STAR-RIS assisted IIOT-MEC task transmission algorithm oriented to efficiency optimization

Abstract

The invention discloses an efficiency optimization-oriented STAR-RIS assisted IIOT-MEC task transmission algorithm. The algorithm comprises the steps of establishing a mathematical model according to an industrial mobile edge computing architecture scene; establishing a non-convex nonlinear quadratic programming problem according to the mathematical model, including establishing an uplink channel transmission expression, a downlink channel transmission expression, a system power consumption expression, a target function and a constraint condition, and obtaining an original optimization problem expression; based on an alternating optimization algorithm, a fractional programming method and a positive semidefinite relaxation method, a non-convex nonlinear quadratic programming problem is converted into a convex problem to be solved. Therefore, by the adoption of the method, signals can be reflected and transmitted at the same time through the STAR-RIS technology, the freedom degree of controlling the radio environment is increased, and the wireless transmission efficiency is improved; in addition, the energy efficiency of the system can be maximized by using an alternating optimization algorithm, a fractional programming method and a positive semidefinite relaxation method.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular to a STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization. Background Art

[0002] With the combination of IoT technology and industrial technology, the Industrial Internet of Things (IioT) has developed rapidly. More and more industrial intelligent mobile devices (such as mobile robots, automatic guided vehicles, etc.) have emerged, accelerating the transformation and development of Industry 4.0. However, the computing power and battery power of mobile devices are limited, and the disadvantages of the cloud computing model that offloads computing tasks to remote cloud processing are becoming increasingly obvious. Mobile Edge Computing (MEC) has emerged as an extension of cloud computing. It offloads delay-sensitive or computing-intensive tasks to edge nodes close to industrial mobile devices for processing, effectively reducing the transmission delay of tasks sent to remote cloud centers and reducing the energy consumption of mobile devices. However, there are many uncertain factors in MEC task offloading in IIoT scenarios, such as mobile device computing resources, industrial task data characteristics, MEC server computing load, and wireless channel quality, which will affect the computing task offloading decision and transmission efficiency.

[0003] At present, the main methods to improve wireless channels include Multiple Input Multiple Output (MIMO) technology, increasing BS transmission power, and micro-station blind spot filling, but none of them can achieve the desired effect. Many studies have shown that intelligent reflecting surfaces (IRS) can change this situation, but this method only considers the case where the IRS reflects the incident wireless signal. In this case, the transmitter and receiver must be located on the same side of the IRS, resulting in a half-space smart radio environment (SRE), so that the terminal equipment is usually located on both sides of the IRS, which seriously limits the flexibility and effectiveness of the IRS.

[0004] Therefore, there is an urgent need for a wireless channel transmission suitable for the IIoT-MEC architecture, which can simultaneously consider the transmission and transmission signals, improve the efficiency of wireless transmission, maximize the system energy efficiency, and provide a reference for wireless communication systems under the future development of IIoT. Summary of the invention

[0005] The purpose of the present invention is to provide a STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization, realize simultaneous reflection and transmission of signals, increase the freedom of manipulating the radio environment, improve wireless transmission efficiency, and maximize system performance.

[0006] In order to achieve the above object, the present invention provides a STAR-RIS assisted IIoT-MEC task transmission algorithm for performance optimization, comprising the following steps:

[0007] S1. Establish a mathematical model based on the industrial mobile edge computing architecture scenario;

[0008] S2, establishing a non-convex nonlinear programming quadratic programming problem according to the mathematical model of step S1;

[0009] S3. Solve non-convex nonlinear quadratic programming problems based on fractional programming methods.

[0010] Preferably, in step S1, a mathematical model is established, specifically as follows:

[0011] A mathematical model is established based on STAR-RIS assisted offloading task transmission in the industrial Internet of Things mobile edge computing scenario. According to the characteristic parameters of IIOT-MEC involving mobile edge servers, industrial mobile devices, and wireless transmission channels, a mathematical model is established for the processing and rate of tasks on mobile devices or edge servers, the power consumed by the system, and the offloading task transmission channel.

[0012] Preferably, in step S2, a non-convex nonlinear programming quadratic programming problem is established, including:

[0013] S21, establishing an uplink channel transmission expression;

[0014] S22, establishing a downlink channel transmission expression;

[0015] S23, establishing a system power consumption expression;

[0016] S24. Establish the objective function and constraints to obtain the original optimization problem expression.

[0017] Preferably, step S3 specifically includes:

[0018] S31. Based on the fractional programming method, the objective function is transformed using Dinkelbach transformation to obtain the transformed objective function;

[0019] S32. Based on the alternating optimization algorithm, the original optimization problem expression is transformed into several sub-problem expressions, and the sub-problem expressions are transformed into convex problems using fractional programming methods and semi-positive definite relaxation methods, and the transformed convex problems are iteratively solved.

[0020] Preferably, step S21 is specifically as follows:

[0021] S B =(h T H Θ T H RB )ωx T +(h R H Θ R H RB )ωx R +n1

[0022]

[0023] In the formula, S B is the signal received by the BS antenna, Θ R , Θ T are the reflection coefficient matrix and transmission coefficient matrix of STAR-RIS respectively, H represents the transposed matrix, H RB is the channel gain, ω is the receive beamforming at the BS, and x R 、x T are the reflected signal and transmitted signal of the MEC server uplink transmission, respectively, R 、p T are the transmission powers of the MEC servers in the transmission area and the MEC servers in the reflection area, respectively. R , S T are the information sent by the transmission area MEC server and the reflection area MEC server, respectively, R 、h T are the channels from the MEC server in the reflection area to STAR-RIS and the channels from the MEC server in the transmission area to STAR-RIS, n1 is the Gaussian noise at the base station, diag() is a diagonal matrix, are the reflection coefficient and transmission coefficient of the Nth unit of STAR-RIS, respectively, N is the number of STAR-RIS units, They are respectively the reflection phase shift and transmission phase shift of the Nth unit of STAR-RIS.

[0024] Preferably, step S22 is specifically expressed as follows:

[0025] x=ω S s1+ω F s2

[0026] Where x is the information sent by BS to industrial mobile devices, ω S ,ω Fare the beamforming vectors transmitted by the transmitting antenna of the BS to the near-end mobile device and the far-end mobile device respectively. s1 and s2 are the information of the near-end mobile device and the far-end mobile device respectively.

[0027] Preferably, step S23 is specifically as follows:

[0028] Based on the STAR-RIS hybrid NOMA technology-assisted IIoT-MEC task transmission model, the energy P consumed by the entire system is obtained. The specific expression is:

[0029]

[0030] Where P cir is the BS circuit power consumption, is the power consumption of the circuit on STAR-RIS, and |||| is the vector 2-norm.

[0031] Preferably, step S24 includes:

[0032] The objective function is:

[0033]

[0034] Where E is the system energy efficiency.

[0035] Among them, the sum rate of the system downlink channel transmission is derived from the following formula:

[0036]

[0037] Under the premise of satisfying the constraints, the objective function is maximized to obtain the original optimization problem. The specific expression is:

[0038]

[0039] st

[0040] C1: γ 11 ≥γ0

[0041] C2: γ 22 ≥γ0

[0042] C3:

[0043] C4:

[0044] C5:

[0045] C6: p T ≤p max

[0046] C7: p R≤p max

[0047] C8: ‖ω‖ 2 ≤1

[0048] C9: ‖ω S ‖ 2 +‖ω F ‖ 2 ≤P B,max

[0049] In the formula, N is a natural number, γ 11 When performing SIC for the BS, the received signal-to-noise ratio of the MEC server in the transmission area is first decoded, γ 22 is the received signal-to-noise ratio of the MEC server in the reflection area when the BS performs SIC decoding, γ0 is the QoS threshold constraint, and p max is the upper limit of system power, P B,max is the beamforming vector threshold.

[0050] Preferably, in step S31, the converted objective function is:

[0051]

[0052] In the formula, η is an introduced auxiliary variable.

[0053] Preferably, in step S32, the original optimization problem expression is converted into several sub-problem expressions, including:

[0054] First, the BS receive beamforming vector is optimized as follows:

[0055] Based on the alternating optimization algorithm, the MEC server transmit power p is fixed T and p R , BS transmit beamforming vector ω S and ω F 、STAR-RIS reflection coefficient Θ R and the transmission coefficient matrix Θ T , the original optimization problem expression is transformed into the BS receive beamforming vector optimization problem expression, and the first optimization problem expression is obtained through the semi-positive definite relaxation method:

[0056]

[0057] st

[0058] tr(G T W)≥γ0(tr(G R W)+σ 2 )

[0059] tr(GR W)≥γ0σ 2

[0060] ||ω|| 2 ≤1

[0061] in,

[0062] tr((G R +G T )W)=tr(G T W)+tr(G R W)

[0063] W=ωω H

[0064] rank(W)=1

[0065] G T =p T (h T H Θ T H RB ) H (h T H Θ T H RB )

[0066] G R =p R (h R H Θ R H RB ) H (h R H Θ R H RB )

[0067] Where tr() is the trace of the matrix;

[0068] The first optimization problem expression is solved to obtain W, and ω is obtained using the maximum eigenvalue recovery variable method.

[0069] Secondly, based on the obtained ω, fix the BS receive beamforming vector ω and the BS transmit beamforming vector ω S and ω F , the reflection coefficient matrix Θ of STAR-RIS R and the transmission coefficient matrix Θ T , the original optimization problem expression is transformed into the MEC server transmit power optimization problem expression, and the second optimization problem expression is obtained through the fractional programming method:

[0070]

[0071] -η1(p T |(h T H Θ T H RB )ω| 2 )-η1(p R |(h R H Θ R H RB )ω| 2 +σ 2 )

[0072]

[0073] st

[0074] p T |(h T H Θ T H RB )ω| 2 ≥γ0(p R |(h R H Θ R H RB )ω| 2 +σ 2 )

[0075] p R |(h R H Θ R H RB )ω| 2 ≥γ0σ 2

[0076] p T ≤p max

[0077] p R ≤p max

[0078] In the formula, α and η1 are introduced auxiliary variables;

[0079] Solve the expression of the second optimization problem and get p T and p R .

[0080] Then, based on the obtained ω, p T and p R , fixed MEC server transmit power p T and p R , BS receive beamforming vector ω, STAR-RIS reflection coefficient Θ Rand the transmission coefficient matrix Θ T , the original optimization problem expression is transformed into the BS transmit beamforming vector optimization problem expression, and the third optimization problem expression is obtained through the semi-positive definite relaxation method:

[0081]

[0082] st

[0083] tr(W S )+tr(W F )≤P B，max

[0084] in,

[0085]

[0086] In the formula, μ1 and μ2 are auxiliary variables introduced to satisfy rank(W S )=1 and rank(W F )=1;

[0087] Solve the third optimization problem expression and get W S , W F , and use the maximum eigenvalue recovery variable method to get ω S ,ω F .

[0088] Finally, based on the obtained ω, p T 、p R ,ω S and ω F , fixed MEC server transmit power p T and p R , BS receive beamforming vector ω, BS transmit beamforming vector ω S and ω F Variables, the original optimization problem expression is transformed into the STAR-RIS reflection coefficient matrix and transmission coefficient matrix optimization problem expression, and the fourth optimization problem expression is obtained through the semi-positive definite relaxation method:

[0089]

[0090] st

[0091] tr(TΦ T )≥γ0(tr(TΦ R )+σ 2 )

[0092] tr(TΦ T )≥γ0σ 2

[0093]

[0094] in,

[0095] T=p T (diag(h T H )H RB ω)(diag(h T H )H RB ω) H

[0096] Φ T =θ T θ T H

[0097] Φ R =θ R θ R H

[0098] In the formula, Φ T , Φ R All are auxiliary variables introduced;

[0099] Solve the expression of the fourth optimization problem and get Φ T , Φ R , and use the maximum eigenvalue recovery method to get Θ T and θ R .

[0100] Therefore, the present invention adopts the above-mentioned STAR-RIS assisted IIoT-MEC task transmission algorithm for performance optimization, which has the following technical effects:

[0101] (1) Using STAR-RIS technology, it can simultaneously reflect and transmit signals, increase the freedom of manipulating the radio environment, and improve wireless transmission efficiency;

[0102] (2) Based on the STAR-RIS hybrid NOMA technology-assisted IIoT-MEC task transmission model, the alternating optimization algorithm is used to transform the original optimization problem expression into several sub-problem expressions, and the fractional programming method and semi-positive definite relaxation method are used to transform the sub-problem expressions into convex problems for iterative solution, which can maximize the system energy efficiency.

[0103] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1The present invention is a system model diagram of an implementation scheme of a STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization. DETAILED DESCRIPTION

[0105] The present invention can be explained in more detail by the following examples. The purpose of disclosing the present invention is to protect all changes and improvements within the scope of the present invention. The present invention is not limited to the following examples.

[0106] like Figure 1 As shown in the figure, wireless transmission is adopted between industrial mobile devices and base stations (BS) and between BS and MEC servers. Assume that the direct communication link between BS and MEC server is blocked by obstacles, which is one of the most challenging scenarios of traditional industrial communication systems. A multi-antenna BS includes M1 receiving antennas and M2 transmitting antennas. The receiving antenna receives the offloading information transmitted by two single-antenna MEC servers through STAR-RIS. STAR-RIS has N elements and is in energy splitting mode: part of the signal emitted from the MEC server to STAR-RIS is reflected and part is transmitted.

[0107] To illustrate the basic design concept, this embodiment sets the transmitting antenna on the BS to send information to two devices, which are defined as the near-end mobile device and the far-end mobile device. The system downlink transmission channel is a Rayleigh channel, and the system uplink channel is a Ricean channel.

[0108] A STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization includes the following steps:

[0109] S1. Establish a mathematical model based on the industrial mobile edge computing architecture scenario, as follows:

[0110] A mathematical model is established based on STAR-RIS assisted offloading task transmission in the industrial Internet of Things mobile edge computing scenario.

[0111] According to the characteristic parameters of IIOT-MEC involving mobile edge servers, industrial mobile devices, and wireless transmission channels, a mathematical model is established for the processing and rate of tasks on mobile devices or edge servers, the power consumed by the system, and the transmission channel for offloaded tasks.

[0112] S2. According to the mathematical model of step S1, a non-convex nonlinear programming quadratic programming problem is established, including the following steps:

[0113] S21. Establish an uplink channel transmission expression, which is specifically expressed as follows:

[0114] like Figure 1As shown in Figure 1, STAR-RIS is divided into a transmission area and a reflection area in the energy splitting mode, and the channel from the MEC server in the transmission area to STAR-RIS is defined. Channel from MEC server to STAR-RIS in the reflection area The above channels are all Rice channels. The reflection coefficient matrix Θ of STAR-RIS R and the transmission coefficient matrix Θ T for:

[0115]

[0116] Where diag() is a diagonal matrix, are the reflection coefficient and transmission coefficient of the Nth unit of STAR-RIS, respectively, N is the number of STAR-RIS units, They are respectively the reflection phase shift and transmission phase shift of the Nth unit of STAR-RIS.

[0117] The reflected signal and transmitted signal of the MEC server uplink transmission are:

[0118]

[0119] In the formula, p R 、p T are the transmission powers of the MEC servers in the transmission area and the MEC servers in the reflection area, respectively. R , S T These are the information sent by the transmission area MEC server and the reflection area MEC server respectively.

[0120] The signal S received by the BS antenna B , calculated as follows:

[0121] S B =(h T H Θ T H RB )ωx T +(h R H Θ R H RB )ωx R +n1

[0122] In the formula, H represents the transposed matrix, H RB is the channel gain, is the receive beamforming at the BS, satisfying ‖ω‖ 2 =1, ‖‖ is the vector 2 norm, n1 is the Gaussian noise at BS, and n1∈(0,σ 2 ), σ is the Gaussian white noise coefficient.

[0123] Assume that BS first decodes the information of MEC server in the transmission area when performing SIC, and the signal-to-noise ratio of the transmission area is γ 11 for:

[0124]

[0125] BS performs SIC decoding on the information of MEC server in the reflection area, and the signal-to-noise ratio of the reflection area is γ 22 for:

[0126]

[0127] S22. Establish a downlink channel transmission expression, as follows:

[0128] The information sent by BS to industrial mobile devices is represented as:

[0129] x=ω S s1+ω F s2

[0130] is the beamforming vector transmitted by the BS’s transmit antenna to the near-end mobile device, is the beamforming vector transmitted by the BS's transmitting antenna to the remote mobile device, s1 and s2 are the information of the near-end mobile device and the remote mobile device respectively.

[0131] The channel from BS to near-end mobile device is defined as The channel from BS to remote mobile device is The above channels are all Rayleigh channels. The near-end mobile device first decodes the information of the remote device, and then decodes its own information. The received signal-to-noise ratio is γ1; the remote mobile device treats the information of the near-end device as interference and decodes the received signal-to-noise ratio is γ2. The specific expression is as follows:

[0132]

[0133] In summary, the sum rate of the system downlink channel transmission can be derived according to the following formula:

[0134]

[0135] S23. Establish a system power consumption expression, as follows:

[0136] In order to enable effective interaction of tasks in complex IIoT environments and improve the channel transmission efficiency of future 6G wireless communications, this embodiment proposes a STAR-RIS hybrid NOMA technology-assisted IIoT-MEC task transmission model. Based on the above model, the energy P consumed by the entire system is calculated, and the specific expression is:

[0137]

[0138] Where P cir is the BS circuit power consumption, This is the power consumption of the STAR-RIS circuit.

[0139] S24. Establish the objective function and constraints to obtain the expression of the original optimization problem, which is as follows:

[0140] Considering the actual application scenario of STAR-RIS, maximizing the system energy efficiency (and the ratio of rate to power) is taken as the objective function of the original optimization problem.

[0141] Among them, the system energy efficiency E is:

[0142]

[0143] The sum rate of the system uplink channel transmission is:

[0144]

[0145] The sum rate of the system downlink channel transmission is:

[0146]

[0147] The original optimization problem of STAR-RIS-assisted IIoT-MEC task transmission for energy efficiency optimization is expressed as:

[0148] maxE

[0149] st

[0150] C1: γ 11 ≥γ0

[0151] C2: γ 22 ≥γ0

[0152] C3:

[0153] C4:

[0154] C5:

[0155] C6: p T ≤p max

[0156] C7: p R ≤p max

[0157] C8:||ω|| 2 ≤1

[0158] C9: ||ωS || 2 +||ω F || 2 ≤P B，max

[0159] In the formula, N is a natural number; C1 and C2 are the service quality (QoS) threshold constraints of the MEC servers in the reflection area and the transmission area respectively; C3 is the sum of the reflection coefficient and the transmission coefficient of the nth unit in STAR-RIS is 1; C4 is the reflection phase shift range of the nth reflection unit of STAR-RIS is between [0, 2π); C5 is the transmission phase shift range of the nth transmission unit of STAR-RIS is between [0, 2π); C6 and C7 limit the transmission power of the transmission area MEC server and the reflection area MEC server of STAR-RIS respectively, so that it is not greater than the threshold p max ; C8 is the unit receiving beamforming of BS, which is not greater than 1; C9 is the beamforming vector transmitted by BS's transmitting antenna to two industrial mobile devices, which must not be greater than the threshold P B，max .

[0160] S3. According to the constraints in step S24, the objective function is maximized, and the non-convex nonlinear programming quadratic programming problem is solved by using an alternating optimization algorithm, as follows:

[0161] S31. Since the objective function of the constructed optimization problem is in fractional form, there are many variables and they are mutually coupled, it is a non-convex nonlinear quadratic programming problem. In order to deal with the fractional form in the objective function, this embodiment uses the Fractional Programming (FP) method to convert the objective function into an easy-to-handle form; among them, the commonly used conversion methods of FP are Charnes-Cooper transformation and Dinkelbach transformation. Since the Charnes-Cooper transformation method introduces two auxiliary variables for iterative optimization, the conversion process is more cumbersome and it is difficult to generalize to solve multi-part fractional programming problems.

[0162] Therefore, this embodiment adopts Dinkelbach transformation to transform the fractional programming problem into a difference form, and transforms the objective function fractional problem. The transformed objective function is:

[0163]

[0164] In the formula, η is an introduced auxiliary variable.

[0165] The above method has simple conversion steps and has the advantage of not introducing additional constraints compared with the Charnes-Cooper transformation.

[0166] S32. Since the principle of the Alternating Optimization (AO) algorithm is to decompose a complex optimization problem into a series of relatively simple sub-problems, select one or more variables to update in each iteration, and keep other variables unchanged, and then update other variables according to the updated variable values, and iterate alternately until the convergence condition is met or the maximum number of iterations is reached, it is suitable for solving multivariable non-convex optimization problems and equality and inequality constraint optimization problems; therefore, this embodiment is based on the AO algorithm, and decomposes the original optimization problem into multiple sub-problems, as follows:

[0167] First, the BS receive beamforming vector is optimized:

[0168] According to the AO algorithm, the target items or constraint items that are not related to the BS receive beamforming vector can be ignored in the transformed optimization problem. Therefore, the MEC server transmit power p is fixed. T and p R , BS transmit beamforming vector ω S and ω F 、STAR-RIS reflection coefficient Θ R and the transmission coefficient matrix Θ T , the specific expression is as follows:

[0169]

[0170] st

[0171] Y 11 ≥γ0

[0172] Y 22 ≥γ0

[0173] ||ω|| 2 ≤1

[0174] In the above formula, since log2(1+γ*) is monotonically increasing, the above expression can be further transformed into:

[0175]

[0176] st

[0177] γ 11 ≥γ0

[0178] Y 22 ≥γ0

[0179] ||ω|| 2 ≤1

[0180] Since the above expression is a quadratic constrained quadratic programming problem (QCQP problem), this embodiment adopts the SDR method to solve it. Therefore, according to the SDR method, the power p consumed by the BS through SIC decoding of the transmission area MEC server information is T |(h T H Θ T H RB )ω| 2 The derivation is as follows:

[0181] p T |(h T H Θ T H RB )ω| 2

[0182] =p T ω H (h T H ΘTH RB ) H (h T H Θ T H RB )ω

[0183] =ω H G T ω

[0184] =tr(G T W)

[0185] In the formula, G T =p T (h T H Θ T H RB ) H (h T H Θ T H RB ), W = ωω H is the auxiliary optimization variable introduced, and tr() is the trace of the matrix. Since the auxiliary optimization variable W is introduced, a constraint condition is added, rank(W) = 1. Among them, since all columns in the matrix W are linearly related, there is only one eigenvalue equal to ω H ω is obviously greater than 0, so W is a semi-positive definite matrix; and this constraint is difficult to handle, so this embodiment directly relaxes it, i.e., semi-positive definite relaxation.

[0186] Similarly, the power consumed by the BS to decode the MEC server information in the transmission area through SIC is p R |(h RH Θ R H RB )ω| 2 The derivation is as follows:

[0187] p R |(h R H Θ R H RB )ω| 2

[0188] =p R ω H (h R H Θ R H RB ) H (h R H Θ R H RB )ω

[0189] =ω R G R ω

[0190] =tr(G R W)

[0191] Among them, G R =p R (h R H Θ R H RB ) H (h R H Θ R H RB ), W = ωω H As an auxiliary optimization variable introduced.

[0192] Combining the above methods, the first optimization problem expression is obtained, as follows:

[0193]

[0194] st

[0195] tr(G T W)≥γ0(tr(G R W)+σ 2 )

[0196] tr(G R W)≥γ0σ 2

[0197] ||ω|| 2 ≤1

[0198] Among them, tr((G R +G T )W)=tr(G T W)+tr(G R W).

[0199] The optimization problem expression after SDR is a convex problem. Therefore, the CVX toolbox is used to solve W and recover the variable ω from W that satisfies the constraints of the original optimization problem. In this embodiment, the maximum eigenvalue recovery variable method is used to recover the variable ω: the principle is to decompose the matrix into the product of the matrix represented by its eigenvalue and eigenvector. In this method, W obtained from the convex optimization problem is a matrix with rank(W)=1. The matrix W is a real symmetric matrix and is decomposed into the following form:

[0200]

[0201] Where Q is a standard orthogonal matrix, W is an m×m Hermial matrix, A is an m×m diagonal matrix, and λ i {i=1,2,…,m} is the eigenvalue. Among them, the column vector q in Q i is the feature vector.

[0202] Secondly, based on the above results, continue to optimize the MEC server transmission power:

[0203] According to the AO algorithm, the BS receive beamforming vector ω and the BS transmit beamforming vector ω are fixed. S and ω F , the reflection coefficient matrix Θ of STAR-RIS R and the transmission coefficient matrix Θ T , the original optimization problem expression is transformed into:

[0204]

[0205] st

[0206] γ 11 ≥γ0

[0207] γ 22 ≥γ0

[0208] p T ≤p max

[0209] p R ≤pma x

[0210] Since the objective function is to maximize the energy efficiency of the system, logarithmic operations are inevitably involved in the above expression. Therefore, by using the transformation idea of ​​the FP method, by introducing some auxiliary variables or additional constraints, the expression of the above non-convex fractional programming problem is further transformed into a simpler form, as follows:

[0211] Based on the FP method, an auxiliary variable α is introduced, and Since log2(1+α)-α is monotonically increasing (α>0), the above optimization problem expression is simplified to:

[0212]

[0213] st

[0214] ||ω S || 2 +||ω F || 2 ≤P B，max

[0215] in,

[0216]

[0217] Introduce the auxiliary variable η1, and use the Dinkelbach transformation in the FP method to further transform the above expression to obtain the second optimization problem expression, which is as follows:

[0218]

[0219] -η1(p T |(h T H Θ T H RB )ω| 2 )-η1(p R |(h R H Θ R H RB )ω| 2 +σ 2 )

[0220]

[0221] st

[0222] p T |(h T H Θ T H RB )ω| 2 ≥γ0(p R |(h RH Θ R H RB )ω| 2 +σ 2 )

[0223] p R |(h R H Θ R H RB )ω| 2 ≥γ0σ 2

[0224] p T ≤pma x

[0225] p R ≤p max

[0226] The objective function of the above MEC server transmit power optimization problem is linearly weighted, and its constraint expressions are all convex problems. Therefore, the CVX toolbox is used to solve it.

[0227] Then, based on the above results, the BS transmit beamforming vector is optimized:

[0228] According to the AO algorithm, the MEC server transmit power p is fixed. T and p R , BS receive beamforming vector ω, STAR-RIS reflection coefficient Θ R and the transmission coefficient matrix Θ T , the original optimization problem formula is transformed into:

[0229]

[0230] st

[0231] ||ω S || 2 +||ω F || 2 ≤P B，max

[0232] Using the FP method, introduce the auxiliary variable α k (k=1,2), transform the above formula as follows:

[0233] make Among them, α k The optimal value of γ is k (k=1,2); therefore, the simplified expression is as follows:

[0234]

[0235] St

[0236] ||ω S || 2 +||ω F || 2 ≤P B，max

[0237] Since the above equation is a QCQP problem, the SDR method is used to solve it. The derivation is as follows:

[0238]

[0239] -μ2(tr(H S W S )+tr(H F W F )+σ 2 )

[0240] Combining the above methods, the third optimization problem expression is obtained, as follows:

[0241]

[0242] -μ2(tr(H S W S )+tr(H F W F )+σ 2 )

[0243] st

[0244] tr(W S )+tr(W F )≤P B，max

[0245] in,

[0246] W S =ω S ω S H

[0247] W F =ω F ω F H

[0248] H S =h S h S H

[0249] H F =h F hF H

[0250] Where W S , W F is the auxiliary variable introduced, μ1 and μ2 are the auxiliary variables introduced, and the constraint condition rank(W S )=1 and rank(W F )=1.

[0251] The solution is obtained by using the CVX toolbox, which is consistent with the solution method of the BS receive beamforming vector optimization problem, that is, using the maximum eigenvalue recovery variable method to recover the vector from W S , W F Recover the ω that satisfies the constraints of the original optimization problem S ,ω F .

[0252] Finally, based on the above results, the STAR-RIS reflection coefficient matrix and transmission coefficient matrix are optimized:

[0253] According to the AO algorithm, the MEC server transmit power p is fixed. T and p R , BS receive beamforming vector ω, BS transmit beamforming vector ω S and ω F Variables, the original optimization problem expression is transformed into:

[0254]

[0255] st

[0256] γ 11 ≥γ0

[0257] Y 22 ≥γ0

[0258]

[0259] Combining the above methods, the fourth optimization problem expression is obtained, which is as follows:

[0260]

[0261] st

[0262] tr(TΦ T )≥γ0(tr(TΦ R )+σ 2 )

[0263] tr(TΦ T )≥γ0σ 2

[0264]

[0265]

[0266] Where T = p T (diag(h T H )H RB ω)(diag(h T H )H RB ω) H , Φ T =θ T θ T H ; Φ R =θ R θ R H ; Add constraint rank(Φ T )=1 and rank(Φ R )=1, and perform semi-positive definite relaxation on it.

[0267] Using the CVX toolbox, the transformed convex problem is solved and the maximum eigenvalue recovery variable method is used to recover the variable from Φ T and Φ R Recover the variable Θ from T and θ R .

[0268] In the process of alternately solving each of the above sub-problems, the FP method, the semi-definite relaxation method (SDR method) and the maximum eigenvalue recovery variable method are used to iteratively solve the transformed convex problem; in the iterative solution process, an auxiliary variable η is introduced, and the η update iteration rule is as follows:

[0269]

[0270] Where t is the number of iterations.

[0271] Since η is non-decreasing after each iteration, the convergence of the algorithm can be guaranteed.

[0272] Therefore, the present invention adopts the above-mentioned STAR-RIS assisted IIoT-MEC task transmission algorithm for performance optimization, which can simultaneously consider the reflected and transmitted signals, increase the freedom of manipulating the radio environment, improve the wireless transmission efficiency, and maximize the system energy efficiency.

[0273] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization, characterized in that: The following steps are involved: S1. Establish a mathematical model based on the industrial mobile edge computing architecture scenario; S2, establishing a non-convex nonlinear programming quadratic programming problem according to the mathematical model of step S1; S3. Solve non-convex nonlinear quadratic programming problems based on fractional programming methods.

2. According to claim 1, a STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization is characterized in that: In step S1, a mathematical model is established, as follows: A mathematical model is established based on STAR-RIS assisted offloading task transmission in the industrial Internet of Things mobile edge computing scenario. According to the characteristic parameters of IIOT-MEC involving mobile edge servers, industrial mobile devices, and wireless transmission channels, a mathematical model is established for the processing and rate of tasks on mobile devices or edge servers, the power consumed by the system, and the offloading task transmission channel.

3. The STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 1, characterized in that: In step S2, a non-convex nonlinear programming quadratic programming problem is established, including: S21, establishing an uplink channel transmission expression; S22, establishing a downlink channel transmission expression; S23, establishing a system power consumption expression; S24. Establish the objective function and constraints to obtain the original optimization problem expression.

4. A STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 1, characterized in that: Step S3 specifically includes: S31. Based on the fractional programming method, the objective function is transformed using Dinkelbach transformation to obtain the transformed objective function; S32. Based on the alternating optimization algorithm, the original optimization problem expression is transformed into several sub-problem expressions, and the sub-problem expressions are transformed into convex problems using fractional programming methods and semi-positive definite relaxation methods, and the transformed convex problems are iteratively solved.

5. The STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 3 is characterized in that: Step S21 is as follows: S B =(h T H Θ T H RB )ωx T +(h R H Θ R H RB )ωx R +n1 In the formula, S B is the signal received by the BS antenna, Θ R , Θ T are the reflection coefficient matrix and transmission coefficient matrix of STAR-RIS respectively, H represents the transposed matrix, H RB is the channel gain, ω is the receive beamforming at the BS, x R 、x T are the reflected signal and transmitted signal of the MEC server uplink transmission, respectively, R , p are the transmission powers of the MEC server in the transmission area and the MEC server in the reflection area, respectively. R , S T are the information sent by the transmission area MEC server and the reflection area MEC server, respectively, R 、h T are the channels from the MEC server in the reflection area to STAR-RIS and the channels from the MEC server in the transmission area to STAR-RIS, n1 is the Gaussian noise at the base station, diag() is a diagonal matrix, are the reflection coefficient and transmission coefficient of the Nth unit of STAR-RIS, respectively, N is the number of STAR-RIS units, They are respectively the reflection phase shift and transmission phase shift of the Nth unit of STAR-RIS.

6. A STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 3, characterized in that: Step S22 is specifically expressed as follows: x=ω S s1+ω F s2 Where x is the information sent by BS to industrial mobile devices, ω S ,ω F are the beamforming vectors transmitted by the transmitting antenna of the BS to the near-end mobile device and the far-end mobile device respectively. s1 and s2 are the information of the near-end mobile device and the far-end mobile device respectively.

7. A STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 3, characterized in that: Step S23 is as follows: Based on the STAR-RIS hybrid NOMA technology-assisted IIoT-MEC task transmission model, the energy P consumed by the entire system is obtained. The specific expression is: Where P cir is the BS circuit power consumption, is the power consumption of the circuit on STAR-RIS, ‖ ‖ is the vector 2 norm.

8. The STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 3 is characterized in that: Step S24 includes: The objective function is: in, The sum rate of the system uplink channel transmission: The sum rate of system downlink channel transmission: In the formula, E represents the system energy efficiency, γ 11 When performing SIC for the BS, the received signal-to-noise ratio of the MEC server in the transmission area is first decoded, γ 22 is the received signal-to-noise ratio of the MEC server in the reflection area when the BS performs SIC decoding, γ1 is the received signal-to-noise ratio of the near-end mobile device decoding the information of the remote device first and then decoding its own information, γ2 is the received signal-to-noise ratio of the remote mobile device decoding the information of the near-end device as interference, and σ is the Gaussian white noise coefficient; Under the premise of satisfying the constraints, the objective function is maximized to obtain the original optimization problem. The specific expression is: In the formula, N is a natural number, γ0 is the QoS threshold constraint, p max is the upper limit of system power, P B,max is the beamforming vector threshold.

9. A STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 4, characterized in that: In step S31, the converted objective function is: In the formula, η is an introduced auxiliary variable.

10. A STAR-RIS-assisted IIoT-MEC task transmission algorithm for performance optimization according to claim 4, characterized in that: In step S32, the original optimization problem expression is converted into several sub-problem expressions, including: First, the BS receive beamforming vector is optimized as follows: Based on the alternating optimization algorithm, the MEC server transmit power p is fixed T and p R , BS transmit beamforming vector ω S and ω F 、STAR-RIS reflection coefficient Θ R and the transmission coefficient matrix Θ T , the original optimization problem expression is transformed into the BS receive beamforming vector optimization problem expression, and the first optimization problem expression is obtained through the semi-positive definite relaxation method: in, tr((G R +G T )W)=tr(G T W)+tr(G R IN) W=oh H rank(W)=1 G T =p T (h T H Θ T H RB ) H (h T H Θ T H RB ) G R =p R (h R H Θ R H RB ) H (h R H Θ R H RB ) Where tr( ) is the trace of the matrix; Solve the first optimization problem expression to obtain W, and use the maximum eigenvalue recovery variable method to obtain ω; Secondly, optimize the transmit power of the MEC server as follows: Based on the obtained ω, fix the BS receive beamforming vector ω and the BS transmit beamforming vector ω S and ω F , the reflection coefficient matrix Θ of STAR-RIS R and the transmission coefficient matrix Θ T , the original optimization problem expression is transformed into the MEC server transmit power optimization problem expression, and the second optimization problem expression is obtained through the fractional programming method: In the formula, α and η1 are introduced auxiliary variables; Solve the expression of the second optimization problem and get p T and p R ; Then, the BS transmit beamforming vector is optimized as follows: Based on the obtained ω, p T and p R , fixed MEC server transmit power p T and p R , BS receive beamforming vector ω, STAR-RIS reflection coefficient Θ R and the transmission coefficient matrix Θ T , the original optimization problem expression is transformed into the BS transmit beamforming vector optimization problem expression, and the third optimization problem expression is obtained through the semi-positive definite relaxation method: in, W S =ω S oh S h W F =ω F oh F H H S =h S h S H H F =h F h F H In the formula, μ1 and μ2 are auxiliary variables introduced to satisfy rank(W S )=1 and rank(W F )=1; Solve the third optimization problem expression and get W S , W F , and use the maximum eigenvalue recovery variable method to get ω S ,ω F ; Finally, the STAR-RIS reflection coefficient matrix and transmission coefficient matrix are optimized as follows: Based on the obtained ω, p T 、p R ,ω S and ω F , fixed MEC server transmit power p T and p R , BS receive beamforming vector ω, BS transmit beamforming vector ω S and ω F Variables, the original optimization problem expression is transformed into the STAR-RIS reflection coefficient matrix and transmission coefficient matrix optimization problem expression, and the fourth optimization problem expression is obtained through the semi-positive definite relaxation method: in, T=p T (diag(h T H )H RB ω)(diag(h T H )H RB (ω) H F T =θ T i T H F R =θ R i R H In the formula, Φ T , Φ R All are introduced auxiliary variables; Solve the expression of the fourth optimization problem and get Φ T , Φ R , and use the maximum eigenvalue recovery method to get Θ T and θ R .

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