MEC system time delay optimization method of STAR-RIS assisted uplink NOMA

Abstract

The invention discloses a time delay optimization method for an MEC system of STAR-RIS assisted uplink NOMA, which relates to the technical field of wireless communication, and comprises the following steps: acquiring channel state information among nodes of the MEC system of STAR-RIS assisted uplink NOMA; the user offloads a task to the base station equipped with the MEC server, and the channel transmission rate between the user and the base station is calculated; calculating local time delay and edge time delay of the user; constructing a time delay minimization problem of joint optimization of user task allocation, user transmitting power, MEC calculation frequency allocation, base station receiving beam forming vector and STAR-RIS coefficient vector; an optimization problem is decomposed into four sub-problems, and the minimum user weighted time delay sum in the system is obtained through iterative solution of an SCA algorithm and an AO algorithm. According to the scheme provided by the invention, the user weighted time delay sum of the system is remarkably reduced.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular to a delay optimization method for a MEC system of STAR-RIS assisted uplink NOMA. Background Art

[0002] With the rapid development of 5G technology and the Internet of Things, the number of wireless devices has exploded, and the application scenarios of the Internet of Things have become more and more diverse, including a large number of computationally intensive and latency-sensitive applications. Such applications require strong computing power to meet their ultra-low latency requirements. In order to meet the low latency requirements, the traditional cloud computing network architecture is gradually shifting to the Mobile Edge Computing (MEC) network. Mobile edge computing reduces the distance between users and cloud servers by sinking part of the user's computing tasks to mobile edge nodes, thereby achieving the purpose of reducing task processing latency. Offloading tasks to MEC servers requires reliable and fast data transmission links, but different devices may have unique channel conditions due to their different locations and fading conditions, so reconfigurable intelligent surfaces (RIS) are needed. RIS is a revolutionary technology that consists of a large number of low-cost passive components, each of which can independently reflect the incident signal with an adjustable phase shift, thereby achieving passive beamforming without the need for any transmit RF chain and improving the user's channel propagation environment. Therefore, RIS can adaptively adjust the transmission parameters to solve the data transmission problem caused by differences in location and channel conditions between different devices. However, traditional RIS can only provide half-space coverage, that is, 180° coverage, which requires the device and MEC server to be located on the same side of RIS, which means that users on the other side of RIS are not within the coverage of RIS. Unlike traditional RIS, the Simultaneous Transmitting And Reflecting-Reconfigurable Intelligent Surface (STAR-RIS) can provide full-space coverage, that is, 360° coverage, which improves the disadvantage of single-sided coverage of traditional RIS. By adjusting the transmission and reflection coefficients of each reconfigurable unit of STAR-RIS, the transmission and reflection signals can be reconfigured, providing more degrees of freedom for signal propagation, thereby significantly improving the flexibility of the communication system. At the same time, in order to improve spectrum efficiency, non-orthogonal multiple access technology (NOMA) is widely used. Its basic idea is to use non-orthogonal transmission at the transmitter and achieve correct demodulation through the successive interference cancellation (SIC) receiver at the receiver. By combining NOMA technology, STAR-RIS technology and MEC technology, the efficiency of task offloading can be improved, thereby meeting the computing requirements of computationally intensive and delay-sensitive tasks. Summary of the invention

[0003] In view of the above existing problems, the present invention is proposed.

[0004] Therefore, the present invention proposes a delay optimization method for a MEC system with STAR-RIS assisted uplink NOMA, so that the weighted delay sum of users in the system is minimized.

[0005] In order to solve the above technical problems, the present invention provides the following technical solutions, a method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA, comprising:

[0006] Acquire the channel state information between each node of the MEC system; the user unloads the task to the base station equipped with the MEC server, and calculates the channel transmission rate between the user and the base station; decompose the total task into local computing tasks and edge computing tasks, calculate the user's local delay and edge delay, and record the maximum value of the two as the user delay; construct a joint optimization problem of user task allocation, user transmit power, MEC computing frequency allocation, base station receive beamforming vector and STAR-RIS coefficient vector with the goal of minimizing the sum of user weighted delays; decompose the constructed original optimization problem into four sub-problems, optimize the user task allocation in the first sub-problem, optimize the MEC computing frequency allocation and user transmit power in the second sub-problem, optimize the base station receive beamforming vector in the third sub-problem, and optimize the STAR-RIS coefficient vector in the fourth sub-problem, iteratively solve the four sub-problems through the alternating optimization algorithm until convergence, and obtain the optimized sum of user weighted delays.

[0007] As a preferred solution of the delay optimization method of the MEC system of STAR-RIS assisted uplink NOMA described in the present invention, wherein: the acquisition of channel state information between nodes of the MEC system includes, in the task unloading stage, STAR-RIS assists the user to unload the task to the base station; the signal received by the base station in the MEC system is expressed as:

[0008]

[0009] Wherein, the symbol k represents the terminal user, when k is r, it represents the user in the reflection area, and when k is t, it represents the user in the transmission area; s k represents the transmitted signal at user k, satisfying E{|s k | 2}=1,P k Indicates its transmission power; represents the channel state information vector from user k to STAR-RIS; represents the channel state information matrix from STAR-RIS to the base station, where represents the x×y-dimensional complex-valued matrix space; represents the transmission and reflection coefficient vector of STAR-RIS during the unloading mission phase, where (·) H represents the conjugate transpose; Θ k =diag(v k ), k∈{t,r} represents the transmission and reflection coefficient matrix of STAR-RIS during the unloading mission phase, where and denote the amplitude and phase coefficients of the nth unit of STAR-RIS, respectively, and satisfy j is an imaginary unit, diag(·) represents the diagonalized matrix; n represents the Gaussian white noise at the base station, which has zero mean and variance σ 2 I M The complex Gaussian distribution is denoted by Where 0 M×1 represents the M×1-dimensional zero vector, I M Represents the M×M-dimensional identity matrix.

[0010] As a preferred solution of the delay optimization method of the MEC system of STAR-RIS assisted uplink NOMA described in the present invention, wherein: the acquisition of channel state information between nodes of the MEC system includes assuming that the base station decodes the received signal using a linear receive beamforming vector, and the recovered signal can be expressed as:

[0011]

[0012] in, represents the receive beamforming vector at the base station.

[0013] As a preferred solution of the delay optimization method of the MEC system of STAR-RIS assisted uplink NOMA described in the present invention, wherein: the calculation of the channel transmission rate between the user and the base station includes assuming that the channel gain of the user satisfies ||GΘ t h t || 2 ≥||GΘ r h r || 2 , where ||·|| represents the two-norm. In the uplink NOMA system, a SIC receiver is configured at the base station, and the co-channel interference is the sum of the channel gains of other users. First, the user with good channel quality is decoded, and the decoded signal is subtracted from the superimposed signal. Then, the user with the second-best channel quality is decoded, and so on, until all the signals are decoded. Therefore, the signal-to-interference-to-noise ratio of the transmission area user t received by the base station is expressed as:

[0014]

[0015] The signal-to-noise ratio of user r in the reflection area received by the base station is expressed as:

[0016]

[0017] Among them, |·| represents modulus;

[0018] The transmission rates of user t and user r are obtained as follows:

[0019] R t =Blog2(1+γ t )

[0020] R r =Blog2(1+γ r )

[0021] Wherein, B represents the transmission bandwidth allocated to the user.

[0022] As a preferred solution of the delay optimization method of the MEC system of STAR-RIS assisted uplink NOMA described in the present invention, wherein: the calculation of the local delay and edge delay of the user includes that the local delay of user k is:

[0023]

[0024] Among them, L k is the total amount of tasks that need to be calculated at user k, l k is the amount of tasks that user k offloads to the MEC server, C is the number of CPU cycles required to process a 1-bit task, is the number of CPU cycles per second at user k;

[0025] Assuming that the base station starts the calculation after receiving the offloading task, the edge delay of user k is:

[0026]

[0027] in, represents the computation frequency assigned to user k by MEC, R k represents the transmission rate of user k. The delay of user k depends on the larger value of the local delay and the edge delay, so the delay of user k should be recorded as:

[0028]

[0029] As a preferred solution of the delay optimization method of the MEC system of STAR-RIS assisted uplink NOMA described in the present invention, the joint optimization problem includes minimizing the sum of user weighted delays, and constructing the optimization problem as follows:

[0030]

[0031] stl k ∈{0,1,…,L k}

[0032]

[0033]

[0034]

[0035] ||w|| 2 =1

[0036]

[0037]

[0038]

[0039] ||GΘ t h t ‖ 2 ≥‖GΘ r h r || 2

[0040] in, ω k represents the weighting coefficient of user k.

[0041] As a preferred solution of the delay optimization method of the MEC system of STAR-RIS assisted uplink NOMA described in the present invention, wherein: the original optimization problem constructed is decomposed into four sub-problems including: given MEC calculation frequency allocation {f t e ,f r e}、User transmission power {P t ,P r}, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,v r}, optimize the user task allocation {l t ,l r};

[0042] Given a MEC, calculate the frequency allocation {f t e ,f r e}、User transmission power {P t ,P r}, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,vr}, optimize the user task allocation {l t ,l r}; Construct the corresponding sub-problems as follows:

[0043]

[0044] stl k ∈{0,1,…,L k}

[0045] By relaxing the discrete variables into continuous variables, we can get l t and l r The closed-form solution of

[0046] Given a user task assignment {l t ,l r}, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,v r}, optimize the MEC calculation frequency allocation {f t e ,f r e} and user transmission power {P t ,P r}; Construct the corresponding sub-problems as follows:

[0047]

[0048]

[0049]

[0050]

[0051] Through the successive convex approximation algorithm, this subproblem is transformed into a convex optimization problem, and the corresponding optimization solution is obtained using standard convex optimization tools such as CVX.

[0052] Given a user task assignment {l t ,l r}、MEC calculates frequency allocation User transmission power {P t ,P r} and the STAR-RIS coefficient vector {v t ,v r}, optimize the base station receive beamforming vector w; construct the corresponding sub-problem as follows:

[0053]

[0054] st‖w‖ 2 =1

[0055] Through the SCA algorithm and the semi-definite relaxation algorithm, the subproblem is transformed into a convex semi-definite programming problem, and the CVX standard convex optimization tool is used to solve it, and finally the optimized base station receive beamforming vector w is obtained.

[0056] As a preferred solution of the delay optimization method of the MEC system of STAR-RIS assisted uplink NOMA described in the present invention, wherein: the original optimization problem constructed is decomposed into four sub-problems including: given user task allocation {l t ,l r}、MEC calculates frequency allocation {f t e ,f r e}、User transmission power {P t ,P r} and the base station receive beamforming vector w, optimize the STAR-RIS coefficient vector {v t ,v r}; Construct the corresponding sub-problems as follows:

[0057]

[0058]

[0059]

[0060]

[0061] ‖GΘ t h t ‖ 2 ≥||GΘ r h r ‖ 2

[0062] Through the SCA algorithm and the SDR algorithm, the subproblem is transformed into an SDP problem, and solved using standard convex optimization tools such as CVX, and finally the optimized STAR-RIS coefficient vector v is obtained. t and v r ;

[0063] The sub-problems are optimized alternately through an iterative algorithm until the objective function converges.

[0064] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and wherein the processor implements the steps of a method for optimizing the delay of a MEC system of STAR-RIS assisted uplink NOMA when executing the computer program.

[0065] A computer-readable storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of a method for optimizing the delay of a MEC system of STAR-RIS assisted uplink NOMA are implemented.

[0066] Beneficial effects of the present invention: The present invention aims to minimize the sum of weighted delays of users, and proposes an iterative algorithm based on semidefinite relaxation (SDR), successive convex approximation (SCA) and alternating optimization (AO) to solve the proposed resource allocation problem. Simulation results show that compared with the traditional RIS-assisted transmission scheme and the STAR-RIS-assisted transmission scheme using the mode switching (MS) protocol, the scheme proposed by the present invention significantly reduces the sum of weighted delays of users in the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0068] Figure 1 A flowchart of a method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA is provided for one embodiment of the present invention.

[0069] Figure 2 A schematic diagram of a system model of a method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA is provided for one embodiment of the present invention.

[0070] Figure 3 A schematic diagram of simulation results of a method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA is provided as an embodiment of the present invention. DETAILED DESCRIPTION

[0071] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0072] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0073] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The term "in one embodiment" that appears in different places in this specification does not necessarily refer to the same embodiment, nor does it refer to a separate or selective embodiment that is mutually exclusive with other embodiments.

[0074] The present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0075] At the same time, in the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "upper, lower, inner and outer" are based on the directions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as limiting the present invention. In addition, the terms "first, second or third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0076] In the present invention, unless otherwise clearly specified and limited, the terms "install, connect, connect" should be understood in a broad sense, for example: it can be a fixed connection, a detachable connection or an integral connection; it can also be a mechanical connection, an electrical connection or a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0077] Example 1, reference Figure 1-Figure 3 , which is the first embodiment of the present invention, and provides a method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA, including:

[0078] The present invention proposes a method for optimizing the delay of a mobile edge computing (MEC) system with uplink non-orthogonal multiple access (NOMA) assisted by a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). The system includes a base station equipped with a MEC server, two terminal users, and a STAR-RIS node. The base station is equipped with M antennas, the user is equipped with a single antenna, and STAR-RIS is equipped with N reconfigurable units. The energy splitting (ES) protocol is used to adjust the signal phase and amplitude to assist the task offloading process from the user to the base station. Successive interference cancellation (SIC) is used at the receiving end to demodulate the signal. Considering that the direct link between the user and the base station is blocked, the user only uses the transmission and reflection signals of STAR-RIS to offload tasks to the base station. The system is as follows: Figure 2 shown.

[0079] The specific steps include:

[0080] Step A: Obtain channel state information between nodes of the MEC system;

[0081] Step B: The user offloads tasks to the base station equipped with the MEC server and calculates the channel transmission rate between the user and the base station;

[0082] Step C: Due to the limited computing power of users, end users need to decompose the total task into local computing tasks and edge computing tasks. The delay of performing task calculation locally is recorded as local delay, and the sum of the delay of task offloading to the base station and the delay of the base station processing task calculation is recorded as edge delay. Calculate the user's local delay and edge delay, and record the maximum value of the two as user delay;

[0083] Step D: Construct a joint optimization problem of user task allocation, user transmit power, MEC calculation frequency allocation, base station receive beamforming vector and STAR-RIS coefficient vector with the goal of minimizing the sum of user weighted delays;

[0084] Step E: Decompose the constructed original optimization problem into four sub-problems. In the first sub-problem, optimize the user task allocation, in the second sub-problem, optimize the MEC calculation frequency allocation and user transmit power, in the third sub-problem, optimize the base station receive beamforming vector, and in the fourth sub-problem, optimize the STAR-RIS coefficient vector. The four sub-problems are iteratively solved by the alternate optimization (AO) algorithm until convergence to obtain the optimized user weighted delay sum.

[0085] The specific steps of step A are as follows:

[0086] In the task offloading phase, STAR-RIS assists the user to offload tasks to the base station. The signal received by the base station in the system can be expressed as:

[0087]

[0088] Wherein, the symbol k represents the terminal user, when k is r, it represents the user in the reflection area, and when k is t, it represents the user in the transmission area; s k represents the transmitted signal at user k, satisfying E{|s k | 2}=1,P k Indicates its transmission power; represents the channel state information vector from user k to STAR-RIS; represents the channel state information matrix from STAR-RIS to the base station, where represents the x×y-dimensional complex-valued matrix space; k∈{t,r} represents the transmission and reflection coefficient vector of STAR-RIS during the unloading mission phase, where (·) H represents the conjugate transpose; Θ k =diag(v k ), k∈{t,r} represents the transmission and reflection coefficient matrix of STAR-RIS during the unloading mission phase, where and denote the amplitude and phase coefficients of the nth unit of STAR-RIS, respectively, and satisfy j is an imaginary unit, diag(·) represents the diagonalized matrix; n represents the Gaussian white noise at the base station, which has zero mean and variance σ 2 I M The complex Gaussian distribution is denoted by Where 0 M×1 represents the M×1-dimensional zero vector, I M Represents the M×M-dimensional identity matrix.

[0089] Assuming that the base station uses a linear receive beamforming vector to decode the received signal, the recovered signal can be expressed as:

[0090]

[0091] in, represents the receive beamforming vector at the base station.

[0092] The specific steps of step B are as follows:

[0093] Without loss of generality, assume that the user's channel gain satisfies ‖GΘ t h t ‖ 2 ≥||GΘ r h r || 2 , where ||·|| represents taking the second norm. In the uplink NOMA system, a SIC receiver is configured at the base station end. The co-channel interference is the sum of the channel gains of other users. The interference to the user mainly comes from users with good channel quality, that is, users with poor channel quality are more susceptible to stronger co-channel interference. In order not to waste resources, users with good channel quality are first decoded, and the decoded signal is subtracted from the superimposed signal. Then, users with suboptimal channel quality are decoded, and so on, until all signals are decoded. Therefore, the signal-to-interference-to-noise ratio of user t in the transmission area received by the base station can be expressed as:

[0094]

[0095] The signal-to-noise ratio of user r in the reflection area received by the base station can be expressed as:

[0096]

[0097] Among them, |·| represents modulus. From equations (3) and (4), we can get the transmission rates of user t and user r respectively:

[0098] R t =Blog2(1+γ t ) (5)

[0099] R r =Blog2(1+γ r ) (6)

[0100] Wherein, B represents the transmission bandwidth allocated to the user.

[0101] The specific steps of step C are as follows:

[0102] The local delay of user k is:

[0103]

[0104] Among them, L k is the total amount of tasks that need to be calculated at user k, l k is the amount of tasks that user k offloads to the MEC server, C is the number of CPU cycles required to process a 1-bit task, is the number of CPU cycles per second at user k.

[0105] Assuming that the base station starts the calculation after receiving the offloading task, the edge delay of user k is:

[0106]

[0107] in, represents the computation frequency assigned to user k by MEC, R k represents the transmission rate of user k. The delay of user k depends on the larger value of its local delay and edge delay, so the delay of user k should be recorded as:

[0108]

[0109] The specific steps of step D are as follows:

[0110] With the goal of minimizing the sum of user weighted delays, the optimization problem is constructed as:

[0111]

[0112] stl k ∈{0,1,…,L k} (10a)

[0113]

[0114]

[0115]

[0116] ||w|| 2 =1

[0117] (10e)

[0118]

[0119]

[0120]

[0121] ||GΘ t h t || 2 ≥||GΘ r h r ||2 (10i)

[0122] in, ω k represents the weighting coefficient of user k. Formula (10a) represents the constraint on the amount of discrete tasks offloaded by the user, Formulas (10b) and (10c) represent the computational frequency constraints assigned to the user by MEC, Formula (10d) represents the transmit power constraint of user k, Formula (10e) represents the normalization constraint of the beamforming vector of the received signal at the base station, Formulas (10f), (10g) and (10h) represent the amplitude and phase constraints of the reconfigurable unit of STAR-RIS, and Formula (10i) is the user decoding order constraint.

[0123] The specific steps of step E are as follows:

[0124] Since the optimization variables in the objective function and the constraints are highly coupled, the original optimization problem constructed is difficult to solve directly. Therefore, in order to solve (P1), the present invention uses the AO algorithm to decompose the original optimization problem constructed into four sub-problems for iterative solution.

[0125] First, given the MEC, the frequency allocation {f t e ,f r e}、User transmission power {P t ,P r}, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,v r}, optimize the user task allocation {l t ,l r}. The corresponding sub-problem (P2) is constructed as follows:

[0126]

[0127] st(10a)

[0128] Since discrete variables are difficult to calculate, consider the discrete variable l k Relaxation to continuous variables The segmented form of formula (9) can be obtained:

[0129]

[0130] From formula (12), we can get that When D k Follow Monotonically decreasing, when When D k Follow is monotonically increasing. Therefore, when hour, Get the minimum value, that is, at this time Get the optimal solution:

[0131]

[0132] And l k The optimal value of must be an integer, so we can conclude that l k The optimal solution is:

[0133]

[0134] in, Represents floor and ceiling respectively.

[0135] Secondly, given a user task assignment {l t ,l r}, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,v r}, optimize the MEC calculation frequency allocation {f t e ,f r e} and user transmission power {P t ,P r}. The corresponding sub-problem (P3) is constructed as follows:

[0136]

[0137] st(10b)-(10d)(15a)

[0138] Since the objective function contains the function max{·}, it is difficult to process directly, so we consider introducing an auxiliary variable {t t ,t r}, then the equivalent form of (P3) can be expressed as:

[0139]

[0140]

[0141]

[0142] Because P t With P r Only exists in R k In, and R k In the denominator, we consider introducing an auxiliary variable {x t ,x r}, then the problem (P3-E1) can be transformed into:

[0143]

[0144] stx t ≤R t (17a)

[0145] x r ≤R r (17b)

[0146]

[0147]

[0148] (15a), (16a), (17e)

[0149] Since there is a coupled variable P in equation (17a) t With P r , decouple it, and formula (4) can be rewritten as:

[0150]

[0151] Although the decoupling between variables is achieved at this time, equation (18) is in the form of a difference between convex functions. Therefore, (17a) is still a non-convex constraint. Therefore, the successive convex approximation (SCA) algorithm is considered to solve the second log2 function of equation (18) at the feasible point P r * Performing a first-order Taylor expansion at , we can obtain the linear lower bound of equation (18):

[0152]

[0153] YesP r The optimal value after iteration can be obtained through multiple iterations. Problem (P3) can be equivalently solved by iteratively solving the following problem (P3-E3):

[0154]

[0155]

[0156] (17b)-(17e) (20b)

[0157] At this time, both the objective function and the constraints are convex, and (P3-E3) is a standard convex optimization problem, which can be solved using standard convex optimization tools such as CVX.

[0158] Then, given a user task assignment {l t ,l r}、MEC calculates frequency allocation User transmission power {P t ,P r} and the STAR-RIS coefficient vector {v t ,v r}, optimize the base station receive beamforming vector w. The corresponding sub-problem (P4) is constructed as follows:

[0159]

[0160] st(10e)

[0161] The solution method is the same as that of problem (P3), introducing auxiliary variables {u t ,u r}, the equivalent form of problem (P4) can be expressed as:

[0162]

[0163]

[0164]

[0165] (10e)

[0166] Due to R t and R r There are coupled variables in the denominator, which is difficult to handle, so an auxiliary variable {y t ,y r}, the problem is transformed into:

[0167]

[0168] sty t ≤R t (23a)

[0169] y r ≤R r (23b)

[0170]

[0171]

[0172] (10e), (22a) (23e)

[0173] Let W = ww H , H k =Gdiag(h k ),k∈{t,r}, equation (10e) can be written as Tr(W)≤1, equations (10f), (10g) and (10h) can be written as 0≤Vk (n,n)≤1,k∈{t,r},n∈{1,…,N}and V t (n,n)+V r (n,n)=1,n∈{1,…,N}, equation (10i) can be written as Tr(H u,t V t )≥Tr(H u,r V r ),in at this time From this we can get:

[0174]

[0175]

[0176] Here, Tr(·) represents the trace of the matrix. At this point, the original problem can be transformed into a semidefinite programming (SDP) problem, but R t The optimization variables in exist in both the numerator and the denominator, and need to be processed. Considering the introduction of auxiliary variables {A1, A2}, the problem is transformed into:

[0177]

[0178] stTr(W)=1 (26a)

[0179] rank(W)=1 (26b)

[0180] W±0 (26c)

[0181]

[0182]

[0183]

[0184] (23b)-(23d)(26g)

[0185] The function on the right side of constraint (26d) is a jointly convex function of A1 and A2, so the constraint is non-convex. Therefore, the SCA algorithm is used to solve the function at the feasible point By performing a first-order Taylor expansion at , we can obtain the linear lower bound of this function, namely:

[0186]

[0187] in, and They represent the optimal solutions of A1 and A2 after iteration respectively. At this time, the problem can be equivalently solved by iteratively solving the following problems (P4-E4):

[0188]

[0189]

[0190] (26a)-(26c),

[0191] (26e)-(26g)(28b)

[0192] Since the rank-one constraint in equation (26b) is non-convex and the rest are convex constraints, the rank-one constraint is relaxed by the semidefinite relaxation (SDR) algorithm. Then, problem (P4-E4) is transformed into a standard convex semidefinite programming (SDP) problem, which can be solved using standard convex optimization tools such as CVX.

[0193] Since the rank-one constraint is relaxed, the solution W * A rank-one solution may not be satisfied, so eigenvalue decomposition needs to be used after variable optimization:

[0194]

[0195] Among them, λ * W * The maximum eigenvalue, u * Represents λ * The corresponding feature vector.

[0196] Finally, given the user task assignment {l t ,l r}、MEC calculates frequency allocation {f t e ,f r e}、User transmission power {P t ,P r} and the base station receive beamforming vector w, optimize the STAR-RIS coefficient vector {v t ,v r}. The corresponding sub-problem (P5) is constructed as follows:

[0197]

[0198] st0≤V k (n,n)≤1,k∈{t,r},n∈{1,…,N} (30a)

[0199] V t (n,n)+V r (n,n)=1,n∈{1,…,N} (30b)

[0200] Tr(H u,t V t )≥Tr(H u,r V r ) (30c)

[0201] V k ±0,k∈{t,r} (30d)

[0202] rank(V k )=1,k∈{t,r} (30e)

[0203] The optimization process of problem (P5) is similar to that of problem (P4), by introducing auxiliary variables {g t ,g r ,z t ,z r ,B1,B2}, the original problem can be equivalently solved by iteratively solving the following problem (P5-E1):

[0204]

[0205]

[0206]

[0207]

[0208] z r ≤R r (31d)

[0209]

[0210]

[0211] (30a)-(30e) (31g)

[0212] in, The expression is:

[0213]

[0214] in, and They represent the optimal solutions of B1 and B2 after iteration. Similar to (P4-E4), (30e) is a non-convex constraint. By using the SDR algorithm to relax the rank-one constraint, problem (P5-E1) is a standard SDP problem and can be solved using standard convex optimization tools such as CVX.

[0215] Since the rank-one constraint is relaxed, the solution for V t* and V r * A rank-one solution may not be satisfied, so eigenvalue decomposition needs to be used after variable optimization.

[0216]

[0217] Among them, λ * express The maximum eigenvalue, u * Represents λ * The corresponding feature vector.

[0218] Subproblems (P2), (P3), (P4) and (P5) are optimized alternately through an iterative algorithm until the objective function converges.

[0219] Table 1 gives the detailed steps of the algorithm used.

[0220] Table 1 Iterative algorithm of the proposed scheme

[0221]

[0222]

[0223] Example 2, reference Figure 2-Figure 3 , which is an embodiment of the present invention, provides a delay optimization method for a MEC system with STAR-RIS assisted uplink NOMA. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through experiments.

[0224] An example of the present invention is realized by MATLAB software simulation, and the system model diagram is shown in FIG. Figure 2 In the simulation experiment, the wireless channels are assumed to be independent of each other and the channel state information is kept constant. The positions of the base station, STAR-RIS, user t and user r are (0,0), (50,10), (70,20) and (60,-10) respectively, in meters. The channel state information h between user k and STAR-RIS k The channel state information G between STAR-RIS and the base station is subject to Rician fading, where k∈{t,r}. Bandwidth B = 1MHz, weighting coefficient ω k =0.5, number of antennas M = 4, noise power σ 2 =-80dBm, the total amount of tasks to be calculated at user k is L k = 350Kb, the CPU speed per second at user k The number of CPU cycles required to process a 1-bit task is C = 750 cycles / bit, and the power limit at user k is The upper limit of the calculation frequency allocated by MEC to users

[0225] Figure 3 This is a graph showing the relationship between the sum of user weighted delays and the number of reconfigurable smart surface elements when delay minimization is performed in an embodiment of the present invention.

[0226] First of all, it should be noted that in order to ensure the fairness of the comparison scheme, the traditional RIS-assisted transmission scheme is to deploy a A transmission-only RIS with a reconfigurable unit and a Reconfigurable unit only reflection RIS. As can be seen from the figure, compared with the communication scenario composed of traditional RIS, the joint optimization scheme assisted by STAR-RIS can further reduce the weighted delay and. This is because STAR-RIS can adjust the amplitude coefficient and phase of transmission and reflection in each RIS unit, while traditional RIS can only adjust the phase of each RIS unit to improve the channel quality. Therefore, the STAR-RIS assisted transmission scheme further improves the transmission rate compared with the traditional RIS assisted transmission scheme, thereby reducing the delay. Compared with the STAR-RIS assisted transmission scheme using the mode switching (MS, Mode Switching) protocol, the ES protocol assisted transmission scheme of STAR-RIS can achieve better optimization results. This is because the amplitude of the reflection unit of the STAR-RIS using the MS protocol can only change between {0, 1}, while the amplitude of the reflection unit of the STAR-RIS using the ES protocol can change continuously between [0, 1], so it has a higher degree of freedom. In addition, it can be seen from the figure that the sum of the weighted user delays in the traditional RIS-assisted transmission scheme, the STAR-RIS-assisted transmission scheme using the MS protocol, and the proposed STAR-RIS-assisted transmission scheme using the ES protocol all decrease with the increase in the number of RIS units. Therefore, the delay can be reduced by deploying more low-cost RIS units, which further proves the benefits of integrating RIS into MEC.

[0227] It should be noted that the above embodiments are only used to illustrate the technical solutions 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 the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

[0228] Example 3

[0229] The third embodiment of the present invention is different from the first two embodiments in that:

[0230] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0231] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0232] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0233] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0234] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0235] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA, characterized by: include, Obtain channel status information between nodes in the MEC system; The user offloads tasks to the base station equipped with the MEC server and calculates the channel transmission rate between the user and the base station; Decompose the total task into local computing tasks and edge computing tasks, calculate the user's local latency and edge latency, and record the maximum value of the two as the user latency; Construct a joint optimization problem of user task allocation, user transmit power, MEC computing frequency allocation, base station receive beamforming vector and STAR-RIS coefficient vector with the goal of minimizing the sum of user weighted delays; The original optimization problem is decomposed into four sub-problems. In the first sub-problem, user task allocation is optimized. In the second sub-problem, MEC calculation frequency allocation and user transmission power are optimized. In the third sub-problem, the base station receive beamforming vector is optimized. In the fourth sub-problem, the STAR-RIS coefficient vector is optimized. The four sub-problems are iteratively solved by the alternating optimization algorithm until convergence to obtain the optimized user weighted delay sum.

2. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA as claimed in claim 1, characterized in that: The acquisition of channel state information between nodes of the MEC system includes, in the task unloading stage, STAR-RIS assists the user to unload the task to the base station; the signal received by the base station in the MEC system is expressed as: Wherein, the symbol k represents the terminal user, when k is r, it represents the user in the reflection area, and when k is t, it represents the user in the transmission area; s k represents the transmitted signal at user k, satisfying E{|s k | 2 }=1,P k Indicates its transmission power; represents the channel state information vector from user k to STAR-RIS; represents the channel state information matrix from STAR-RIS to the base station, where represents the space of complex-valued matrices of dimension x×y; represents the transmission and reflection coefficient vector of STAR-RIS during the unloading mission phase, where (·) H represents the conjugate transpose; Θ k =diag(v k ), k∈{t,r} represents the transmission and reflection coefficient matrix of STAR-RIS during the unloading mission phase, where and denote the amplitude and phase coefficients of the nth unit of STAR-RIS, respectively, and satisfy j is an imaginary unit, diag(·) represents the diagonalized matrix; n represents the Gaussian white noise at the base station, which has zero mean and variance σ 2 I M The complex Gaussian distribution is denoted by Where 0 M×1 represents the M×1-dimensional zero vector, I M Represents the M×M-dimensional identity matrix.

3. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA as claimed in claim 2, characterized in that: The acquisition of channel state information between nodes of the MEC system includes assuming that the base station decodes the received signal using a linear receive beamforming vector, and the recovered signal is expressed as: in, represents the receive beamforming vector at the base station.

4. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA as claimed in claim 3, characterized in that: The calculation of the channel transmission rate between the user and the base station includes assuming that the channel gain of the user satisfies ||GΘ t h t || 2 ≥||GΘ r h r || 2 , where ||·|| represents the two-norm. In the uplink NOMA system, a SIC receiver is configured at the base station, and the co-channel interference is the sum of the channel gains of other users. First, the user with good channel quality is decoded, and the decoded signal is subtracted from the superimposed signal. Then, the user with the second-best channel quality is decoded, and so on, until all the signals are decoded. Therefore, the signal-to-interference-to-noise ratio of the transmission area user t received by the base station is expressed as: The signal-to-noise ratio of user r in the reflection area received by the base station is expressed as: Among them, |·| represents modulus; The transmission rates of user t and user r are obtained as follows: R t =Blog2(1+γ t ) R r =Blog2(1+γ r ) Wherein, B represents the transmission bandwidth allocated to the user.

5. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA as claimed in claim 4, characterized in that: The calculation of the local delay and edge delay of the user includes that the local delay of user k is: Among them, L k is the total amount of tasks that need to be calculated at user k, l k is the amount of tasks that user k offloads to the MEC server, C is the number of CPU cycles required to process a 1-bit task, is the number of CPU cycles per second at user k; Assuming that the base station starts calculating after receiving the offloading task, the edge delay of user k is: in, represents the computation frequency assigned to user k by MEC, R k represents the transmission rate of user k; The delay of user k is recorded as:

6. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA as claimed in claim 5, characterized in that: The joint optimization problem includes minimizing the sum of weighted user delays, and constructing the optimization problem as follows: s.t.l k ∈{0,1,…,L k } ||w|| 2 ＝1 ||GΘ t h t || 2 ≥||GΘ r h r || 2 in, ω k represents the weighting coefficient of user k.

7. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA as claimed in claim 6, characterized in that: The original optimization problem is decomposed into four sub-problems, including: given MEC calculation frequency allocation User transmission power {P t ,P r }, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,v r }, optimize the user task allocation {l t ,l r }; Calculate frequency allocation at a given MEC User transmission power {P t ,P r }, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,v r }, optimize the user task allocation {l t ,l r }; Construct the corresponding sub-problems as follows: s.t.l k ∈{0,1,…,L k } By relaxing the discrete variables into continuous variables, we get l t and l r The closed-form solution of Given a user task assignment {l t ,l r }, base station receive beamforming vector w and STAR-RIS coefficient vector {v t ,v r }, optimize MEC calculation frequency allocation With user transmission power {P t ,P r }; Construct the corresponding sub-problems as follows: Through the successive convex approximation algorithm, the current sub-problem is transformed into a convex optimization problem, and the CVX standard convex optimization tool is used to solve it, and the corresponding optimization solution is obtained as follows: Given a user task assignment {l t ,l r }、MEC calculates frequency allocation User transmission power {P t ,P r } and the STAR-RIS coefficient vector {v t ,v r }, optimize the base station receive beamforming vector w; construct the corresponding sub-problem as follows: s.t.||w|| 2 =1 Through the SCA algorithm and the semi-definite relaxation algorithm, the current sub-problem is transformed into a convex semi-definite programming problem, and the CVX standard convex optimization tool is used to solve it to obtain the optimized base station receive beamforming vector w.

8. A method for optimizing the delay of a MEC system with STAR-RIS assisted uplink NOMA as claimed in claim 7, characterized in that: The original optimization problem is decomposed into four sub-problems, including: given user task assignment {l t ,l r }、MEC calculates frequency allocation User transmission power {P t ,P r } and the base station receive beamforming vector w, optimize the STAR-RIS coefficient vector {v t ,v r }; Construct the corresponding sub-problems as follows: ||GΘ t h t || 2 ≥||GΘ r h r || 2 Through the SCA algorithm and the SDR algorithm, the current sub-problem is transformed into an SDP problem, and the CVX standard convex optimization tool is used to solve it, and finally the optimized STAR-RIS coefficient vector v is obtained. t and v r ; The sub-problems are optimized alternately through an iterative algorithm until the objective function converges.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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