge computing resource allocation and the Lagrange multiplier μ* satisfies the following KKT conditions:

[0179]

[0180]

[0181] For a given μ, the optimal edge computing resource can be directly obtained according to formula (17), which is formulated as

[0182]

[0183] In order to satisfy the constraint (9h) The numerator of formula (20) must satisfy Right now Since μ≠0 and The Lagrange multiplier μ is monotonically decreasing, so the famous binary search method can be used to find Find the optimal Lagrange multiplier μ* within the range to satisfy formula (18), and the relevant termination coefficient is ∈1. Algorithm 1 summarizes the solution process of the optimization problem (10). Its computational complexity is mainly determined by the solution The Lagrange multiplier μ is determined by the formula (20) and the binary search method. Computing edge computing resources The complexity is The total computational complexity of Algorithm 1 is is the maximum number of iterations. u , μ l Represents a binary search range.

[0184]

[0185] in, represents the initial termination coefficient, represents the termination coefficient of the t1th iteration, represents the termination coefficient of the t1+1th iteration, obj() represents the corresponding objective function value, represents the amount of unloaded data at the t1th iteration, represents the amount of unloaded data at the t1+1th iteration, and They represent the edge computing resources of the t1th and t1+1th iterations respectively.

[0186] When jointly optimizing communication resources, the computing resources are fixed. Given the offloaded data volume l and edge computing resources f e The optimization problem (9) can be simplified to

[0187]

[0188] The difficulty in solving equation (21) lies in: (1) the objective function takes the form of a segmented objective function introduced by taking the maximum; (2) the objective function is a sum of fractional functions with respect to the MUD vector W and the reference phase shift θ. To solve these two problems, the following transformations are performed.

[0189] When the original optimization problem is solved optimally, there must be a total delay Therefore, the total delay D k Replaced with edge computing latency By removing the constant term, problem (21) can be reformulated as

[0190]

[0191] By introducing the auxiliary variable β, problem (22) can be transformed into the following equivalent form:

[0192]

[0193] Among them, auxiliary variables β=[β1,…,β k ,…,β K ] T .

[0194] Its Lagrangian form is

[0195]

[0196] Among them, {λ k}≥0 represents the Lagrangian multiplier. Therefore, the augmented Lagrangian form of problem (23) can be expressed as

[0197]

[0198] Assuming that the solution of the optimization problem (25) is (W*,θ*,β*), then there must be a set of Lagrange multipliers λ* that satisfy the following KKT condition

[0199]

[0200] The superscript * indicates the optimal solution. Represents the derivative symbol.

[0201] According to formula (28), (29) and Can get

[0202]

[0203] The solution to the above augmented Lagrangian problem consists of two steps: (1) for a given Lagrangian multiplier λ and auxiliary variable β, jointly optimize the MUD vector W and the reference phase shift θ; (2) use the modified Newton method to update the Lagrangian multiplier λ and auxiliary variable β until convergence. The detailed process is shown in Algorithm 2. For convenience, define the following two auxiliary functions

[0204]

[0205]

[0206]

[0207] Where ∈2 and ζ represent the termination coefficient and the Lagrange multiplier update coefficient respectively, and the superscripts (t2) and (t2+1) represent the t2th iteration and t2+1th iteration respectively.

[0208] Now, let’s focus on the first step, optimizing W and θ. Given a set of solutions for {λ, β, e}, the optimization problem (25) can be simplified to the following weighted sum rate maximization problem:

[0209]

[0210] Using the equivalence between the sum rate maximization problem and the MSE minimization problem, problem (40) can be transformed into a modified MSE minimization problem. When other optimization variables are fixed, the MSE minimization problem is convex for each optimization variable and is therefore easier to solve. Specifically, by introducing the auxiliary variable The modified MSE function of the kth wireless device WD on the i-th subcarrier is defined as

[0211]

[0212] The superscript * indicates conjugation. Indicates real value.

[0213] Then, by introducing the weighting parameter Problem (40) can be equivalently transformed into the following problem:

[0214]

[0215] Among them, ρ k,i is the weighting parameter, the auxiliary variable Υ and the weighting parameter ρ represent the variable Υ k,i and ρk,i A collection of Compared with problem (40), the newly formed problem (42) uses fractional programming to remove the complex SINR term from the log(·) function, so it is easier to solve. In the remainder of the present invention, problem (42) will be decoupled into four sub-problems, and the optimal solution of each sub-problem is given respectively.

[0216] 1) Optimizing the weighting parameter ρ: With the MUD vector W, the reference phase shift θ, and the auxiliary variable Υ fixed, the subproblem about the weighting parameter ρ can be expressed as

[0217]

[0218] The above is an unconstrained convex problem, which can be solved by letting the objective function be related to the weight parameter ρ k,i The first-order partial derivative of is equal to 0, and the optimal solution of the weighted parameter can be obtained as

[0219]

[0220] Among them, r k,i represents the signal-to-noise ratio (SINR) of the kth user on the ith subcarrier.

[0221] 2) Optimizing auxiliary variables Υ: With the MUD vector W, the reference phase shift θ, and the weighting parameter ρ fixed, the subproblem about the auxiliary variable Υ can be expressed as

[0222]

[0223] Similar to the solution of problem (43), by letting the objective function be expressed with respect to the auxiliary variable Υ k,i The first-order partial derivative of is equal to 0, and the auxiliary variable Υ is obtained k,i The optimal value is

[0224]

[0225] 3) Optimizing the MUD vector W: With the reference phase shift θ, weighting parameter ρ and auxiliary variable Υ fixed, the subproblem of the MUD vector W is formulated as

[0226]

[0227] For convenience, we define equivalent channels The objective function (47a) can be simplified to the function

[0228]

[0229] In order to further simplify the expression of function g1, define intermediate variables:

[0230]

[0231] Substituting formulas (49)-(52) into function g1, function g1 can be restated as

[0232]

[0233] Finally, subproblem (47) can be simplified to

[0234]

[0235] Among them, the intermediate variable O k,i is a K×I matrix whose (k,i)th element is 1 and the other elements are 0. Since matrices A and D k,i are all semi-positive definite matrices, so the simplified subproblem (54) is a standard convex optimization problem and can be solved using existing convex optimization toolboxes, such as CVX, to improve solution efficiency.

[0236] 4) Optimizing the reference phase shift θ: With the MUD vector W, weighting parameter ρ and auxiliary variable Υ fixed, the subproblem about the reference phase shift θ can be simplified to

[0237]

[0238] For convenience, define the intermediate variable φ i =[φ i,1 ,…,φ i,M ] T , Subproblem (55) can be restated as

[0239]

[0240] Among them, the matrix Λ i , vector υ i and scalar ζ i , They are defined as

[0241]

[0242] Because the reference phase shift θ to be optimized is embedded in N complex functions, it is still difficult to solve the problem directly (56). Next, a feasible solution is adopted, which is to split the original problem into M sub-problems, optimize each element of the reference phase shift θ separately, fix the other M-1 elements, and iteratively update θ until convergence.

[0243] To do this, we first split the objective function (56b) element-wise into

[0244]

[0245] Fixing other elements and considering only the mth element, the relevant objective function can be expressed as

[0246]

[0247] because Equation (a) holds true. The reference phase shift θ of the mth reflection unit m The sub-problem can be expressed as

[0248]

[0249] Defining intermediate variables Substituting constraints (21b) and (21c) into the objective function (62a), the optimization problem (62) can be reformulated as

[0250]

[0251] Among them, the objective function

[0252]

[0253] The objective function (63a) is the sum of I complex functions containing trigonometric terms and quadratic terms. Therefore, it is difficult to calculate the partial derivative of the objective function and obtain a closed-form solution. In order to solve this problem, some articles propose to analyze the characteristics of the objective function (63a) with the help of a large number of numerical experiments. A large number of numerical simulations show that the objective function (63a) has only one minimum point in [-π,π]. Therefore, its minimum point must be the minimum point or two boundary points. Figure 3 Several examples of numerical simulation are given (by Figure 3 It can be seen that the minimum point must be the minimum point or two boundary points). Based on this discovery, a three-step search method can be used to find the optimal solution, which can be summarized as follows:

[0254] Step 1: Narrow the search range: Initialize the starting point and search step h>0 in the range of [-π,π]. If the target function g3(θ0+h)<g3(θ0), continue to search forward; otherwise, search backward until the target function g3(θ m ) value increases.

[0255] Step 2: Find the minimum point by continuously splitting the search range Until a predefined threshold is reached, which can be set as a relative rate of change or a limit on absolute error.

[0256] Step 3: Compare The objective function g3(θ m) value, determining the minimum value and its corresponding phase shift can effectively improve the accuracy and efficiency of the optimization process, ensure that the optimal phase shift and its corresponding objective function value are found, and thus improve system performance.

[0257] In practical applications, in order to reduce hardware consumption and cost, IRS is usually implemented using a limited low-resolution phase shifter. Assume that the reference phase shift θ of IRS is m It is controlled by b bits and is evenly distributed in the range of [-π,π), that is,

[0258]

[0259] The IRS optimization design subproblem under the discrete phase model can be expressed as

[0260]

[0261] It can be observed that, except for constraint (66b), the discrete IRS design subproblem is almost the same as the continuous IRS design subproblem. Perform a one-dimensional exhaustive search to find the optimal θ. Specifically, alternately optimize each element in BPSθ and fix the other elements until convergence. Check the feasible set one by one All feasible solutions in , and the non-ideal IRS reflection model is used to calculate the relevant reflection coefficient of each subcarrier. Then, the reference phase shift θ that can minimize the objective function is selected. m As the optimal value, Algorithm 3 summarizes the method of jointly optimizing W and θ given λ and β.

[0262]

[0263] The detailed solutions to the four sub-problems of MUD vector W, weight parameter ρ, auxiliary variable Υ and reference phase shift θ are given above. After the appropriate initial values ​​of W and θ are given, the above four optimization variables are updated alternately until the target converges.

[0264] Algorithm 4 gives the specific process of solving problem (42).

[0265]

[0266]

[0267] The performance of the proposed algorithm is evaluated based on a large number of simulation results. Figure 4As shown in Figure 1, a three-dimensional single-cell MEC system is considered, with a BS coverage radius of 300m. In order to improve the communication capacity, an IRS is deployed at the edge of the cell, with a height sufficient to build an additional reflection link to assist data offloading. Two users are randomly distributed in a circle with a radius of r = 5m, and the distance from the center of the circle to the coordinate origin / BS is set to Lm. The detailed location information of the BS and IRS is shown in the location model in Table 2.

[0268] Table 2 Simulation parameter settings

[0269]

[0270] In the IRS-assisted multi-user OFDMMEC system studied in the present invention, it is assumed that the number of carriers I = 8. The center carrier frequency and bandwidth are f c =2.4GHz and B = 100MHz, the noise power σ 2 =3.98×10 -15 W. Define the distances from BS to WD, BS to IRS, and IRS to WD as d BW d BI and d IW Then the distance-dependent large-scale fading can be expressed as

[0271]

[0272] Where κ represents the path loss index, and C0 is the path loss when the reference distance d0 = 1m. Here, let C0 = -30dB, and assume that the path loss indexes of the BS-WD link, BS-IRS link, and IRS-WD link are κ BW =3.5,κ BI =2.2 and κ IW =2.2. For small-scale fading, a Rice fading channel model is considered, then the channel H of BS-WD can be expressed as

[0273]

[0274] Among them, β BW represents the Rice factor, H LoS and H NLoS They represent the Rayleigh fading components of LoS and non-LoS respectively. BW →∞, channel H is equivalent to a LoS channel; when β BW =0, it is equivalent to a Rayleigh fading channel. BW , β BI and β IW Respectively represent the Rician factors of BS-WD, BS-IRS, and IRS-WD channels. Here, let β BW =0, βBI →∞ and β IW = 0. Small-scale fading H multiplied by distance-dependent large-scale fading L (d BW ), the complete BS-WD channel can be obtained. The channels of BS-IRS and IRS-WD can also be generated using the above method. The default settings related to communication are shown in Table 2. In addition, the settings related to calculation are shown in the calculation model module of Table 2.

[0275] In order to test the convergence of the proposed algorithm, Figure 5 The weighted sum delay changes with the number of iterations. The simulation results show that for the two outermost alternating optimization algorithms, namely Algorithm 4 and Algorithm 2, the proposed algorithm can achieve convergence within 2 iterations and 10 iterations, respectively, regardless of whether continuous phase shift or discrete phase shift is used. For the innermost Algorithm 3, when continuous phase shift is used, the proposed algorithm can achieve convergence within 10 iterations, and when discrete phase shift is used, the proposed algorithm can achieve convergence within 5 iterations. Figure 6 The weighted sum delay is given in the low-resolution scenario with the change of resolution b. The simulation results show that when b = 5, a sufficiently high resolution level has been reached, and increasing the value of b will no longer significantly improve the system performance.

[0276] Combination Figure 5 (c) The algorithm convergence speed and Figure 6 The influence of resolution b on system performance shows that in actual communication systems, it is more economical and effective to use low-resolution IRS phase shifters.

[0277] To evaluate the performance of the proposed algorithm, we also compared it with the following benchmark solutions for fairness:

[0278] IdealModel: Directly apply the optimization design based on the ideal phase-shift model to the actual system.

[0279] WithoutIRS: Traditional communication network without RIS.

[0280] RandomPhaseShift: The reference phase shift θ is randomly selected in [-π,π], and other optimization variables are optimized using the proposed algorithm.

[0281] Figure 7The weighted sum delay achieved by the proposed algorithm in the discrete phase shift and continuous phase shift scenarios is shown as a function of the number of BS antennas. It can be observed that the proposed algorithm can achieve better performance than the "w / o, IRS" and "w / IRS, Random" schemes over a range of different BS antenna numbers, confirming the beneficial effect of deploying an IRS with optimized phase shift design in wireless communication systems. In addition, it can be observed that the performance of the proposed algorithm is better than the "w / IRS, IdealModel" scheme, confirming the importance of adopting a non-ideal IRS reflection model in IRS-assisted broadband communication systems.

[0282] Figure 8 The WD weight and delay are plotted as a function of the number of IRS units M. Figure 8 A similar conclusion is drawn in , that is, compared with other schemes, the proposed algorithm can achieve better system performance. In addition, with the increase of the number of IRS units, the performance gap between the proposed algorithm and the "w / IRS, IdealModel" scheme becomes more and more obvious. This is because when the number of IRS units is small, the signal power received by the BS from the direct link is dominant, and as the number of IRS units increases, the signal power received from the reflection link gradually increases, making the performance loss caused by the imperfect IRS hardware structure more and more obvious.

[0283] Fig. 9 The variation of WD weighted sum delay with edge computing capacity under different schemes is presented. It can be observed that for all schemes, when the total edge computing capacity f total When it is small, the WD weighted sum delay increases with the total edge computing capacity f total The increase of the edge computing capacity is significantly reduced; when the total edge computing capacity f total After increasing to a certain threshold, i.e. 30×10 11 cycle / s, the weighted sum delay decreases slowly. This is because when f total When the value of is small, the edge computing delay is dominant, and when f total When it reaches a sufficiently large value, the data offloading latency dominates, and it becomes meaningless to continue to increase the computing power of the edge server. Therefore, it can be considered that appropriately increasing the computing power of the edge server is economically effective.

[0284] Fig.10The variation of WD weighted sum delay with user location L is described. It can be observed that in the traditional scheme without IRS, the WD weighted sum delay increases with the increase of distance L. In the “w / IRS, Random” scheme, the advantage of deploying IRS is only apparent when the distance between WD and IRS is less than 20m. In contrast, the advantage of IRS can be apparent when the distance between WD and IRS is less than 100m in the proposed algorithm. This observation indicates that higher IRS beamforming gain can be obtained through complex phase shift design in the near IRS domain, thereby expanding the signal coverage. In addition, at d = 280m, the weighted sum delay of WD reaches the maximum value, and then, for the “w / IRS, Proposed” scheme with IRS and the “w / IRS, IdealModel” scheme, the weighted sum delay decreases with the increase of distance L. This is because when d < 280m, the signal power received by the base station from the direct link is dominant, while when d > 280m, the signal power received from the reflected link composed of WD-IRS-BS is dominant.

[0285] Fig.11 It shows how the WD weighted sum delay changes with the number of users in a multi-device scenario. It can be observed that for all schemes, the average delay of WD increases with the increase in the number of users. There are two reasons for this phenomenon: one is that the edge computing resources allocated to each WD are reduced; the other is that the beam gain achieved at each WD end is reduced. The former problem can be solved by equipping edge servers with stronger computing power, while the latter problem can be solved by deploying more IRSs in the MEC system to form a stronger beam. From the simulation results, compared with the "w / IRS, IdealModel" scheme, the algorithm proposed in the present invention can reduce the average WD delay from 2.24ms to 2.07ms when K=5. This also further illustrates the importance of considering non-ideal phase shift models in broadband systems.

[0286] Based on the non-ideal phase shift model, the present invention studies the resource allocation problem in the IRS-assisted broadband MEC system. On the basis of meeting the limited edge computing capacity constraints and non-ideal IRS models, including continuous and discrete phase shift models, the weighted and delayed WD is minimized by jointly optimizing the MUD vector, IRS reference phase shift, WD offload data volume and edge computing resources. There are multiple coupling variables in the original problem, which is difficult to solve directly. Therefore, the present invention adopts the BCD technology to split the original problem into a computational design sub-problem and a communication design sub-problem, and alternately optimizes the computational and communication variables therein. Among them, according to the KKT condition, the original communication design sub-problem is converted into a weighted and rate maximization problem. Using the equivalence relationship between weighted and rate maximization and MSE minimization, the original problem is converted into a multivariable problem and solved by the BCD method. The simulation results verify the importance of considering the imperfect response characteristics of the non-ideal IRS reflection unit and the related phase shift design. In addition, the complexity of the proposed algorithm is analyzed and the rapid convergence of the algorithm is verified by numerical simulation.

[0287] 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 method for optimizing latency in non-ideal intelligent metasurface-assisted broadband edge computing, characterized in that: The steps are as follows: Step 1: A non-ideal IRS model is constructed based on the data unloading of users to a base station equipped with an edge server under the assistance of IRS. Based on the phase shift model, communication model and calculation model of the non-ideal IRS model, an optimization problem of jointly optimizing the amount of user unloaded data, edge computing resources, MUD vector and the reference phase shift of IRS to minimize the weighted sum delay of all users is constructed; Step 2: Use the block coordinate descent algorithm to jointly optimize computing resources and communication resources.

2. The delay optimization method in non-ideal intelligent metasurface-assisted broadband edge computing according to claim 1 is characterized in that: The non-ideal IRS model considers a broadband multi-user orthogonal frequency division multiplexing system with I subcarriers, K single-antenna users unload a certain ratio of computing data to a BS equipped with an edge server with the assistance of IRS, and each user is equipped with a wireless device; The edge server and BS are deployed together and connected by wired optical fiber; it is assumed that the antenna spacing at the BS and the element spacing of the IRS are large enough to make the small-scale fading of different antennas and reflective elements independent of each other.

3. The delay optimization method in non-ideal intelligent metasurface assisted broadband edge computing according to claim 2 is characterized in that: In the communication model, let represents the transmission distance from the base station BS to the kth wireless device on the i-th subcarrier, Indicates the frequency domain channel from the base station to the IRS, represents the frequency domain channel from IRS to the kth wireless device; represents the reflection matrix of the i-th subcarrier, φ i,m It represents the phase shift coefficient of the i-th subcarrier on the m-th reflection unit and satisfies the following functional relationship: Among them, θ m represents the reference phase shift of the mth IRS, θ=[θ1,...,θ M ] T represents the reference phase shift vector, F(θ m ,f i ) represents the reference phase shift and center frequency f at the mth IRS i The reflection amplitude function, G(θ m ,f i ) is the reference phase shift and center frequency f at the mth IRS i The phase shift function of represents the transmission signal of K wireless devices on the i-th subcarrier, s k,i Indicates the information symbol to be transmitted, [·] T represents transpose; and satisfies Let P t represents the transmission power of the wireless device, then the received signal on the i-th subcarrier at the BS is expressed as in, represents the noise vector, satisfying n t represents the number of antennas of the nth base station, represents complex Gaussian distribution, σ 2 represents the noise power; Let w k,i represents the multi-user detection MUD vector of the kth user on the i-th subcarrier, then the signal of the kth user on the i-th subcarrier recovered at the BS is Expressed as The signal-to-interference-to-noise ratio of the kth user on the i-th subcarrier is Correspondingly, the offloading rate of the kth user on the i-th subcarrier is R k,i (In k,i ,Φ i )=Blog[1+r k,i (In k,i ,Φ i )]; The total transmission rate of the kth user is: in, 4. The delay optimization method in non-ideal intelligent metasurface assisted broadband edge computing according to claim 3 is characterized in that: The computing model adopts a partial offloading application model in which computing data can be arbitrarily divided: the wireless device offloads part of the computing data to the edge server for remote processing, and the other part of the data is calculated locally; wherein the local calculation is: let L k , and c k denote the total input data volume, unloaded data volume and number of CPU cycles required to calculate each bit of input data of the kth wireless device respectively; then the local calculation delay is expressed as in, is the local computing capacity of the kth wireless device; in edge computing: and They represent the total computing power of the edge server and the edge computing resources allocated to the kth wireless device, respectively, satisfying Edge computing latency usually includes the offloading latency of computing data and the computing latency on the edge server. The edge computing latency is expressed as The total delay of the kth wireless device is 5. The method for optimizing latency in non-ideal intelligent metasurface-assisted broadband edge computing according to any one of claims 2 to 4, characterized in that: By optimizing the amount of data offloaded from wireless devices Edge computing resources Multi-user detection MUD vector of base station The reference phase shift θ of the IRS minimizes the weighted sum delay of all wireless devices, and the resulting optimization problem is: in, represents the weight of the kth wireless device, represents the total delay of the kth wireless device, φ i,m represents the phase shift coefficient of the ith subcarrier on the mth reflection unit, F(θ m ,f i ) represents the reference phase shift θ at the mth IRS m and the center frequency f i The reflection amplitude function, G(θ m ,f i ) is the reference phase shift θ at the mth IRS m and the center frequency f i The phase shift function of the wireless device; the amount of data offloaded Should be a value between 0 and the total input data size L k integer; represents the total computing power of the edge server; the multi-user detection MUD vector of the kth user w k,i represents the multi-user detection MUD vector of the k-th user on the i-th subcarrier, represents the edge computing resources of the kth wireless device.

6. The delay optimization method in non-ideal intelligent metasurface assisted broadband edge computing according to claim 5 is characterized in that: The method for jointly optimizing computing resources and communication resources using a block coordinate descent algorithm is as follows: first, fix the communication resources, optimize the offload data volume and edge computing resources; then fix the computing resources, optimize the receiving vector of the base station BS and the reference phase shift of the IRS until convergence; convert the segmented objective function into a form that is easier to solve, and use the equivalence between sum rate maximization and MSE minimization. The sub-problem of communication resources is converted into a multivariable problem, which is solved using a block coordinate descent algorithm to solve the reference phase shift of each IRS, and then iteratively update the reference phase shift θ until convergence.

7. The delay optimization method in non-ideal intelligent metasurface assisted broadband edge computing according to claim 6 is characterized in that: When the communication resources are fixed, the method to optimize the amount of offloaded data and edge computing resources is: for a given base station's received MUD vector W and reference phase shift θ, the optimization problem is simplified to: st(f),(g),(h) 1) Optimizing the amount of unloaded data: Given a set of solutions {W,θ,f e }, you can set Get the optimal amount of unloaded data in, represents the local computing delay corresponding to the optimal offloaded data volume, represents the edge computing latency corresponding to the optimal amount of unloaded data when other optimization variables are given, Indicates the optimized amount of unloaded data; Since the amount of data to be unloaded must be a positive integer, the optimal amount of data to be unloaded is for in, and Respectively represent rounding down and rounding up; 2) Optimize edge computing resources e :First given A set of solutions, by taking the optimal amount of offloaded data Substituted into the objective function, the optimization problem is reformulated as st(g),(h) The above optimization problem is a strictly convex problem, and the optimal solution satisfies the KKT condition; the corresponding Lagrangian function is expressed as Among them, μ ≥ 0 is a non-negative Lagrange multiplier; the optimal edge computing resource and the Lagrange multiplier μ* satisfies the following KKT conditions: For a given Lagrange multiplier μ, the optimal edge computing resource is In order to meet the constraints Need to meet Right now Since the Lagrange multiplier μ≠0 and The Lagrange multiplier μ is monotonically decreasing. Using the binary search method, Find the optimal Lagrange multiplier μ* in the range of .

8. The method for optimizing latency in non-ideal intelligent metasurface-assisted broadband edge computing according to claim 6 or 7, characterized in that: The method for fixing the computing resources and optimizing the receiving vector of the base station BS and the reference phase shift of the IRS is: Given the amount of data to be uninstalled and edge computing resources e When , the optimization problem is simplified to st(b),(c),(d),(e) When the above optimization problem is solved optimally, there must be a total delay D k Equal to the local computing latency And equal to the edge computing latency The total delay D k Replaced with edge computing latency And removing the constant term, the optimization problem is reformulated as st(b),(c),(d),(e) By introducing the auxiliary variable β, the optimization problem is transformed into: (b),(c),(d),(e) Among them, auxiliary variables β=[β1,...,β k ,...,β K ] T ; The Lagrangian form of the above optimization problem is: Among them, {λ k }≥0 represents the Lagrangian multiplier; therefore, the augmented Lagrangian form of the optimization problem is expressed as: st(b),(c),(d),(e) Assume that the solution to the optimization problem is (W*,θ*,β*), then there must be a set of Lagrange multipliers λ* that satisfy the following KKT conditions: The superscript * indicates the optimal solution. represents the derivative symbol; according to get The solution to the above augmented Lagrangian problem includes two steps: (1) for a given Lagrangian multiplier λ and auxiliary variable β, jointly optimize the MUD vector W and the reference phase shift θ; (2) use the modified Newton method to update the Lagrangian multiplier λ and auxiliary variable β until convergence.

9. The delay optimization method in non-ideal intelligent metasurface-assisted broadband edge computing according to claim 8 is characterized in that: Given A set of solutions, the augmented Lagrangian form of the optimization problem is simplified to the weighted sum rate maximization problem: st(b),(c),(d),(e) Using the equivalence between the sum rate maximization problem and the MSE minimization problem, the weighted sum rate maximization problem is transformed into a modified MSE minimization problem; when other optimization variables are fixed, the MSE minimization problem is convex for each optimization variable. By introducing auxiliary variables The modified MSE function of the kth wireless device on the ith subcarrier is: The superscript * indicates conjugation. Indicates taking real value; By introducing the weighting parameter The weighted sum rate maximization problem is equivalently converted to the optimization problem P1: st(b),(c),(d),(e) Among them, ρ k,i is the weighting parameter, the auxiliary variable Υ and the weighting parameter ρ represent the variable Υ k,i and ρ k,i The optimization problem P1 is decoupled into four sub-problems, and the optimal solution of each sub-problem is given respectively: 1) With the MUD vector W, the reference phase shift θ and the auxiliary variable Υ fixed, the subproblem about the weight parameter ρ is expressed as By letting the objective function be about the weight parameter ρ k,i The first-order partial derivative of is equal to 0, and the optimal solution of the weighted parameter is: Among them, r k,i represents the signal-to-noise ratio of the kth user on the i-th subcarrier; 2) With the MUD vector W, the reference phase shift θ and the weighting parameter ρ fixed, the subproblem about the auxiliary variable Υ is expressed as By letting the objective function be about the auxiliary variable Υ k,i The first-order partial derivative of is equal to 0, and the auxiliary variable Υ is obtained k,i The optimal value is 3) With the reference phase shift θ, weighting parameter ρ and auxiliary variable Υ fixed, the subproblem about the MUD vector W is formulated as the optimization problem P2 Defining Equivalent Channels The objective function of the optimization problem P2 is simplified to the function Define intermediate variables: Function g1 can be reformulated as The optimization problem P2 is simplified to Among them, the intermediate variable O k,i is a K×I matrix with the (k,i)th element being 1 and the other elements being 0; since matrices A and D k,i They are all semi-positive definite matrices, and are solved using the existing convex optimization toolbox to obtain the optimized MUD vector W; 4) With the MUD vector W, weight parameter ρ and auxiliary variable Υ fixed, the subproblem about the reference phase shift θ is simplified to st(b)-(d) Define the intermediate variable φ i =[φ i,1 ,...,φ i,M ] T , and The above subproblem is reformulated as optimization problem P3 st(b)-(d) Among them, the matrix Λ i , vector υ i and scalar ζ i They are The reference phase shift θ to be optimized is embedded in N complex functions. The optimization problem P3 is split into M sub-problems. Each element of the reference phase shift θ is optimized separately, and the other M-1 elements are fixed. θ is updated iteratively until convergence. The objective function is divided into Fix other elements and only consider the mth element. The objective function is expressed as The reference phase shift θ of the mth RIS unit m The sub-problem of is expressed as optimization problem P3: st(b)-(d) Defining intermediate variables Substituting constraints (b) and (c) into the objective function of optimization problem P3, optimization problem P3 can be reformulated as optimization problem P4: stθ m ∈[-π,π], Among them, the objective function The three-step search method is used to find the optimal solution of the optimization problem P4: Step 1: Narrow the search range: Initialize the starting point and search step h>0 in the range of [-π,π]; if the target function g3(θ0+h)<g3(θ0), continue to search forward; otherwise, search backward until the target function g3(θ m ) value increases; Step 2: Find the minimum point by continuously splitting the search range until a predefined threshold is reached; Step 3: Compare the minimum points The objective function g3(θ m ) value, determine the minimum value and the corresponding phase shift.

10. The method for optimizing latency in non-ideal intelligent metasurface-assisted broadband edge computing according to claim 9, characterized in that: Assume the reference phase shift of IRS is θ m Controlled by b bits and evenly distributed in the range of [-π,π), then: The IRS optimization design subproblem under the discrete phase model is expressed as Alternately optimize each element in the benchmark phase shift θ, fixing the other elements until convergence; check the feasible set one by one All feasible solutions in the above formula are used to calculate the relevant reflection coefficient of each subcarrier using the non-ideal IRS reflection model, and the reference phase shift θ that minimizes the objective function is selected. m as the optimal value.

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