A Method for Maximizing Energy Efficiency in a Hybrid NOMA IRS-Assisted MEC System

Abstract

The present invention relates to the field of wireless communication technologies, and discloses a method for maximizing energy efficiency in a hybrid NOMA IRS-assisted MEC system. An IRS-assisted MEC system based on hybrid NOMA transmission is established. The system includes K single-antenna users, an intelligent reflecting surface, a single-antenna base station (BS), and an MEC server at the BS side. The K users with limited performance are divided into different sub-channels, and two users share a sub-channel. The two users in the same sub-channel adopt a hybrid NOMA transmission mode. With the assistance of the IRS, all users simultaneously offload some or all of their data to the MEC server for computing within T max . The method for maximizing energy efficiency provided by the present invention has a wide application range and excellent compatibility, and can flexibly allocate resources to meet users' requirements under different data volumes, different channel conditions, and different local user computing performances.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly to a method for maximizing energy efficiency in a hybrid NOMA-based IRS-assisted MEC system. Background Art

[0002] In the upcoming 6G network, Internet of Things (IOT) devices will experience rapid growth, such as fully automated driverless vehicles, industrial Internet, super smart homes / cities, etc. However, due to the limited resources of the devices themselves, they cannot meet the requirements of low energy consumption and high energy efficiency in the network. Mobile edge computing (MEC), as a viable solution, is deployed at the edge of the network. Nearby users offload some data to the edge server to relieve their own burdens and improve the system performance. However, relying solely on mobile edge computing to meet the deployment of IOT devices in the 6G network is limited. For example, when the channel is blocked or the channel condition is poor. Intelligent reflecting surface (IRS) is regarded as an emerging technology deployed in future networks, which can well solve this problem. It has the advantages of low cost, low power consumption, and easy deployment. By adjusting the amplitude or phase shift of the incident signal, it can improve the communication conditions between the transmitter and the receiver, that is, relieve the local computing pressure and achieve a faster transmission rate and lower energy consumption during wireless communication transmission.

[0003] At the same time, by adopting non-orthogonal multiple access (NOMA) technology, multiple tasks can be superimposed on one channel to simultaneously transmit data, and the data is decoded by SIC, further improving the spectrum utilization rate and energy efficiency. However, when the channel conditions and data volumes of users are different, it is difficult to ensure that users offload data to the base station simultaneously. The hybrid NOMA transmission method can solve this problem. Among them, hybrid NOMA means that multiple users start using the NOMA transmission method. Since some users cannot complete data transmission during NOMA, a separate time block is used for data transmission. For example, J. Zhu et al. studied the multi-user MEC scenario of two users using hybrid NOMA transmission, and minimized the weighted sum of delay and energy consumption by optimizing time, power, and user grouping.

[0004] On the other hand, energy efficiency, as a key metric in the industrial field, is defined as the ratio of the total data volume to the consumed energy and can reveal the operating state of the system. In existing research work, the main focuses are on minimizing latency, minimizing energy consumption, and maximizing throughput, with less attention paid to energy efficiency. With the large-scale deployment of Internet of Things devices in future 6G networks, the industrial demand for green communication will be even higher, especially for the energy efficiency of the system. In this context, it is an inevitable trend to maximize the energy efficiency in an intelligent reflecting surface-assisted mobile edge computing system through resource allocation strategies. Summary of the Invention

[0005] (1) Technical Problems to be Solved

[0006] Aiming at the deficiencies of the prior art, the present invention provides a method for maximizing the energy efficiency in a hybrid NOMA-based IRS-assisted MEC system. By optimizing the transmission power, time, computing resources, and IRS phase shift, it provides an optimal resource allocation strategy for maximizing the energy efficiency of the system. The proposed method has a wide application range and excellent compatibility, and can flexibly allocate resources to meet users' requirements under different data volumes, different channel conditions, and different local user computing performances. At the same time, it provides a valuable solution for the practical deployment of intelligent reflecting surfaces.

[0007] (2) Technical Solutions

[0008] The present invention provides the following technical solutions:

[0009] A method for maximizing the energy efficiency in a hybrid NOMA-based IRS-assisted MEC system, comprising the following steps:

[0010] S1. Establish an IRS-assisted MEC system based on hybrid NOMA transmission. The system includes K single-antenna users, an intelligent reflecting surface, a single-antenna base station (BS), and an MEC server at the BS side. The K users with limited performance are divided into different sub-channels, and two users share a sub-channel. The two users in the same sub-channel adopt the hybrid NOMA transmission mode. With the assistance of the IRS, all users unload part or all of their data to the MEC server for computing within time T. max simultaneously.

[0011] S2. According to the transmission protocol and system model adopted in step S1, list the data volume corresponding to the local user computing and unloading within time T max and the corresponding total energy consumption.

[0012] S3. The energy efficiency is defined as the ratio of the amount of computed data to the total energy. To maximize the energy efficiency of users, it is necessary to constrain the total energy of each user, the minimum amount of computed data of the user, the maximum completion time of the system, and the phase shift of the IRS, and jointly optimize the local operation frequency, transmission power, transmission time in different stages, and IRS phase shift.

[0013] S4. The problem described in step S3 is a non-convex fractional problem, and there is a coupling relationship between variables. According to the Dinkelbach iterative algorithm of the generalized fractional programming theory, the fractional programming problem is converted into a form that is easy to solve, and the converted problem is decomposed into two equivalent sub-problems, namely maximizing the user channel gain and maximizing the energy efficiency of the user.

[0014] S5. For the two sub-problems described in S4, first analyze and derive the closed-form solution of the optimized phase shift of the IRS to obtain the maximum user channel gain. On this basis, introduce auxiliary variables for problem conversion, and combine the SCA method to convert the non-convex problem into a convex problem to obtain the optimized solution of the energy efficiency.

[0015] Preferably, in step S1, the set of two users in the same sub-channel is K = {m 1 , m 2}. Suppose the IRS has N reflecting meta-surfaces, each meta-surface consists of V adjacent units with the same reflection coefficient, and the IRS is passive, with an amplitude of 1 and a discrete phase shift. For any user k, where k ∈ K, the channel gains of user k-BS, user k-IRS, and IRS-BS are h d,k , h r,k and G respectively, where and Then the composite channel gain is g k = G H Φh r,k + h d,k , where is the diagonal reflection matrix of the IRS, and there is L represents the number of levels of the discrete phase shift of the IRS, and for the reflecting surface Δβ = 2π / L, there is θ n ∈ F = {0, Δβ,..., (L - 1)Δβ}, n = {1, 2, ··· N}. In the following description, the design in one sub-channel will be focused on, and such a design is also applicable to other sub-channels.

[0016] Preferably, in step S1, it is assumed that the local user always performs data operations within T max time, and part of the data is offloaded to the edge server in the same sub-channel using hybrid NOMA. Hybrid NOMA is divided into two transmission methods, and it is assumed that user m1 First, perform decoding. These two transmissions are as follows: ① User m 1 and User m 2 First, use NOMA to unload data to the MEC server simultaneously in the shared time block t no User m finishes unloading first, and then User m 1 uses a dedicated time block 2 to unload the remaining offloading data to the MEC server; ② User m and User m 1 First, use NOMA to unload data to the MEC server within t 2 simultaneously. User m no finishes unloading the data first, and then User m 2 uses a dedicated time block 1 to transmit the remaining offloading data to the MEC server. Preferably, in step S2, for user k, the amount of data and energy for local operation within time T

[0017] are L max = T loc,k = T max f k / C k , where f k represents the operation frequency of user k during local operation, and C k represents the number of cycles required for the central processing unit of user k to process 1 bit of data. ε k is the effective capacitance coefficient of the processor chip at user k; during the unloading process in the shared time block t no the amounts of data of user m 1 and m 2 are respectively:

[0018]

[0019]

[0020] where p k,no and g k,no respectively represent the transmission power and channel gain of user k in the shared time block, σ 2 represents the noise power, and B represents the channel bandwidth; in the individual time block, the amount of data transmitted by user k is:

[0021]

[0022] where p k,s and gk,s Denote the transmission power and channel gain of user k in a separate time block; the energy consumed by user k to transmit data during the transmission is

[0023] E k,up = t k,s (p k,s + p k,c ) + t no (p k,no + p k,c ) (4)

[0024] p k,c Denote the constant loop power consumption of user k during the transmission; according to the above description, two transmission modes can be achieved by controlling the user's transmission power, that is, ① ② When the transmission power is 0, it indicates that the offloading process does not exist, that is, the corresponding time block is also 0.

[0025] Preferably, in step S3, for the time block t = {t k,s , t no}, the transmission power local operation frequency f k and the discrete phase shift matrix of the intelligent reflecting surface are optimized, where K = {m 1 , m 2}; the specific problem is modeled as:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Among them, C1 and C2 are the user time constraints of the resource block, C3 is the user energy constraint, C4 represents the constraint of the local operation frequency of user K, C5 means that the calculation amount of each user should be greater than or equal to the minimum calculation data amount, and C6 is the constraint of the phase shift of the intelligent reflecting surface.

[0034] Preferably, in step S4, let r k,s = |g k,s |2 / σ 2 and r k,no = |g k,no | 2 / σ 2 where First, according to the Dinkelbach algorithm in the fractional programming theory, the problem is transformed into a form that is easy to solve, that is Since the transformed problem is non-convex and there are coupling relationships between variables; for the convenience of solving, the discrete phase shift of the IRS and other variables can be decomposed into two equivalent sub-problems to solve, that is

[0035]

[0036]

[0037]

[0038] 5a - 5e (7).

[0039] Preferably, in the step S5, the variables corresponding to the problem P2 are discrete. For the convenience of solving, the constraint conditions are continuously processed, that is, let θ k,n ∈[0, 2π], and finally the obtained value is discretized, specifically as follows:

[0040]

[0041]

[0042] where θ k,n ∈[0, 2π] means that the phase of the k-th user in the n-th group of the intelligent reflecting surface is between [0, 2π]; here, the form of |g k | is transformed

[0043]

[0044] where |α k,n | = 1; at this time, the triangle inequality is used:

[0045]

[0046] where is the element of the n-th group Because |α k,n | = 1 makes this equation hold; therefore, the upper bound of the phase shift can be obtained as:

[0047]

[0048] This value is for the individual time block tk,s The optimal value of the internal phase shift. Next, it is necessary to balance the channel gains of the two users to obtain the shared time block t no of the optimal phase shift. From the above We can obtain and Here, let

[0049]

[0050] Here may not satisfy the unit modulus value, and it is necessary to find a unit modulus vector closest to it, which can be expressed by the following formula

[0051]

[0052] Since 0 ≤ v ≤ 1, so let Quantize each phase to its nearest point, making θ n ∈ F, we can obtain

[0053]

[0054] Using to find Φ [v] , and further find the channel gains corresponding to the users; then, introduce the auxiliary variable E k,s = p k,s t k,s , E k,no = p k,no t no , and substitute them into problem P2, we can obtain the modeling:

[0055]

[0056]

[0057]

[0058]

[0059] 8a~8b,8d (15d)

[0060] Define the variable Since the expression of (15b) is still a non-convex constraint, so next let

[0061]

[0062] where

[0063]

[0064]

[0065] Preferably, in step S5, in combination with the SCA method, first use the first-order Taylor expansion to obtain the upper bound expressed as This expansion is Then define the subspace here In the following description, k = m 2 Always holds; let the m-th iteration of the given local point be Therefore, at the given local point

[0066]

[0067] where

[0068]

[0069]

[0070]

[0071] Therefore

[0072]

[0073] Equivalent to The lower bound of, making its minimum value greater than or equal to Then, the problem can be modeled and expressed as

[0074]

[0075]

[0076] 8a~8b,8d,19a,19c (24b)

[0077] According to P6, the optimal solution can be solved.

[0078] (III) Beneficial effects

[0079] Compared with the prior art, the method for maximizing the energy efficiency in the hybrid NOMA IRS-assisted MEC system provided by the present invention has the following beneficial effects:

[0080] 1. The method for maximizing the energy efficiency in the hybrid NOMA IRS-assisted MEC system provides an optimal resource allocation strategy for realizing the maximization of the system's energy efficiency by optimizing the transmission power, time, computing resources, and IRS phase shift.

[0081] 2. Method for maximizing energy efficiency in the IRS-assisted MEC system with hybrid NOMA. The proposed method has a wide range of applications and excellent compatibility, and can meet the needs of users with different data volumes, different channel conditions, and different local user computing performances, and flexibly allocate resources. At the same time, it provides a valuable solution for the actual deployment of intelligent reflecting surfaces. Description of the Drawings

[0082] Figure 1 Schematic diagram of the principle and composition structure of the IRS-assisted MEC system for NOMA transmission in the embodiments of the present invention;

[0083] Figure 2 Protocol diagram of the method for maximizing energy efficiency in the embodiments of the present invention;

[0084] Figure 3 Iterative convergence diagram of the optimization method for maximizing energy efficiency in the embodiments of the present invention;

[0085] Figure 4 Experimental simulation diagram of energy efficiency when the maximum completion time is reached in the embodiments of the present invention;

[0086] Fig. 5(a) is an experimental simulation diagram of energy efficiency when the number of IRS units changes in the embodiments of the present invention;

[0087] Fig. 5(b) is an experimental simulation diagram of throughput when the number of IRS units changes in the embodiments of the present invention. Detailed Embodiments

[0088] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0089] Embodiment 1:

[0090] Please refer to Figure 1 -5, the method for maximizing energy efficiency in the IRS-assisted MEC system with hybrid NOMA provided by the embodiments of the present invention includes the following steps:

[0091] S1. Establish an IRS-assisted MEC system based on hybrid NOMA transmission. The system includes K single-antenna users, an intelligent reflecting surface, a single-antenna base station (BS), and an MEC server at the BS side. The K users with limited performance are divided into different sub-channels, and two users share a sub-channel. The two users in the same sub-channel adopt the hybrid NOMA transmission method. With the assistance of the IRS, all users are at Tmax Meanwhile, part or all of the data is unloaded to the MEC server for operation.

[0092] The set of two users on the same subchannel is K = {m 1 , m 2}. Suppose the IRS has N reflecting metasurfaces, each of which consists of V adjacent units with the same reflection coefficient, and the IRS is passive, with an amplitude of 1 and discrete phase shifts. For any user k, where k ∈ K, the channel gains of user k-BS, user k-IRS, and IRS-BS are h d,k , h r,k and G, respectively, where and Then the composite channel gain is g k = G H Φh r,k + h d,k , where is the IRS diagonal reflection matrix, and there is L represents the number of levels of the discrete phase shift of the IRS. For the reflecting surface, Δβ = 2π / L, and θ n ∈ F = {0, Δβ,..., (L - 1)Δβ}, n = {1, 2, ··· N}. In the following description, the design in one subchannel will be focused on.

[0093] Suppose the local user always performs data operations within T max time. Part of the data is unloaded to the edge server using hybrid NOMA on the same subchannel. Hybrid NOMA is divided into two transmission modes, and it is assumed that user m 1 decodes first. These two transmissions are as follows: ① User m 1 and user m 2 first use NOMA to unload data to the MEC server simultaneously in the shared time block t no . User m 1 finishes unloading first, and then user m 2 uses the dedicated time block to unload the remaining data to the MEC server; ② User m 1 and user m 2 first use NOMA to unload data to the MEC server within t no . User m 2 finishes unloading the data first, and then user m 1 uses the dedicated time block to transmit the remaining unloaded data to the MEC server.

[0094] S2. List the amount of data corresponding to local user operations and offloading within time T, as well as the corresponding total energy consumption, according to the transmission protocol and system model adopted in step S1. max For user k, within time T, the amount of data and energy for local operations are

[0095] L max = T loc,k f max / C k where f k represents the operation frequency of user k during local operations, C represents the number of cycles required for the central processing unit of user k to process 1 bit of data, and ε k is the effective capacitance coefficient of the processor chip at user k; during the sharing time block t k the amounts of data for user m k and m no during the offloading process are respectively: 1 2 k,no where p

[0096]

[0097]

[0098] and g k,no respectively represent the transmission power and channel gain of user k during the sharing time block, k,no σ represents the noise power, and B represents the channel bandwidth; during the individual time block, the amount of data transmitted by user k is: 2

[0099]

[0100] where p k,s and g k,s represent the transmission power and channel gain of user k during the individual time block; during the transmission process, the energy consumed by user k to transmit data is

[0101] E k,up = t k,s k,s (p k,s + p k,c ) + t no (p k,no + p k,c ) (4)

[0102] p k,c represents the constant loop power consumption of user k during the transmission process; according to the above description, by controlling the user transmission power, two transmission methods can be achieved, namely ① ② When the transmission power is 0, it indicates that the offloading process does not exist, that is, the corresponding time block is also 0.

[0103] S3. The energy efficiency is defined as the ratio of the amount of computed data to the total energy. To maximize the energy efficiency of users, it is necessary to constrain the total energy of each user, the minimum amount of computed data of the user, the maximum completion time of the system, and the phase shift of the IRS, and jointly optimize the local computing frequency, transmission power, transmission time in different stages, and IRS phase shift.

[0104] For the time block t = {t k,s , t no}, the transmission power the local computing frequency f k and the discrete phase shift matrix of the intelligent reflecting surface are optimized, where K = {m 1 , m 2}; the specific problem is modeled as:

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112] Among them, C1 and C2 are the user time constraints of the resource block, C3 is the constraint of the user energy, C4 represents the constraint of the local computing frequency of user K, C5 means that the computing amount of each user should be greater than or equal to the minimum amount of computed data, and C6 is the constraint of the phase shift of the intelligent reflecting surface.

[0113] S4. The problem described in step S3 is a non-convex fractional problem, and there are coupling relationships between variables. According to the Dinkelbach iterative algorithm of the generalized fractional programming theory, the fractional programming problem is converted into a form that is easy to solve, and the converted problem is decomposed into two equivalent sub-problems, that is, maximizing the user channel gain and maximizing the user's energy efficiency.

[0114] Let r k,s = |g k,s | 2 / σ 2 and r k,no = |gk,no | 2 / σ 2 , where First, according to the Dinkelbach algorithm in fractional programming theory, the problem is transformed into a form that is easy to solve, that is Since the transformed problem is non-convex and there are coupling relationships between variables; to facilitate the solution, the discrete phase shift of the IRS and other variables can be decomposed into two equivalent sub-problems for solution, that is

[0115]

[0116]

[0117]

[0118] 5a - 5e (7).

[0119] S5. For the two sub-problems described in S4, first analyze and deduce the closed-form solution of the optimized phase shift of the IRS to obtain the maximum user channel gain. On this basis, introduce auxiliary variables for problem transformation, and combine the SCA method to transform the non-convex problem into a convex problem to obtain the optimized solution of energy efficiency.

[0120] The variables corresponding to problem P2 are discrete. To facilitate the solution, the constraint conditions are continuousized, that is, let θ k,n ∈[0, 2π], and finally discretize the obtained value, specifically as follows:[[]]

[0121]

[0122]

[0123] where θ k,n ∈[0, 2π] means that the nth group of phases of user k on the intelligent reflecting surface is between [0, 2π]; here, transform the form of |g k |

[0124]

[0125] where |α k,n | = 1; at this time, use the triangle inequality:[[]]

[0126]

[0127] where is the element of the nth group Because |α k,n | = 1 makes this equation hold; therefore, the upper bound of the phase shift can be obtained as:[[]]

[0128]

[0129] This value is for the individual time block t k,s the optimal value of the inner phase shift. Next, it is necessary to balance the channel gains of the two users to obtain the shared time block t no the optimal phase shift. From the above We can obtain and Here, set

[0130]

[0131] Here it may not satisfy the unit modulus value, and it is necessary to find a vector with the nearest unit modulus value, which can be expressed by the following formula

[0132]

[0133] Since 0 ≤ v ≤ 1, so let Quantize each phase to its nearest point, making θ n ∈ F, we can obtain

[0134]

[0135] Using to find Φ [v] , and further find the channel gains corresponding to the users; then, introduce the auxiliary variable E k,s = p k,s t k,s , E k,no = p k,no t no , and substitute them into problem P2, we can obtain the modeling:

[0136]

[0137]

[0138]

[0139]

[0140] 8a~8b,8d (15d)

[0141] Define the variable Since the expression of (15b) is still a non-convex constraint, so next let

[0142]

[0143] Among them

[0144]

[0145]

[0146] Combined with the SCA method, first use the first-order Taylor expansion to obtain and represent The expansion is The upper bound of; then define the subspace here In the following description, k = m 2 Always holds; let the m-th iteration of the given local point be Therefore, at the given local point

[0147]

[0148] Among them

[0149]

[0150]

[0151]

[0152] Therefore

[0153]

[0154] Is equivalent to The lower bound of, making its minimum value greater than or equal to Thus, the problem can be modeled and represented as

[0155]

[0156]

[0157] 8a~8b,8d,19a,19c (24b)

[0158] According to P6, the optimal solution can be solved.

[0159] Embodiment 2:

[0160] Please refer to Figure 1 -5, the present invention provides a technical solution: a method for maximizing the energy efficiency in a hybrid NOMA IRS-assisted MEC system, including the following steps:

[0161] S1, System model

[0162] Among them, the system includes K single-antenna users, an intelligent reflecting surface, a single-antenna base station (BS), and an MEC server at the BS side. The server has no power constraint and is connected to the power grid, so the energy and time consumption during the operation can be ignored; the IRS has N reflecting metasurfaces, and each metasurface consists of V adjacent units with the same reflection coefficient. It is assumed that the IRS is passive, with an amplitude of 1 and discrete phase shifts. The K users with limited performance are divided into different subchannels, and two users share one subchannel. The two users in the same subchannel adopt the hybrid NOMA transmission mode. With the assistance of the IRS, all users unload some or all of their data to the MEC server for operation simultaneously within T max In the following description, the design in one subchannel will be focused on, and such a design is also applicable to other subchannels.

[0163] It is assumed that the BS can obtain perfect channel state information and user information. For user k, where the channel gains of user k-BS, user k-IRS, and IRS-BS are h d,k , h r,k and G respectively, where and then the composite channel gain is g k =G H Φh r,k +h d,k , is the diagonal reflection matrix of the IRS, L represents the number of levels of the discrete phase shift of the IRS. For the reflecting surface, Δβ = 2π / L, and there is θ n ∈F = {0, Δβ,..., (L - 1)Δβ}, n = {1, 2, ··· N}.

[0164] S2. Communication protocol

[0165] In the protocol of the present invention, it is assumed that the downlink transmission process is ignored, and the energy and time consumption during the decoding process are ignored. It is also assumed that the local operation is always performing data operations within T max time. As Figure 2 is the hybrid NOMA protocol diagram of the present invention. In both transmission modes, it is assumed that user m 1 decodes first. Therefore, the descriptions of these two transmission modes are as follows.

[0166] ① User m 1 and user m 2 first use NOMA to unload data to the MEC server simultaneously within the shared time block t no . During this process, user m 1The data unloading is completed, and then user m 2 utilizes a separate time block to transmit the remaining unloaded data to the MEC server.

[0167] ② User m 1 and user m 2 first use NOMA to unload data to the MEC server simultaneously within the shared time block t no . During this process, the data unloading of user m 2 is completed, and then user m 1 utilizes a unique time block to transmit the remaining unloaded data to the MEC server.

[0168] S3. Unloading and computing model

[0169] Within the shared time block t no , the two users use NOMA to upload data simultaneously. Assume that m 1 decodes the unloaded data first. Therefore, the signal of user m 2 acts as interference to user m 1 . The data volumes of user m 1 and user m 2 are respectively expressed as

[0170]

[0171]

[0172] where and respectively represent the transmission powers of user m 1 and user m 2 in the shared time block, σ 2 represents the noise power, and B represents the channel bandwidth. In the separate time block, the data volume transmitted by user k is

[0173]

[0174] where p k,s represents the transmission power of user k in the separate time block. During the transmission process, the energy consumed by user k to transmit data is

[0175] E k,up = t k,s (p k,s + p k,c ) + t no (p k,no + p k,c ) (4)

[0176] pk,c Respectively, it is expressed as the constant loop power consumption of user k during transmission. At T max Within, the amount of data computed by the local user is

[0177]

[0178] where f k represents the computing frequency of user k during local computing, and C k represents the number of cycles required by the central processing unit for user k to compute 1 bit of data; during the computing process, the energy consumed by user k is

[0179]

[0180] where ε k represents the effective capacitance coefficient of the processor chip of user k. According to the protocol, by controlling the transmission power of the user, two transmission modes can be obtained, namely ① ② When the transmission power of the corresponding time block is 0, it indicates that the offloading process does not exist, that is, the corresponding time block is also 0.

[0181] S4. Problem Modeling

[0182] In the present invention, to maximize the energy efficiency of the user, the energy efficiency is expressed as:

[0183]

[0184] Therefore, the initial optimization problem is expressed as:

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192] where C1 and C2 are the user time constraints on the resource block, C3 is the energy constraint on the user, C4 represents the constraint on the local computing frequency of user K, C5 represents that the local computing and data offloading volume of each user should be greater than or equal to the required minimum computing data volume; C6 is the constraint on the discrete phase shift of the intelligent reflecting surface in the uplink.

[0193] S5, Problem Solving and Algorithms

[0194] Initial problem P 0 is a fractional programming problem and contains discrete variables, so it is a non-convex problem, that is, an NP-hard problem, and the problem needs to be further transformed. First, use the Dinkelbach method to transform the fractional programming problem into the form of the product of the numerator minus the denominator and the coefficient. Secondly, derive the closed-form solution of IRS. Then, introduce auxiliary variables for a series of transformations. Finally, combine the SCA method to transform the non-convex problem into a convex problem and obtain the optimal solution.

[0195] Specifically, here let Use the Dinkelbach algorithm to transform the objective function Since there is a coupling relationship between the transmission power, IRS phase shift and transmission time block, constraints C3, C5, C6 and the transformed objective function are non-convex. Therefore, the initial problem is decomposed into two sub-problems for solution

[0196]

[0197]

[0198] s.t.8a - 8e (11)

[0199] The variables corresponding to problem P2 are discrete, so the constraint conditions of the problem need to be continuousized. That is, let θ k,n ∈[0, 2π] represents that the phase of the k-th user in the n-th group of the intelligent reflecting surface is between [0, 2π]. That is, the corresponding problem is modeled as

[0200]

[0201]

[0202] Here, transform the form of |g k |

[0203]

[0204] where |α k,n | = 1. At this time, using the triangle inequality, we have:

[0205]

[0206] where is the element of the n-th group Because |α k,n | = 1 makes equation (14) hold. Therefore, the upper bound of the phase shift can be obtained as:

[0207]

[0208] This value is for the individual time block t k,s The optimal value of the inner phase shift. Next, it is necessary to balance the channel gains of the two users to obtain the shared time block t no The optimal phase shift within. From the above It can be obtained and Here, let

[0209]

[0210] Here It may not satisfy the unit modulus value. Therefore, it is necessary to find a unit modulus vector closest to it, which can be expressed by the following formula

[0211]

[0212] Since 0 ≤ v ≤ 1, let Make Quantize Each phase of to its closest point, making θ n ∈ F. Therefore, obtain

[0213]

[0214] Furthermore, utilize To find Φ [v] , and then the channel gain corresponding to user k can be found. After finding the IRS phase shift, the transmission power is only coupled with the time slot. Therefore, an auxiliary variable E k,s = p k,s t k,s , E k,no = p k,no t no , And substitute it into problem P3 to obtain the problem formulation:

[0215]

[0216]

[0217]

[0218]

[0219] 8a~8b,8d (19f)

[0220] Among them, the variable For (19c), it is still a non-convex constraint. Therefore, in the next step, let

[0221]

[0222]

[0223]

[0224] Combined with the SCA method, first use the first-order Taylor expansion to obtain The expansion is the upper bound of; here define the subspace In the following description, k = m 2 always holds; and as the m-th iteration of the given local point. Therefore, at the given local point

[0225]

[0226] where

[0227]

[0228]

[0229]

[0230] Therefore

[0231]

[0232] is equivalent to the lower bound of, making its minimum value greater than or equal to Thus, the problem can be modeled as

[0233]

[0234]

[0235] 8a~8b,8d,19a,19d(28b)

[0236] Since problem P6 is a convex problem, the corresponding optimal solution can be obtained. The algorithm steps of the present invention are described as follows

[0237] Algorithm 1: Two-step iterative optimization algorithm based on Dinkelbach-SCA (P6)

[0238] 1. Set the maximum tolerance error ε > 0, the maximum number of iterations M, and

[0239] 2. Initialization t no [m] n , where m represents the number of iterations, m = 0, n represents the transmission mode, n = {Mode 1, Mode 2}.

[0240] 3. Obtain the IRS phase shift matrix Optimal solution.

[0241] 4. for m = 1:M

[0242] Given case, use cvx to solve problem P6 and obtain Optimal solution, and obtain the energy efficiency according to the optimization variables

[0243] If abs

[0244] Obtain the maximum energy efficiency of transmission n in problem P6

[0245] else

[0246] Update

[0247] end

[0248] end

[0249] 5. if

[0250] Obtain the maximum energy efficiency

[0251] else

[0252] Obtain the maximum energy efficiency

[0253] End.

[0254] Next, the performance of the present invention is verified through experimental simulation. Set the intelligent reflecting surface N = 5, and each reflecting surface has V = 20 elements. We consider a 2D coordinate setting, where the coordinates of the base station BS are (40,0), the coordinates of the intelligent reflecting surface are (0,4), and for the user positions, two settings are considered. The first setting: the coordinates of user 1 are (0,0), and the coordinates of user 2 are (-15,0), at this time the IRS and the users are asymmetrically deployed; the second setting: the coordinates of user 1 are (10,0), and the coordinates of user 2 are (-10,0), at this time the IRS and the users are symmetrically deployed. Under such settings, the large-scale fading is set to -30dBm per meter, and the path loss exponents of the IRS-user, IRS-BS, and user-BS channels are 2.5, 2.5, and 3.2 respectively, and the channels for the corresponding small-scale fading are Rayleigh fading. Other parameters are shown in the following table.

[0255]

[0256] Figure 3 The figure shows the iterative convergence graph of the proposed hybrid NOMA and TDMA with the same minimum amount of computation offloading data for two users. The simulation graph of this figure is based on the asymmetric deployment of the IRS and the users, and the two users have the same amount of computation data. The figure verifies the convergence of the iterative optimization algorithm we proposed. At the same time, the hybrid NOMA scheme is better than the TDMA scheme in terms of energy efficiency. Along with the increase of the same minimum amount of computation offloading data for the two users, the energy efficiency of the proposed hybrid NOMA scheme and TDMA scheme gradually decreases, because when the amount of data that the users require to process increases, the growth rate of energy consumption is faster than the growth rate of the data volume.

[0257] As Figure 4 , considering the symmetric deployment of the IRS and the users, the two users have the same minimum amount of computation data. It can be seen from the figure that as the maximum completion time increases, the energy efficiency of each scheme is continuously increasing, because when the maximum completion time increases, less energy is consumed to meet the computing requirements. The scheme with IRS assistance is significantly better than the scheme without IRS assistance in terms of energy efficiency, further verifying that the IRS can significantly improve the system performance. And compared with other schemes, the proposed scheme can achieve the maximum energy efficiency, but compared with the TDMA optimization solution scheme, the performance gap is not large, because with IRS assistance, the channel conditions of the system can be greatly improved, and combined with the adoption of NOMA transmission, the spectrum and energy efficiency can be greatly improved. However, compared with the continuous phase shift of the IRS, in order to save the cost of the IRS, optimizing the discrete phase shift of the IRS causes partial loss of performance.

[0258] Figure 5 considers the asymmetric deployment of the IRS and the users, where the two users have the same minimum amount of computing data. The figures depict the variations in the corresponding energy efficiency and throughput of each scheme with the change in the number of IRS elements. As can be seen from Figures 5(a) and (b), as the number of IRS elements increases, the energy efficiency and throughput of each scheme gradually increase. Because when the number of IRS elements is increasing, more signals will offload data in the IRS-related channels, enabling a large amount of data to be computed within the maximum completion time while consuming less energy. In Figure 5(a), the scheme optimized with the maximum computing energy efficiency as the objective has a higher energy efficiency than the scheme optimized with the throughput as the objective. However, as can be seen from Figure 5(b), the throughput situation is the opposite. Therefore, it can be seen that there are differences in the resource allocation strategies for maximizing throughput and maximizing energy efficiency. Combining Figures 5(a) and (b), it can be known that during the process of increasing the number of IRS units, the scheme optimized with the computing energy efficiency as the objective has a more obvious growth rate, and the hybrid NOMA scheme is better than the TDMA scheme. In the case of optimizing with the throughput as the objective, although the throughput of the hybrid NOMA is much more than that of the TDMA scheme, its corresponding computing energy efficiency is slightly less than that of the TDMA.

[0259] The method for maximizing the energy efficiency in the IRS-assisted MEC system with hybrid NOMA provided by the above embodiments of the present invention provides an optimal resource allocation strategy for achieving the maximum energy efficiency of the system through the optimization of transmission power, time, computing resources, and IRS phase shift; the proposed method has a wide application range and excellent compatibility, and can flexibly allocate resources to meet the users' different data volumes, different channel conditions, and different local user computing performances; at the same time, it provides a valuable solution for the actual deployment of intelligent reflecting surfaces.

[0260] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for maximizing energy efficiency in a hybrid NOMA IRS-assisted MEC system, characterized in that, it includes the following steps: S1. Establish an IRS-assisted MEC system based on hybrid NOMA transmission. The system includes K single-antenna users, an intelligent reflecting surface, a single-antenna base station BS, and an MEC server at the BS side. The K users with limited performance are divided into different sub-channels, and two users share one sub-channel. The two users in the same sub-channel adopt the hybrid NOMA transmission mode. With the assistance of the IRS, all users unload some or all of their data to the MEC server for computing within T max simultaneously; S2. List the amount of data corresponding to the local user's operations and offloading within time T, as well as the corresponding total energy consumption, according to the transmission protocol and system model adopted in step S1 max ; In the step S2, for user k, the amount of data and energy locally computed within time T max is L k,loc = T max f k / C k , where f k represents the computing frequency of user k during local computing, C k represents the number of cycles required for the central processing unit to compute 1 bit of data for user k, and ε k is the effective capacitance coefficient of the processor chip at user k; during the offloading process in the shared time block t no , the amounts of data of users m 1 and m 2 are respectively: where p k,no and g k,no represent the transmission power and channel gain of user k in the shared time block respectively, σ 2 represents the noise power, and B represents the channel bandwidth; in a separate time block, the amount of data transmitted by user k is: where p k,s and g k,s represent the transmission power and channel gain of user k in a separate time block; the energy consumed by user k to transmit data during the transmission is E k,up = t k,s (p k,s + p k,c ) + t no (p k,no + p k,c ) (4) p k,c It represents the constant loop power consumption of user k during transmission; according to the above description, two transmission modes can be achieved by controlling the user transmission power, namely ① ② When the transmission power is 0, it indicates that the offloading process does not exist, that is, the corresponding time block is also 0; S3. The energy efficiency is defined as the ratio of the amount of computed data to the total energy. To maximize the energy efficiency of users, it is necessary to constrain the total energy of each user, the minimum amount of computed data of the user, the maximum completion time of the system, and the phase shift of the IRS, and jointly optimize the local computing frequency, transmission power, transmission time in different stages, and IRS phase shift; In the said step S3, for the time block t = {t k,s , t no}, the transmission power local operation frequency f k and the discrete phase shift matrix of the intelligent reflecting surface are optimized, where K = {m 1 , m 2}; The specific problem is modeled as: where C1 and C2 are the user time constraints of the resource block, C3 is the constraint of the user energy, C4 represents the constraint of the local computing frequency of user K, C5 means that the computed amount of each user should be greater than or equal to the minimum amount of computed data, and C6 is the constraint of the phase shift of the intelligent reflecting surface; S4. The problem described in step S3 is a non-convex fractional problem, and there is a coupling relationship between variables. According to the Dinkelbach iterative algorithm of the generalized fractional programming theory, the fractional programming problem is converted into a form that is easy to solve, and the converted problem is decomposed into two equivalent sub-problems, namely maximizing the user channel gain and maximizing the energy efficiency of the user; In step S4, let r k,s = |g k,s | 2 / σ 2 and r k,no = |g k,no | 2 / σ 2 , where First, according to the Dinkelbach algorithm in fractional programming theory, the problem is transformed into a form that is easy to solve, that is Since the transformed problem is non-convex and there are coupling relationships between variables; for the convenience of solving, the discrete phase shift of the IRS and other variables can be decomposed into two equivalent sub-problems for solution, that is 5a - 5e(7); S5. For the two sub-problems described in S4, first analyze and derive the closed-form solution of the optimized phase shift of the IRS to obtain the maximum user channel gain. On this basis, introduce auxiliary variables for problem transformation, and combine the SCA method to convert the non-convex problem into a convex problem to obtain the optimized solution of the energy efficiency; In the step S5, the variable corresponding to the problem P2 is discrete. For the convenience of solution, the constraint conditions are continuously processed, that is, let θ k,n ∈[0, 2π], and finally the obtained value is discretized, specifically as follows: where θ k,n ∈ [0, 2π] indicates that the phase of the nth group of the IRS for user k is between [0, 2π]; here, transform the form of |g k | wherein |α k,n | = 1; At this time, using the triangle inequality: wherein is an element of the n-th group because |α k,n | = 1 makes this equation hold; therefore, the upper bound of the phase shift can be obtained as: This value is for the individual time block tk ,s The optimal value of the inner phase shift. Next, it is necessary to balance the channel gains of the two users to obtain the shared time block t no The best phase shift. From the above We can obtain and Set here Here It may not satisfy the unit modulus value. It is necessary to find a unit modulus vector closest to it, which can be expressed by the following formula Since 0 ≤ v ≤ 1, let quantize each phase to its nearest point, so that θ n ∈ F, we can obtain Utilize to obtain Φ [v] , and further obtain the channel gain corresponding to the user; then, introduce an auxiliary variable E k,s = p k,s t k,s , E k,no = p k,no t no , and substitute them into problem P2, and a model can be obtained: 8a~8b,8d(15d) Define variables Since the expression in (15b) is still a non-convex constraint, we then let where 2. The method for maximizing energy efficiency in a hybrid NOMA IRS-assisted MEC system according to claim 1, characterized in that, In the step S1, the set of two users on the same subchannel is K = {m 1 , m 2}. Suppose the IRS has N reflecting metasurfaces, each of which consists of V adjacent cells with the same reflection coefficient, and the IRS is passive, with an amplitude of 1 and discrete phase shifts. For any user k, where k ∈ K, the channel gains of user k-BS, user k-IRS, and IRS-BS are h d,k , h r,k and G, respectively, where and Then the composite channel gain is g k = G H Φh r,k + h d,k , where is the diagonal reflection matrix of the IRS, and L represents the number of levels of the discrete phase shift of the IRS. For the reflecting surface, Δβ = 2π / L, and θ n ∈ F = {0, Δβ,..., (L - 1)Δβ}, n = {1, 2, ··· N}. In the subsequent description, the design in one subchannel will be focused on, and such a design is also applicable to other subchannels.

3. The method for maximizing energy efficiency in a hybrid NOMA IRS-assisted MEC system according to claim 1, characterized in that, In the step S1, it is assumed that the local user always performs data operations within time T max and some data are offloaded to the edge server on the same sub-channel using hybrid NOMA. Hybrid NOMA is divided into two transmission modes, and it is assumed that user m 1 decodes first. These two transmissions are respectively: ① User m 1 and user m 2 first offload data to the MEC server using NOMA in the shared time block t no first. After user m 1 has finished offloading, then user m 2 uses a dedicated time block to offload the remaining offloading data to the MEC server; ② User m 1 and user m 2 first offload data to the MEC server using NOMA within t no first. After the data of user m 2 has been offloaded, then user m 1 uses a dedicated time block to transmit the remaining offloading data to the MEC server.

4. The method for maximizing energy efficiency in a hybrid NOMA IRS-assisted MEC system according to claim 1, characterized in that, In step S5, in combination with the SCA method, first use the first-order Taylor expansion to obtain an upper bound of ; then define a subspace here. In the following description, k = m 2 always holds; let the m-th iteration of the given local point be . Therefore, at the given local point This expansion is the upper bound of; then define a subspace In the following description, k = m 2 always holds; let the m-th iteration of the given local point be Therefore, at the given local point where therefore corresponding to the lower bound of, such that its minimum value is greater than or equal to Therefore, the problem can be modeled as 8a~8b,8d,19a,19c (24b) The optimized solution can be obtained according to P6.

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