Wireless power supply mobile edge calculation optimization algorithm based on UC and NOMA assistance in nonlinear EH mode

Abstract

The invention provides a wireless power supply mobile edge computing (WPT)-MEC (wireless power supply mobile edge computing) optimization algorithm assisted by a user cooperation (UC) and a non-orthogonal multiple access technology (NOMA) in a non-linear energy harvesting (EH) mode, the transmission power, the user unloading time and the user unloading power among different energy beams of the HAP are jointly optimized, the energy and the computing resources are fully utilized, the energy utilization rate of the HAP is improved, and the energy utilization rate of the HAP is improved. According to the method, the system weight sum calculation rate (WSCR) is maximized, and the system weight sum calculation rate (WSCR) is maximized. The model is non-convex, so that a formulation problem is difficult to solve. In order to solve the problem, an iterative optimization algorithm based on successive convex approximation (SCA) is provided, firstly, a variable substitution method is utilized to re-express a non-convex optimization problem, the non-convex optimization problem is converted into a form which is easier to process, and then the SCA is utilized to solve the non-convex optimization problem. A numerical result shows that compared with a reference scheme, the scheme provided by the invention can generate better system performance.

Description

Technical Field

[0001] The present invention relates to a computational offloading method in a nonlinear energy harvesting (EH) mode in the field of Wireless Powered Transmission Mobile Edge Computing (WPT-MEC), and proposes an iterative optimization algorithm based on a successive convex approximation (SCA) method to solve the problem. Background Art

[0002] In recent years, the Internet of Things (IoT) has been widely used in various fields such as public services, Internet of Vehicles, smart retail, and smart homes. However, with the increasing demand for computing resources and network bandwidth, this large-scale data collection and intensive computing processing have brought huge challenges to the existing IoT. Due to the limited processing performance and battery capacity of IoT devices, resource-constrained IoT devices cannot meet the execution of computing-intensive tasks. In order to address the above problems, it is proposed to offload computing tasks to the cloud with super computing power for processing. However, cloud servers are usually far away from mobile devices, and the high latency generated cannot meet the real-time requirements of devices. In contrast, the MEC server in Mobile Edge Computing (MEC) is closer to the device, and this conflict can be resolved by offloading computing resources to the vicinity of IoT devices, greatly improving the computing power of IoT devices and reducing computing latency.

[0003] Although MEC technology can significantly reduce computing latency and energy consumption, the limited battery capacity of mobile devices has become a bottleneck affecting network performance. Due to a series of problems such as battery energy and power density limitations, slow charging speed, poor reliability, large size and weight, the battery capacity of mobile devices cannot be infinitely expanded. To overcome this bottleneck, technologies such as renewable energy harvesting (EH) [8] and wireless power transfer (WPT) can be used. Compared with renewable EH (such as solar radiation and wind energy), WPT is usually powered by the grid. It can provide stable and reliable energy for mobile devices by sending radio frequency signals through power beacons (PB) or hybrid access points (HAP). Therefore, wireless powered mobile edge computing (WPT-MEC), which combines the two advanced technologies of WPT and MEC, will emerge as a new network paradigm. WPT-MEC can not only improve the computing power of mobile devices, but also alleviate the problem of energy shortage of mobile devices.

[0004] At present, there are quite a lot of studies on the joint application of WPT and MEC. For example, the paper "Zheng, X., et al., Intelligent computing for WPT-MEC-aided multi-source data stream. Eurasip Journal on Advances in Signal Processing, 2023.2023 (1)" studies an algorithm based on particle swarm optimization to jointly optimize charging and unloading strategies to minimize the delay of device processing computing data streams. The paper "Zhang, YZ, et al. Decentralized Computation Offloading over Wireless-Powered Mobile-Edge Computing Networks. in IEEE International Conference on Artificial Intelligence and Information Systems (ICAIIS). 2020. Dalian, PEOPLES RCHINA." studies decentralized computing offloading based on wireless mobile edge computing, constructs a decentralized game model based on multi-user scenarios, and obtains the optimal computing cost of the system through the proposed computing offloading game theory. The paper "Deng, X., et al., Wireless Powered Mobile Edge Computing: Dynamic Resource Allocation and Throughput Maximization. Ieee Transactions on Mobile Computing, 2022.21(6): p.2271-2288." studies a WPT-MEC system consisting of multiple base stations and multiple users. By jointly optimizing the allocation of communication, computing and energy resources, a dynamic throughput maximization algorithm based on Lyapunov optimization is proposed, and it is shown that the system throughput increases with the backlog of the queue.

[0005] In addition, non-orthogonal multiple access (NOMA) technology can schedule multiple terminals at the same time and share the same radio resources in time, space and spectrum, improving spectrum efficiency and user access. Therefore, combining MEC technology with NOMA technology can improve system performance more comprehensively. The authors of the document "Fang, F., et al., Optimal Resource Allocation for Delay Minimization in NOMA-MEC Networks. Ieee Transactions on Communications, 2020.68(12): p.7867-7881." combined NOMA technology with MEC technology, studied the problem of minimizing task delay in NOMA-MEC networks, and proposed a binary search iterative algorithm to achieve the minimum task delay. The authors of documents

[18] and

[19] both tried to apply NOMA and WPT technologies simultaneously in multi-user MEC systems, so that multiple users can simultaneously offload their computing tasks in the same frequency band. The paper "Shi, L., et al., Computation Energy Efficiency Maximization for a NOMA-Based WPT-MEC Network. Ieee Internet of Things Journal, 2021.8(13): p.10731-10744." studies the problem of maximizing the computational energy efficiency of a NOMA-based WPT-MEC network under a partial unloading scheme. For the non-convex fractional programming problem, an iterative algorithm based on Dingkelbach is proposed to solve the optimal resource allocation solution. The paper "Zhou, F. and RQ Hu, Computation Efficiency Maximization in Wireless-Powered Mobile Edge Computing Networks. Ieee Transactions on Wireless Communications, 2020.19(5): p.3170-3184." studied the problem of maximizing the system computing efficiency of WPT-MEC networks in two modes: partial offloading and binary offloading, and compared the two methods, Time Division Multiple Access (TDMA) technology and NOMA technology. The research results show that NOMA is superior to TDMA in computing efficiency.

[0006] However, in the NOMA-based multi-user WPT-MEC network scenario studied in the above literature, the dual near-far effect caused by the deployment of energy transmitters and MEC servers in HAP is not taken into account. This will lead to inequality in energy collection and computational offloading between users, and the performance of users far away from HAP cannot be guaranteed. Some studies have found that the purpose of solving the dual near-far effect can be achieved by using user cooperation (UC) to enable mobile devices to work together. The literature "He, B., et al. Collaborative Computation Offloading in Wireless Powered Mobile-Edge Computing Systems. in IEEE Global Communications Conference (IEEE GLOBECOM). 2019. Waikoloa, HI." studied the combination of UC and TDMA, considering the case where the direct communication link between a user and the base station is blocked, and collaborative communication is carried out through another user in the form of relay. The paper "Hu, X., K.-K. Wong, and K. Yang, Wireless Powered Cooperation-Assisted Mobile Edge Computing. Ieee Transactions on Wireless Communications, 2018.17(4): p.2375-2388." proposed a Harvest-The-Offload (HTT) protocol based on TDMA technology. Considering the situation where both users have computing tasks, UC is used to overcome the dual near-far effect and energy constraint problems. In order to maximize the effective computing efficiency, the paper "Wang, L., et al. Effective Computational Efficiency Maximization in Cooperative NOMA Based MEC System. in 14th IEEE International Conference on Wireless Communications and Signal Processing (WCSP). 2022. Nanjing, PEOPLES R CHINA." Considering the case of unloading interruption, NOMA and UC are introduced into the WPT-MEC network at the same time. The study first derives the power outage probability of the two users, and then jointly optimizes the unloading time and power allocation.

[0007] The above studies mainly focus on the linear energy collection model in the WPT stage, while the conversion efficiency of the actual EH receiver from RF to DC will be affected by the input power. When the input power exceeds a certain value, the output power will change nonlinearly with the input power. The literature "Jiang, R., et al., Power Minimization in SWIPT Networks With Coexisting Power-Splitting and Time-Switching Users Under Nonlinear EH Model. Ieee Internet of Things Journal, 2019.6(5): p.8853-8869." considers the reality and actual scenarios of nonlinear energy collection and studies the performance optimization in the SWIPT (Simultaneous Wireless Information and Power Transfer) network. By jointly optimizing the beamforming vector, power splitting (PS) ratio and time switching (TS) factor of the HAP, the required transmission power of the HAP is minimized. However, the system model in the above study does not consider computational offloading and cannot be applied to the WPT-MEC system. Therefore, it is necessary to further consider the WPT-MEC network system under the nonlinear EH model and study the power allocation problem between different beams of its multi-antenna energy transmitter (ET) and the system performance optimization problem. At the same time, how to establish its system model and obtain reasonable unloading decisions and resource allocation strategies is an urgent problem to be solved in the field of wireless power mobile edge computing. Summary of the invention

[0008] The present invention provides a WPT-MEC optimization algorithm based on NOMA and UC assistance under a nonlinear EH model. The HAP integrated with the MEC server charges the user device in an energy beamforming manner. The user device uses the collected energy for local calculations, and unloads part of the computing tasks to the MEC server for processing through UC and uplink NOMA technology. By jointly optimizing the transmission power, user unloading time and user unloading power between different energy beams of the HAP, energy and computing resources are fully utilized to maximize the system weighted and computing rate. The contributions of the present invention are as follows:

[0009] (1) This paper considers a more practical nonlinear energy harvesting model, and in order to overcome the dual near-far effect, NOMA and UC are simultaneously introduced into the WPT-MEC system. In the partial unloading mode, by jointly optimizing the transmission power between different energy beams of HAP, user unloading time and user unloading power, energy and computing resources are fully utilized to maximize the weighted and computing rate of all users.

[0010] (2) An iterative optimization algorithm based on SCA is proposed. First, the original non-convex problem is transformed into an easily tractable form through variable substitution. Then, SCA is used to solve the non-convex problems caused by the nonlinear EH model and NOMA technology respectively. Finally, the algorithm is iterated until convergence.

[0011] (3) The simulation results show that the algorithm can significantly improve the performance under different conditions (such as different distances between users and HAPs, different calculation frequencies of users, different transmission powers of HAPs, etc.). In addition, the algorithm proposed in this paper can provide more stable performance to adapt to changes in the operating environment.

[0012] The technical solution adopted by the present invention is: a wireless power supply mobile edge computing optimization algorithm based on user collaboration and NOMA assistance in a nonlinear EH mode, including the following system models:

[0013] A multi-user WPT-MEC system under a nonlinear energy harvesting model includes a multi-antenna hybrid access point HAP integrated with a MEC server and K user cooperative fogs, К={1,2,...,K}. Each cooperative fog is composed of single-antenna users working in half-duplex mode, and the distances between the two users and the HAP are different, namely, the far user (FU) and the near user (NU). In the kth cooperative fog, the distances between FU and HAP, NU and HAP, and FU and NU are defined as d f,a d n,a , and d f,n , and d n,a ≤d f,a , d f,n ≤d f,a. It is assumed that the HAP is powered by the grid, has a stable energy source, and uses energy beamforming based on RF signals to charge user devices. Each user device is equipped with an EH circuit, which can perform computational offloading with the collected energy. Assuming that the computing tasks of each user are independent and divisible, the user's computing tasks can be arbitrarily divided into two parts, one part is calculated locally at the user, and the other part is offloaded to the MEC server for execution through uplink NOMA. Among them, downlink WPT and local computing can be performed simultaneously, and downlink WPT and uplink computing offloading follow the HTT protocol. For the offloading of uplink computing, partial offloading based on NOMA is adopted, and the computing tasks of each user are divided into two parts, which are remotely calculated on the HAP and locally calculated at the user. Compared with complete offloading, partial offloading is suitable for complex tasks consisting of multiple parallel segments, which is more conducive to reducing latency.

[0014] A block-based TDMA scheme is adopted, with each block lasting T seconds, and it is assumed that each block experiences independent and identically distributed Rayleigh fading. The time allocation structure for the near and far users in the kth cooperative fog when performing computation offloading mainly consists of three stages, namely, the wireless power transmission stage, the computation offloading stage, and the computation result return stage. In order to take advantage of the UC while maintaining the NOMA advantage, the two time slots t1 and t2 are used for the NOMA uplink transmission supported by UC. In the t1 time slot, FU simultaneously offloads part of the computation tasks to HAP and NU through uplink NOMA. In the t2 time slot, part of the tasks of FU and NU are offloaded to HAP on the same time-frequency resource block through NOMA technology. Among them, part of NU's tasks include its own computation tasks and computation tasks that help FU forward the offload. Due to the powerful computing power of HAP and the small amount of computation results, the result calculation and return time t3 is generally ignored, that is, t3≈0. In order to complete the corresponding computation tasks in each time period, the total system time allocation constraint satisfies t0+t1+t2≤T.

[0015] In the time slot t0, the HAP with N antennas can provide stable unlimited energy transmission to 2K single-antenna users at the same time. is the transmit power of the corresponding beam. The HAP transmit power is subject to a fixed value The restriction of , produces the following energy constraint:

[0016]

[0017] In order to match the actual EH circuit on the user's wireless device, this paper adopts a nonlinear EH model based on the logistic function. Through the data fitting method, the output EH value of the user receiver in the kth cooperative fog is a function of the input radio frequency (RF) power. In the WPT phase of the t0 time slot, the wireless energy collected by each user in the cooperative fog can be defined as:

[0018]

[0019] in is the downlink channel power gain from HAP to the FU and NU of the kth cooperative fog, 0<μ<1 is the energy conversion efficiency of the user, In the nonlinear EH model, M represents the maximum energy harvested at the receiver when the EH circuit reaches saturation, a represents the nonlinear EH rate relative to the input power, and b represents the minimum on-voltage of the EH circuit, that is, a and b are determined by the resistance, capacitance and circuit sensitivity, and are related to the specifications of the EH circuit. c and d represent two parameters.

[0020] Under the nonlinear EH model, the energy harvested by the user in time slot t0 is:

[0021]

[0022] In order to reduce the complexity of the system, this paper focuses on two NOMA users in a cooperative fog, namely FU and NU. At stage t1, FU transmits at power and P f,n The superposition signal is sent to HAP and NU. Among them, NU is regarded as a NOMA strong user and HAP is regarded as a NOMA weak user. After passing through their respective channels, the signals received by HAP and NU can be defined as:

[0023]

[0024] in, and x f,n are the signals sent by FU to HAP and NU respectively, f,a and h f,n are the uplink channel power gains from FU to HAP and NU respectively. Constant z a and z nDenote the additive white Gaussian noise (AWGN) at HAP and NU, respectively. Assuming that each receiving node knows the corresponding channel state information (CSI), the successive interference cancellation (SIC) technique can be used. HAP and NU can decode their respective signals, then the achievable transmission rate from FU to HAP and NU is:

[0025]

[0026]

[0027] Where B represents the offload bandwidth.

[0028] Therefore, the computational effort from FU to HAP and NU can be expressed as and l f,n , the amount of task data offloaded is subject to the following constraints:

[0029]

[0030] l f,n ≤t1R f,n (10)

[0031] Then the energy consumption of FU unloading through NOMA at stage t1 is:

[0032]

[0033] At stage t2, FU and NU transmit at power and P n,a The superposition signal is sent to the HAP. Part of the computational tasks of FU and NU are offloaded to the HAP on the same time-frequency resource block, where NU is regarded as a NOMA strong user and FU is regarded as a NOMA weak user. Similar to the t1 stage, the received signal of the receiving end HAP is:

[0034]

[0035] in, and x n,a are the signals sent by FU and NU to HAP respectively in this stage, h n,ais the uplink channel power gain from NU to HAP. When decoding information at HAP, uplink NOMA decoding is first performed on strong users, that is, HAP first detects NU information, treats FU information as noise, then uses SIC to remove NU information, and further decodes FU information. Therefore, the achievable transmission rate from FU and NU to HAP is:

[0036]

[0037] The computational effort of offloading FU and NU to HAP is recorded as and l n,a , the amount of task data offloaded is subject to the following constraints:

[0038]

[0039] Then the energy consumption of FU and NU unloading through NOMA at stage t2 is:

[0040]

[0041] Local computing phase: Each user computes his or her own portion of the task locally. i,loc , where i = 1, 2. Let C f and C n The number of CPU cycles required to calculate 1 bit of data for the user, f i Represents the computing power of the user, also known as the CPU frequency. Each user can perform calculations in the entire time block without being interrupted by any information or energy transmission, then the local computing rate of FU and NU is:

[0042]

[0043] The corresponding computational energy consumption can be defined as:

[0044]

[0045] Among them, κ i is the effective capacitance coefficient and depends on the hardware of the user's device.

[0046] In summary, the goal of the present invention is to maximize the system's computation rate, i.e., the weighted sum of the number of bits computed within a time block T, by utilizing the system's limited energy and computational resources in the context of a nonlinear EH model. By jointly optimizing power allocation, system time allocation, and resource allocation strategies, the weighted sum computation rate of all users is maximized, which can be expressed in mathematical form as:

[0047]

[0048] Among them, P a ={pa,f ,p a,n ,}, They represent the power allocation vector of the base station for WPT, the power allocation vector of the user for information transmission and the vector of the amount of computing tasks, respectively. t={t0,t1,t2} represents the time allocation vector. q1 and q2 represent the weights of the near and far end users. C1 represents the WPT energy constraint at the HAP; C2 represents the total delay limit of the entire system; C3, C4 and C5 represent that the amount of computing data offloaded by the user does not exceed the maximum value that can be offloaded; and are the local computing time limits of FU and NU. C6 and C7 represent that the user needs to perform its local calculation within the maximum tolerance delay; C8 and C9 represent the total energy consumption constraints of FU and NU, respectively, that is, the energy consumption of each user does not exceed the energy harvested in its WPT stage.

[0049] Since the expression of the user offloading data size and the nonlinear energy harvesting model adopted are relatively complex, the optimization variables of problem P1 are strongly coupled under the constraints and cannot be directly solved using a convex optimization algorithm. In this section, problem P1 is first reformulated using the variable substitution method. Then, SCA is applied to further transform the objective function, computation offloading constraints, and energy limit constraints into a convex approximation, and an iterative optimization algorithm is proposed to solve the reformulated objective problem.

[0050] The above nonlinear EH mode based on user collaboration and NOMA-assisted wireless power mobile edge computing optimization algorithm is obtained according to the following steps:

[0051] (1) Re-statement of the problem

[0052] The non-convexity of the optimization problem P1 is due to the user transmission power P at each stage. a , P u and duration t are coupled in constraints C3-C5 and C8-C9. Therefore, in order to solve this non-convex optimization problem, a new replacement vector β = [β f , β n ], where β i =-a|h i,a | 2 p a,i -b),i={f,n}; vector in To decouple the following constraints. According to the variable β i =-a|h i,a | 2 p a,i -b),i={f,n}, we can get:

[0053]

[0054] The constraint C1 in P1 can be rewritten as:

[0055]

[0056] According to equations (2), (3), (4) and (20), constraints C8 and C9 are rewritten as:

[0057]

[0058] Therefore, by substituting the above replacement variables and equations (22)-(25) into the original problem P1, we can obtain the reformulated problem P2:

[0059]

[0060] stC1:t0+t1+t2≤T

[0061]

[0062] C7:(23),(24),(25)

[0063]

[0064] For the variable β in equations (24) and (25), i , t0 is about the convex function t0M / (1+β i ) coupling, and using the first-order convexity condition to approximate the convex function:

[0065]

[0066] in, and The feasible point for obtaining the optimal value of the problem at the mth iteration. Then, the constraints in equations (24) and (25) are transformed into:

[0067]

[0068] For the expression of the amount of user unloaded tasks, according to the characteristic of maintaining convexity in the perspective function, if the function F(x)=log2(1+x) is concave, then its perspective function tF(x / t)=tlog2(1+x / t) is also concave when t>0. This property can be used to determine the expression t2Blog2[1+(I f2,a |h f,a | 2 ) / (|n a | 2 t2)] and t1Blog2[1+(I f,n |h f,n | 2 ) / (|nn | 2 t1)] are all concave functions. However, the expression of constraint C2 t1Blog2[1+(I f1,a |h f,a | 2 ) / (I f,n |h f,a | 2 +|n a | 2 t1)] and C4 are still non-convex functions, so problem P2 is still non-convex.

[0069] To solve the above problem, we first rewrite the two non-convex expressions into two classical convex difference (DC) forms about I and t. Then we use the SCA method to transform it into a convex expression so that the corresponding constraints of problem P2 can be handled. The convex difference form of the two functions is expressed as:

[0070]

[0071] Among them, s1(I, t1), v1(I, t1), s2(I, t2) and v2(I, t2) are concave functions, which are expressed as follows:

[0072]

[0073] By using the SCA method, the expressions v1(I, t1) and v2(I, t2) are approximately replaced by first-order Taylor expansions, namely:

[0074]

[0075] in t2 (k) represents the value at the kth iteration, and Indicates that v1(I,t1) is t1 (k) The gradient on and Indicates that v2(I,t2) is t2 (k) The gradients on can be expressed as:

[0076]

[0077]

[0078] After approximate substitution, problem P2 can be transformed into:

[0079]

[0080] Where L = q1(lf,loc +l f,a +l f,n +l fn,a )+q2(l n,loc +l n,a ), Problem P3 is a convex problem and can be solved using the CVX toolbox. Using SCA technology, Problem P2 is solved by iteratively solving the approximate Problem P3.

[0081] The specific process of solving the target problem P3 using the SCA-based iterative optimization algorithm is as follows:

[0082]

[0083] The beneficial effects of the present invention are as follows: In the nonlinear EH mode, the present application maximizes the system weighted and computing rate by jointly optimizing the transmission power, user unloading time and user unloading power between different energy beams of HAP based on user collaboration and NOMA-assisted wireless power mobile edge computing. The new method not only improves the energy utilization and computing performance of the system, but also shows stable adaptability and reliability under different environmental conditions. This opens up a new path for the integration of WPT technology and mobile edge computing, and is expected to promote technological innovation and practical applications in related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is the system model diagram;

[0085] Figure 2 It is a time slot structure diagram;

[0086] Figure 3 It is a graph of the relationship between the system weighted sum calculation rate and the number of iterations;

[0087] Figure 4 is a graph showing the relationship between HAP transmit power and system weighted and calculated rate;

[0088] Figure 5 It is a graph comparing the time block length and the system weighted sum calculation rate;

[0089] Figure 6 It is a graph showing the relationship between the user's CPU frequency and the system's weighted and calculated rate;

[0090] Figure 7 Graph showing the relationship between the distance between NU and HAP and the system weighted sum calculation rate. DETAILED DESCRIPTION

[0092] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments: The wireless power mobile edge computing optimization algorithm based on user collaboration and NOMA assistance in the nonlinear EH mode proposed by the present invention has a system model such as Figure 1 As shown in Figure 1, in a multi-user WPT-MEC system under a nonlinear energy harvesting model, there is a multi-antenna hybrid access point HAP integrated with a MEC server and K user cooperative fogs, К = {1, 2, ..., K}. Each cooperative fog is composed of single-antenna users working in half-duplex mode, and the distances from the two users to the HAP are different, namely FU and NU, as shown in Figure 1. Figure 1 In the kth cooperative fog, the distances between FU and HAP, NU and HAP, and FU and NU are defined as d f,a d n,a , and d f,n , and d n,a ≤d f,a , d f,n ≤d f,a . It is assumed that the HAP is powered by the grid, has a stable energy source, and uses energy beamforming based on RF signals to charge user devices. Each user device is equipped with an EH circuit, which can perform computational offloading with the collected energy. Assuming that the computing tasks of each user are independent and divisible, the user's computing tasks can be arbitrarily divided into two parts, one part is calculated locally at the user, and the other part is offloaded to the MEC server for execution through uplink NOMA. Among them, downlink WPT and local computing can be performed simultaneously, and downlink WPT and uplink computing offloading follow the HTT protocol. For the offloading of uplink computing, partial offloading based on NOMA is adopted, and the computing tasks of each user are divided into two parts, which are remotely calculated on the HAP and locally calculated at the user. Compared with complete offloading, partial offloading is suitable for complex tasks consisting of multiple parallel segments, which is more conducive to reducing latency.

[0093] A block-based TDMA scheme is adopted, each block lasts for T seconds, and it is assumed that each block experiences independent and identically distributed Rayleigh fading. The time allocation structure for the k-th near and far users in the cooperative fog when performing computation offloading is as follows: Figure 2As shown. It mainly consists of three stages, namely the wireless power transmission stage, the calculation offloading stage and the calculation result return stage. In order to maintain the advantages of NOMA while taking advantage of the UC, the two time slots t1 and t2 are used for NOMA uplink transmission supported by UC. In the t1 time slot, FU simultaneously unloads part of the calculation tasks to HAP and NU through uplink NOMA. In the t2 time slot, part of the tasks of FU and NU are offloaded to HAP on the same time-frequency resource block through NOMA technology. Among them, some of NU's tasks include its own calculation tasks and the calculation tasks that help FU forward the offload. Due to the powerful computing power of HAP and the small amount of calculation results, the result calculation and return time t3 is generally ignored, that is, t3≈0. In order to complete the corresponding calculation tasks in each time period, the total system time allocation constraint satisfies t0+t1+t2≤T.

[0094] In the time slot t0, the HAP with N antennas can provide stable unlimited energy transmission to 2K single-antenna users at the same time. is the transmit power of the corresponding beam. The HAP transmit power is subject to a fixed value The restriction of , produces the following energy constraint:

[0095]

[0096] In order to match the actual EH circuit on the user's wireless device, this paper adopts a nonlinear EH model based on the logistic function. Through the data fitting method, the output EH value of the user receiver in the kth cooperative fog is a function of the input RF power. In the WPT phase of the t0 time slot, the wireless energy collected by each user in the cooperative fog can be defined as:

[0097]

[0098] in is the downlink channel power gain from HAP to the FU and NU of the kth cooperative fog, 0<μ<1 is the energy conversion efficiency of the user, In the nonlinear EH model, M represents the maximum energy harvested at the receiver when the EH circuit reaches saturation, a represents the nonlinear EH rate relative to the input power, and b represents the minimum on-voltage of the EH circuit, that is, a and b are determined by the resistance, capacitance and circuit sensitivity, and are related to the specifications of the EH circuit. c and d represent two parameters.

[0099] Under the nonlinear EH model, the energy harvested by the user in time slot t0 is:

[0100]

[0101] In order to reduce the complexity of the system, this paper focuses on two NOMA users in a cooperative fog, namely FU and NU. At stage t1, FU transmits at power and P f,n The superposition signal is sent to HAP and NU. Among them, NU is regarded as a NOMA strong user and HAP is regarded as a NOMA weak user. After passing through their respective channels, the signals received by HAP and NU can be defined as:

[0102]

[0103] in, and x f,n are the signals sent by FU to HAP and NU respectively, f,a and h f,n are the uplink channel power gains from FU to HAP and NU respectively. Constant z a and z n denote the AWGN at HAP and NU respectively. Assuming that each receiving node knows the corresponding CSI, SIC technology can be used. HAP and NU can decode their respective signals, then the achievable transmission rate from FU to HAP and NU is:

[0104]

[0105] Where B represents the offload bandwidth.

[0106] Therefore, the computational effort from FU to HAP and NU can be expressed as and l f,n , the amount of task data offloaded is subject to the following constraints:

[0107]

[0108] l f,n ≤t1R f,n (10)

[0109] Then the energy consumption of FU unloading through NOMA at stage t1 is:

[0110]

[0111] At stage t2, FU and NU transmit at power and P n,a The superposition signal is sent to the HAP. Part of the computational tasks of FU and NU are offloaded to the HAP on the same time-frequency resource block, where NU is regarded as a NOMA strong user and FU is regarded as a NOMA weak user. Similar to the t1 stage, the received signal of the receiving end HAP is:

[0112]

[0113] in, and x n,a are the signals sent by FU and NU to HAP respectively in this stage, h n,a is the uplink channel power gain from NU to HAP. When decoding information at HAP, uplink NOMA decoding is first performed on strong users, that is, HAP first detects NU information, treats FU information as noise, then uses SIC to remove NU information, and further decodes FU information. Therefore, the achievable transmission rate from FU and NU to HAP is:

[0114]

[0115] The computational effort of offloading FU and NU to HAP is recorded as and l n,a , the amount of task data offloaded is subject to the following constraints:

[0116]

[0117] Then the energy consumption of FU and NU unloading through NOMA at stage t2 is:

[0118]

[0119] Local computing phase: Each user computes his or her own portion of the task locally. i,loc , where i = 1, 2. Let C f and C n The number of CPU cycles required to calculate 1 bit of data for the user, f i Represents the computing power of the user, also known as the CPU frequency. Each user can perform calculations in the entire time block without being interrupted by any information or energy transmission, then the local computing rate of FU and NU is:

[0120]

[0121] The corresponding computational energy consumption can be defined as:

[0122]

[0123] Among them, κ i is the effective capacitance coefficient and depends on the hardware of the user's device.

[0124] In summary, the goal of the present invention is to maximize the system's computation rate, i.e., the weighted sum of the number of bits computed within a time block T, by utilizing the limited energy and computational resources of the system in the context of a nonlinear EH model. By jointly optimizing power allocation, system time allocation, and resource allocation strategies, the weighted sum computation rate of all users is maximized, which can be expressed in mathematical form as:

[0125]

[0126] Among them, P a ={p a,f ,p a,n ,}, They represent the power allocation vector of the base station for WPT, the power allocation vector of the user for information transmission and the vector of the amount of computing tasks, respectively. t={t0,t1,t2} represents the time allocation vector. q1 and q2 represent the weights of the near and far end users. C1 represents the WPT energy constraint at the HAP; C2 represents the total delay limit of the entire system; C3, C4 and C5 represent that the amount of computing data offloaded by the user does not exceed the maximum value that can be offloaded; and are the local computing time limits of FU and NU. C6 and C7 represent that the user needs to perform its local calculation within the maximum tolerance delay; C8 and C9 represent the total energy consumption constraints of FU and NU, respectively, that is, the energy consumption of each user does not exceed the energy harvested in its WPT stage.

[0127] Since the expression of the user offloading data size and the nonlinear energy harvesting model adopted are relatively complex, the optimization variables of problem P1 are strongly coupled under the constraints and cannot be directly solved using a convex optimization algorithm. In this section, problem P1 is first reformulated using the variable substitution method. Then, SCA is applied to further transform the objective function, computation offloading constraints, and energy limit constraints into a convex approximation, and an iterative optimization algorithm is proposed to solve the reformulated objective problem.

[0128] The above nonlinear EH mode based on user collaboration and NOMA-assisted wireless power mobile edge computing optimization algorithm is obtained according to the following steps:

[0129] (1) Re-statement of the problem

[0130] The non-convexity of the optimization problem P1 is due to the user transmission power P at each stage. a , P u and duration t are coupled in constraints C3-C5 and C8-C9. Therefore, in order to solve this non-convex optimization problem, a new replacement vector β = [β f , β n ], where β i =-a|h i,a | 2 p a,i -b),i={f,n}; vector in I f,n =p f,n t1, I n,a =p n,at2 to decouple the following constraints. According to the variable β i =-a|h i,a | 2 p a,i -b),i={f,n}, we can get:

[0131]

[0132] The constraint C1 in P1 can be rewritten as:

[0133]

[0134] According to equations (2), (3), (4) and (20), constraints C8 and C9 are rewritten as:

[0135]

[0136] Therefore, by substituting the above replacement variables and equations (22)-(25) into the original problem P1, we can obtain the reformulated problem P2:

[0137]

[0138] stC1:t0+t1+t2≤T

[0139]

[0140] C7:(23),(24),(25)

[0141]

[0142] For the variable β in equations (24) and (25), i , t0 is about the convex function t0M / (1+β i ) coupling, and using the first-order convexity condition to approximate the convex function:

[0143]

[0144] in, and The feasible point for obtaining the optimal value of the problem at the mth iteration. Then, the constraints in equations (24) and (25) are transformed into:

[0145]

[0146] For the expression of the amount of user unloaded tasks, according to the characteristic of maintaining convexity in the perspective function, if the function F(x)=log2(1+x) is concave, then its perspective function tF(x / t)=tlog2(1+x / t) is also concave when t>0. This property can be used to determine the expression of constraints C2 and C3 in problem P2 and t1Blog2[1+(I f,n |h f,n | 2 ) / (|n n | 2 t1)] are all concave functions. However, the expression of constraint C2 And C4 are still non-convex functions, so problem P2 is still non-convex.

[0147] To solve the above problem, we first rewrite the two non-convex expressions into two classical convex difference (DC) forms about I and t. Then we use the SCA method to transform it into a convex expression so that the corresponding constraints of problem P2 can be handled. The convex difference form of the two functions is expressed as:

[0148]

[0149] Among them, s1(I, t1), v1(I, t1), s2(I, t2) and v2(I, t2) are concave functions, which are expressed as follows:

[0150]

[0151] By using the SCA method, the expressions v1(I, t1) and v2(I, t2) are approximately replaced by first-order Taylor expansions, namely:

[0152]

[0153] in t2 (k) represents the value at the kth iteration, and Indicates that v1(I,t1) is The gradient on and Indicates that v2(I,t2) is t2 (k) The gradients on can be expressed as:

[0154]

[0155] After approximate substitution, problem P2 can be transformed into:

[0156]

[0157] Where L = q1(l f,loc +l f,a +l f,n +l fn,a )+q2(l n,loc +l n,a), Problem P3 is a convex problem and can be solved using the CVX toolbox. Using SCA technology, Problem P2 is solved by iteratively solving the approximate Problem P3.

[0158] The specific process of solving the target problem P3 using the SCA-based iterative optimization algorithm is as follows:

[0159]

[0160] Experimental analysis:

[0161] In this section, simulations are used to verify the convergence of the proposed scheme and evaluate its performance. In the simulations, considering the reciprocity of the uplink and downlink channels, assuming that their channel gains are equal, the wireless channel between NU, FU, and HAP is set to a composite channel h i,j =(10) -(3 / 2) (d i,j ) -(β / 2) g i,j (i,j∈{1,2,3}), where d f,a d n,a and d f,n They represent the distance from FU to HAP, the distance from NU to HAP, and the distance from FU to NU, β is the path loss index, and g i,j represents Rayleigh fading with zero mean and unit variance. The detailed information of the main simulation parameters is shown in the following table:

[0162]

[0163] In order to provide a comprehensive study, the baseline scenario for the simulation is described below:

[0164] 1) NOMA-UC MEC solution is the mobile edge computing combining UC and NOMA in the nonlinear EH mode proposed in this paper;

[0165] 2) TDMA-UC MEC scheme is a traditional time division multiple access scheme without NOMA in nonlinear EH mode combined with UC mobile edge computing;

[0166] 3) NOMA-MEC solution does not use UC in nonlinear EH mode, but only uses NOMA mobile edge computing;

[0167] 4) Only offloading calculation scheme: In the scheme proposed in this paper, only calculation offloading is performed, that is, f,loc =0, l n,loc =0;

[0168] 5) Only local computing solution is the solution proposed in this paper that only performs computing offloading, that is, f,a =0, l fn,a=0, l n,a =0.

[0169] Figure 3 The weighted sum computation rate (WSCR) varies with the number of iterations. Higher power and lower path loss index can improve the performance of WSCR. From the convergence of the proposed scheme, it can be seen that the proposed scheme basically reaches convergence after about 8 iterations, indicating that it converges quickly and has high efficiency.

[0170] Figure 4 The weighted sum calculation rate under different schemes changes with the increase of the maximum transmission power of HAP. Among them, the MEC scheme based on NOMA-UC proposed in this paper has the highest WSCR performance, that is, the communication and computing efficiency of the proposed scheme is better at higher power. The WSCR of TDMA-UC MEC and NOMA-MEC is lower than that of NOMA-UC MEC, but better than the baseline scheme of only offloading calculation. The scheme of only offloading calculation performs the worst. This scheme does not adopt the method of partial offloading, and the amount of task of user local calculation is l f,loc =0, l n,loc = 0. At the same time, the energy harvested by the user cannot support a large amount of computing offloading, so the computing efficiency is low. This shows again that the MEC solution combined with NOMA-UC can more effectively improve the computing rate, especially under high transmission power conditions.

[0171] Figure 5 is the relationship between the time block length T and the weighted sum calculation rate. As the time block length T increases, the WSCR values ​​of all schemes increase slightly. This is because as T increases, the above schemes can achieve more flexible resource allocation, which helps to improve the calculation rate of the system. It can be seen from the figure that the proposed NOMA-UC MEC scheme has the best performance, and its WSCR also increases significantly with the increase of T. The performance of TDMA-UC MEC and NOMA-MEC schemes is inferior to NOMA-UC MEC, respectively. The WSCR of the offloading calculation scheme is the lowest, and it increases less with the change of T.

[0172] Figure 6The relationship between the user's CPU frequency and the weighted sum calculation rate is shown, and the performance of five different computing and communication schemes is compared. With the increase of CPU frequency, the WSCR of all schemes except the only computing offload has a small increase. Since the only computing offload scheme does not perform local calculations, the increase of the user's CPU frequency will not affect the calculation rate of the scheme. The proposed NOMA-UC MEC scheme can perform best at different CPU frequencies, while the performance of only local or only offloaded calculations is limited. Since the computing resources of MEC are not used, the scheme that only performs local calculations has the smallest result, but as the user's CPU frequency increases, its local computing power also increases. In the stage where MEC computing resources are limited, the results of the first three schemes increase with the increase of CPU frequency. This is because the more computing resources MEC has, the higher the computing rate of the user device.

[0173] Figure 7 is the relationship between the distance between NU and HAP and the weighted sum calculation rate. In order to evaluate the impact of user location, it is assumed that the AP and the two users are placed in a straight line, that is, d f,a =8m,d n,a =λd f,a , d f,n =(1-λ)d f,a , where λ∈[0.5,0.75]. When the distance between AP and U2 increases, the two users will get closer and closer. Obviously, the achievable WSCR decreases as the distance increases. This is because the longer the distance, the worse the channel condition. Figure 7 It can be seen that the NOMA-UC MEC scheme proposed in the present invention has the best performance under the same distance conditions, followed by TDMA-UC MEC and the calculation-only offloading scheme. This is because applying UC to the two schemes can make the channel gain between the two users better. The performance of the NOMA-MEC scheme without user collaboration is the worst, because the channel gain of U2 decreases with increasing distance. However, when the distance between AP and U2 becomes larger, the distance between the two users is closer, so the UC-MEC scheme can better compensate for channel attenuation.

[0174] Based on the above analysis and discussion of the present invention, it can be known that the mobile edge computing optimization algorithm for wireless energy transmission based on user collaboration and NOMA assistance in the nonlinear EH mode proposed in the present invention studies the power allocation problem between different beams of multi-antenna energy transmitters and the system performance optimization problem. By jointly optimizing the transmission power, user unloading time and user unloading power between different energy beams of HAP, the system weighted and computing rate is maximized. And an iterative optimization algorithm based on SCA is proposed to solve the non-convex problems caused by NOMA unloading and nonlinear energy harvesting models. Compared with other methods, the method proposed in the present invention can produce better system performance.

Claims

1. The wireless power supply mobile edge computing optimization algorithm based on UC and NOMA assistance in nonlinear EH mode includes the following system models: (1) A multi-user wireless powered transmission mobile edge computing (WPT-MEC) system under a nonlinear energy harvesting (EH) model is considered, including a multi-antenna hybrid access point (HAP) integrated with a MEC server and K user cooperative fogs, К = {1, 2, ..., K}; each cooperative fog is composed of single-antenna users working in half-duplex mode, and the distances between the two users and the HAP are different, namely, the far user (FU) and the near user (NU); in the kth cooperative fog, the distances between FU and HAP, NU and HAP, and FU and NU are defined as d f,a ,d n,a , and d f,n , and d n,a ≤d f,a , d f,n ≤d f,a ; Assume that the HAP is powered by the grid, has a stable energy source, and uses energy beamforming based on RF signals to charge user devices; each user device is equipped with an EH circuit, which can perform computing offloads using the collected energy; Assume that each user's computing task is independent and divisible, the user's computing task can be arbitrarily divided into two parts, one part is calculated locally at the user, and the other part is offloaded to the MEC server through uplink non-orthogonal multiple access (NOMA); Among them, Downlink WPT and local computing can be performed simultaneously. Downlink WPT and uplink computing offloading follow the Harvest-The-Offload (HTT) protocol. For uplink computing offloading, partial offloading based on NOMA is adopted to divide the computing task of each user into two parts, remote computing on the HAP and local computing at the user. Compared with complete offloading, partial offloading is suitable for complex tasks consisting of multiple parallel segments and is more conducive to reducing latency. (2) A block-based time division multiple access (TDMA) scheme is adopted, with each block lasting T seconds, and it is assumed that each block experiences independent and identically distributed Rayleigh fading. The time allocation structure for the k-th cooperative fog users during computation offloading mainly consists of three stages, namely, the wireless power transmission stage, the computation offloading stage, and the computation result return stage. In order to take advantage of the UC while maintaining the NOMA advantage, the two time slots t1 and t2 are used for the NOMA uplink transmission supported by the UC. In the t1 time slot, the FU simultaneously offloads part of the computation tasks to the HAP and NU through uplink NOMA. In the t2 time slot, part of the tasks of the FU and NU are offloaded to the HAP on the same time-frequency resource block through the NOMA technology. Among them, part of the tasks of the NU include its own computation tasks and the computation tasks that help the FU forward the offloaded tasks. Due to the powerful computing power of the HAP and the small amount of computation results, the result calculation and return time t3 is generally ignored, that is, t3≈0. In order to complete the corresponding computation tasks in each time period, the total system time allocation constraint satisfies t0+t1+t2≤T. (3) In the time slot t0, a HAP with N antennas can provide stable unlimited energy transmission to 2K single-antenna users at the same time. is the transmit power of the corresponding beam; the HAP transmit power is subject to a fixed value The restriction of , produces the following energy constraint: In order to match the actual EH circuit on the user's wireless device, this paper adopts a nonlinear EH model based on the logistic function. Through the data fitting method, the output EH value of the user receiver in the kth cooperative fog is a function of the input radio frequency (RF) power. In the WPT phase of the t0 time slot, the wireless energy collected by each user in the cooperative fog can be defined as: in is the downlink channel power gain from HAP to the FU and NU of the kth cooperative fog, 0<μ<1 is the energy conversion efficiency of the user, For receiving RF power; in the nonlinear EH model, M represents the maximum energy harvested at the receiver when the EH circuit reaches saturation, a represents the nonlinear EH rate relative to the input power, b represents the minimum on-voltage of the EH circuit, that is, a and b are determined by the resistance, capacitance and circuit sensitivity, and are related to the specifications of the EH circuit, and c and d represent two parameters; Under the nonlinear EH model, the energy harvested by the user in time slot t0 is: (4) In order to reduce the complexity of the system, this paper focuses on two NOMA users in a cooperative fog, namely FU and NU. At stage t1, FU transmits at power and P f,n The superimposed signal is sent to HAP and NU; NU is regarded as a NOMA strong user and HAP is regarded as a NOMA weak user; after passing through their respective channels, the signals received by HAP and NU can be defined as: in, and x f,n are the signals sent by FU to HAP and NU respectively, f,a and h f,n are the uplink channel power gains from FU to HAP and NU respectively; the constant z a and z n denotes the additive white Gaussian noise (AWGN) at HAP and NU respectively; assuming that each receiving node knows the corresponding channel state information (CSI), the successive interference cancellation (SIC) technique can be used; HAP and NU can decode their respective signals, then the achievable transmission rate from FU to HAP and NU is: Where B represents the offload bandwidth; Therefore, the computational effort from FU to HAP and NU can be expressed as and l f,n , the amount of task data offloaded is subject to the following constraints: l f,n ≤t1R f,n (10) Then the energy consumption of FU unloading through NOMA at stage t1 is: At stage t2, FU and NU transmit at power and P n,a The superimposed signal is sent to the HAP; part of the computational tasks of FU and NU are offloaded to the HAP on the same time-frequency resource block, where NU is regarded as a NOMA strong user and FU is regarded as a NOMA weak user; similar to the t1 stage, the received signal of the receiving end HAP is: in, and x n,a are the signals sent by FU and NU to HAP respectively in this stage, h n,a is the uplink channel power gain from NU to HAP; when decoding information at HAP, uplink NOMA decoding is first performed on strong users, that is, HAP first detects NU information, treats FU information as noise, then uses SIC to remove NU information, and further decodes FU information; therefore, the achievable transmission rate from FU and NU to HAP is: The computational effort of offloading FU and NU to HAP is recorded as and l n,a , the amount of task data offloaded is subject to the following constraints: L f,n +l n,a ≤t2R n,a (16) Then the energy consumption of FU and NU unloading through NOMA at stage t2 is: (5) Local computing phase: Each user calculates his or her own portion of the task locally. i,loc , where i = 1, 2; let C f and C n The number of CPU cycles required to calculate 1 bit of data for the user, f i Represents the computing power of the user, also known as the CPU frequency; each user can perform calculations in the entire time block without being interrupted by any information or energy transmission, then the local computing rate of FU and NU is: The corresponding computational energy consumption can be defined as: Among them, κ i is the effective capacitance coefficient, which depends on the hardware of the user's device; (6) The goal of this paper is to maximize the system's computational rate, i.e., the weighted sum of the number of computational bits in a time block T, by utilizing the limited energy and computational resources of the system in the context of the nonlinear EH model; by jointly optimizing the power allocation, system time allocation, and resource allocation strategies, the weighted sum computational rate of all users is maximized, which can be expressed in mathematical form as: Among them, P a ={p a,f ,p a,n ,}, t={t0, t1, t2} respectively represents the power allocation vector of the base station for WPT, the power allocation vector of the user for information transmission, the vector of the amount of computing tasks and the time allocation vector, q1 and q2 represent the weights of the near and far end users; C1 represents the WPT energy constraint at the HAP; C2 represents the total delay limit of the entire system; C3, C4 and C5 represent that the amount of computing data offloaded by the user does not exceed the maximum value that can be offloaded; is the local computing time limit of FU and NU; C6 and C7 represent that the user needs to perform its local computing within the maximum tolerance delay; C8 and C9 represent the total energy consumption constraints of FU and NU respectively, that is, the energy consumption of each user does not exceed the energy harvested in its WPT stage; Since the expression of the user offloading data size and the adopted nonlinear energy harvesting model are relatively complex, the optimization variables of problem P1 are strongly coupled under the constraints and cannot be directly solved using a convex optimization algorithm. In this section, problem P1 is firstly reformulated using the variable substitution method. Then, SCA is applied to further transform the objective function, computational offloading constraints and energy limit constraints into a convex approximation, and an iterative optimization algorithm is proposed to solve the reformulated objective problem.

2. According to the wireless power mobile edge computing optimization algorithm based on user collaboration and NOMA assistance in the nonlinear EH mode described in claim 1, the problem is solved: The non-convexity of the optimization problem P1 is due to the user transmission power P at each stage. a , P u and duration t are coupled in constraints C3-C5 and C8-C9; therefore, in order to solve this non-convex optimization problem, a new replacement vector β = [β f , β n ], where β i =-a|h i,a | 2 p a,i -b),i={f,n}; vector in I f,n =p f,n t1, I n,a =p n,a t2 to decouple the following constraints; according to the variable β i =-a|h i,a | 2 p a,i -b),i={f,n}, we can get: The constraint C1 in P1 can be rewritten as: According to equations (2), (3), (4) and (20), constraints C8 and C9 are rewritten as: Therefore, by substituting the above replacement variables and equations (22)-(25) into the original problem P1, we can obtain the reformulated problem P2: For the variable β in equations (24) and (25), i , t0 is about the convex function t0M / (1+β i ) coupling, and using the first-order convexity condition to approximate the convex function: in, and Obtain the feasible point of the optimal value for the problem at the mth iteration; then, transform the constraints in equations (24) and (25) into: For the expression of the amount of user unloaded tasks, according to the characteristic of maintaining convexity in the perspective function, if the function F(x) = log2(1+x) is concave, then its perspective function tF(x / t) = tlog2(1+x / t) is also concave when t>0; using this property, we can determine the expressions of constraints C2 and C3 in problem P2 and t1Blog2[1+(I f,n |h f,n | 2 ) / (|n n | 2 t1)] are all concave functions; however, the expression for constraint C2 and C4 are still non-convex functions, so problem P2 is still non-convex; To solve the above problem, we first rewrite the two non-convex expressions into two classical convex difference (DC) forms about I and t; then use the SCA method to transform it into a convex expression so that the corresponding constraints of problem P2 can be handled. The convex difference form of the two functions is expressed as: Among them, s1(I, t1), v1(I, t1), s2(I, t2) and v2(I, t2) are concave functions, which are expressed as follows: By using the SCA method, the expressions v1(I, t1) and v2(I, t2) are approximately replaced by first-order Taylor expansions, namely: in represents the value at the kth iteration, ▽v1(I (k) ) and ▽v1(t1 (k) ) indicates that v1(I,t1) is The gradient on ▽v2(I (k) )and Indicates that v2(I,t2) is The gradients on can be expressed as: After approximate substitution, problem P2 can be transformed into: Where L = q1(l f,loc +l f,a +l f,n +l fn,a )+q2(l n,loc +l n,a ), Problem P3 is a convex problem and can be solved using the CVX toolbox; Problem P2 is solved by iteratively solving the approximate problem P3 using the SCA technique; The specific process of solving the target problem P3 using the SCA-based iterative optimization algorithm is as follows: 1: Initialization And suppose the number of iterations m = 0, and the tolerance ε = 10 -3 2: When |L k+1 -L k |≥ε 3: Update the solution of the kth iteration {β (k)* ,F (k)* ,l (k)* ,t (k)* }; 4: Update L k -L k-1 ; 5: Update k = k + 1 until the value of the target problem converges 6: Output optimization results {β * ,F * ,l * ,t * }.

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