NOMA-MEC system energy consumption minimization resource optimization method based on user cooperation and unmanned aerial vehicle assistance

Abstract

The invention provides an unmanned aerial vehicle (UAV)-assisted non-orthogonal multiple access (NOMA) and mobile edge computing (MEC) four-node system based on user cooperation, and aims to solve the problem of energy consumption of the system, so that the problem of energy consumption of the system can be solved, and the system can be applied to the field of mobile edge computing (MEC) of the UAV-assisted non-orthogonal multiple access (NOMA) of the UAV-assisted non-orthogonal multiple access (NOMA) of the UAV-assisted mobile edge computing (MEC) of the UAV-assisted non-orthogonal multiple access (NOMA) of the UAV-assisted mobile edge computing (MEC) of the UAV-assisted non-orthogonal multiple access (NOMA) of the UAV-assisted non-orthogonal multiple access (NOMA). In the system, a far-end user cooperates with a near-end user, the near-end user helps to forward a computing task of the far-end user, and the computing task is unloaded by adopting a communication mode of combining NOMA (Non-Orthogonal Multiple Access) and TDMA (Time Division Multiple Access). The total energy consumption of the system is minimized by jointly optimizing the unloading bit number of the user, the transmitting power of the user and the unmanned aerial vehicle and the time allocation of each stage. In order to meet the time delay constraint, a task allocation algorithm based on a successive convex approximation (SCA) method and a Lagrange duality method is provided, a non-convex problem is converted into a convex problem by using a variable substitution method, and the optimal transmitting power, task allocation strategy and time allocation are solved through iterative optimization. Simulation results show that the algorithm has good convergence, and shows optimal performance when compared with other reference schemes.

Description

Technical Field

[0001] The present invention relates to a resource optimization method for minimizing energy consumption of a non-orthogonal multiple access (NOMA) mobile edge computing (MEC) system based on user collaboration and unmanned aerial vehicle (UAV) assistance, and proposes an iterative optimization algorithm based on the successive convex approximation (SCA) method to solve the problem. Background Art

[0002] The rapid development and widespread use of Internet of Things (IoT) devices and computing-intensive applications, especially the high latency sensitivity and explosive growth of data volume, require terminal devices to have significant computing capabilities. However, the computing power of terminal devices is limited and cannot meet the growing computing needs. Mobile Edge Computing (MEC) provides powerful computing resources at the edge of the network and can optimize performance according to the needs of specific applications, thereby improving the responsiveness and reliability of applications. Especially when processing latency-sensitive tasks (such as online games and augmented reality applications), MEC effectively responds to these challenges by providing flexible computing and data processing services, significantly improving the performance of IoT devices and the service quality of applications.

[0003] The basic principle of mobile edge computing is to deploy cloud servers at access points (APs) so that the computing tasks of user devices can be offloaded and completed at the edge of the wireless network, thereby freeing the heavy computing load of user devices and extending their battery life. Although MEC technology can improve the computing power of users through auxiliary computing, since MEC servers are usually fixed on ground APs, it is difficult to dynamically adjust according to user needs or network conditions, and the coverage of fixed-location MEC servers is limited and may not effectively cover all user devices that require computing services.

[0004] Due to their high flexibility, easy deployment and low cost, drones can be used as aerial base stations to provide line-of-sight (LoS) transmission to ground users, which can achieve more dynamic and extensive computing service coverage, and therefore has attracted widespread attention. The MEC system supported by drones can not only effectively make up for the limitations of traditional MEC systems, but also provide efficient and low-latency computing services in various complex scenarios (such as earthquakes, floods, mountainous areas, etc.), thereby improving user experience and network performance. The document "Deng, C.; Fang, X.; Wang, X. UAV-enabled mobile-edge computing for AI applications: Joint model decision, resource allocation, and trajectory optimization. IEEE Internet of Things Journal 2022, 10, 5662-5675" proposes an air-ground integrated wireless network that combines mobile edge computing and drones as aerial base stations to support computationally intensive and delay-sensitive artificial intelligence applications, aiming to minimize service delays and optimize energy consumption. The paper "Zeng, Y.; Chen, S.; Cui, Y.; Yang, J.; Fu, Y. Joint resource allocation and trajectory optimization in UAV-enabled wirelessly powered MEC for large area. IEEE Internet of Things Journal 2023, 10, 15705-15722" studies a wireless powered mobile edge computing framework based on collaboration between UAVs and central cloud. In this system, for UAVs serving large areas, the waiting delay of MEC servers and energy transmitters (ET) is minimized under the controllable energy consumption of user devices.The paper “Liu, J.; Mao, Y.; Zhang, J.; Letaief, KB Delay-optimal computation task scheduling for mobile-edge computing systems. In Proceedings of the 2016 IEEE international symposium on information theory (ISIT), 2016; pp. 1451-1455” studied the delay optimization problem of computing task scheduling in mobile edge computing systems and proposed a delay-optimal computing task scheduling algorithm. By optimizing task allocation and scheduling strategies, the total system delay was significantly reduced. The paper “Liu, Y.; Xiong, K.; Ni, Q.; Fan, P.; Letaief, KB UAV-assisted wireless powered cooperative mobile edge computing: Joint offloading, CPU control, and trajectory optimization. IEEE Internet of Things Journal 2019, 7, 2777-2790” proposed a UAV-assisted wireless powered cooperative MEC system, in which the UAV equipped with a MEC server can provide computing services for sensor devices. The computing resources of idle users in the system are also taken into consideration. Users with computing tasks can offload the tasks to UAVs and nearby idle users for auxiliary computing. An optimization problem is formulated to minimize the total energy consumption of UAVs.

[0005] The paper "Xu, D.; Xu, D. Cooperative task offloading and resource allocation for UAV-enabled mobile edge computing systems. Computer Networks 2023, 223, 109574" proposes a cooperative task offloading scheme for UAV-assisted mobile edge computing systems to solve the problem of high energy consumption when UEs are widely distributed. Specifically, the system consists of a UAV as a MEC server to provide computing services for multiple near-end and far-end UEs. Each far-end UE first sends its task to the near-end UE, and then the near-end user offloads its own task and the tasks of the far-end UE to the UAV.

[0006] Although UAVs combined with mobile edge computing technology have significant advantages in improving the computing power and energy efficiency of system equipment, as the number of IoT nodes increases, the amount of tasks uploaded to UAVs also increases. This significantly increases the energy consumption of UAVs when performing computing and communication tasks at the same time, which may shorten the flight time of UAVs or fail to complete computing tasks within the specified delay range. To solve the energy consumption problem faced by UAVs in computing and communication tasks, UAVs can be used as relays to optimize the efficiency of task offloading and data transmission. Introducing UAVs as relay nodes can not only share computing tasks, but also enhance the reliability and stability of communication links. By establishing a relay link between ground equipment and remote servers, UAVs can provide better line-of-sight transmission, thereby reducing signal attenuation and transmission delay. The literature "Hu, X.; Wong, K.-K.; Yang, K.; Zheng, Z. Task and bandwidth allocation for UAV-assisted mobile edge computing with trajectory design. In Proceedings of the 2019 IEEE Global Communications Conference (GLOBECOM), 2019; pp. 1-6" studies a UAV-based MEC architecture. UAV acts as a computing server to help user devices calculate their tasks, and acts as a relay to further offload user tasks to access points for calculation. System energy consumption is minimized by jointly optimizing task allocation, bandwidth allocation, and UAV trajectory. The paper "Hu, X.; Wong, K.-K.; Yang, K.; Zheng, Z. UAV-assisted relaying and edge computing: Scheduling and trajectory optimization. IEEE Transactions on Wireless Communications 2019, 18, 4738-4752" minimizes the weighted total energy consumption of UAVs and user devices by jointly optimizing computing resource scheduling, bandwidth allocation, and UAV trajectory, and proposes an alternating iterative optimization algorithm. Numerical results show that this method has significant advantages in processing computationally intensive and delay-sensitive tasks.

[0007] The above research works all consider traditional wireless access technologies. However, in drone-assisted MEC networks, due to the sharp increase in edge user data, traditional wireless access technologies may not be suitable for scenarios with large-scale device access, resulting in tight wireless spectrum resources. Therefore, non-orthogonal multiple access technology is introduced as a promising technology to encourage multi-user spectrum sharing to improve spectrum efficiency and provide large-scale connectivity. Combining MEC with non-orthogonal multiple access (NOMA) can effectively improve the computing efficiency of multi-user access MEC. The paper "Zeng, S.; Huang, X.; Li, D. Joint Communication and Computation Cooperation in Wireless-Powered Mobile-Edge Computing Networks With NOMA. IEEE Internet of Things Journal 2023, 10, 9849-9862" proposes a cooperative computing offloading scheme for the basic three-node wireless power supply MEC scenario, which combines NOMA technology to overcome the "double near-far" effect through joint communication and computing cooperation. In order to further overcome the influence of the "double near-far" effect, the paper "Zhang, G.; Wang, X.; Shan, M.; Ren, J.; Lu, W. Time allocation improvement method for UAV-based wireless energy transfer cooperative mobile edge. Physical Communication 2022, 55, 101861" considers the time slot allocation optimization of the UAV-assisted wireless power cooperative MEC system, which includes an access point and two mobile devices. The purpose is to minimize the total transmission energy of the UAV under the constraints of computing tasks and delays. The paper "Lu, W.; Ding, Y.; Gao, Y.; Chen, Y.; Zhao, N.; Ding, Z.; Nallanathan, A. Secure NOMA-based UAV-MEC network toward a flying eavesdropper. IEEE Transactions on Communications 2022, 70, 3364-3376" studies the application of non-orthogonal multiple access technology in UAV and mobile edge computing networks to provide computational offloading services in large-scale access situations, and proposes a secure communication scheme for NOMA-based UAV-MEC systems against flying eavesdroppers.The paper "Liu, Z.; Qi, J.; Shen, Y.; Ma, K.; Guan, X. Maximizing energy efficiency in UAV-assisted NOMA-MEC networks. IEEE Internet of Things Journal 2023" studies a UAV-assisted NOMA-MEC communication network architecture, in which drones serve mobile users as aerial base stations and relay nodes, and maximize the energy efficiency of the entire system by jointly optimizing users' communication scheduling, resource allocation, and UAV flight trajectory.

[0008] However, in the face of complex geographical environments in reality, ground users and drones may not be able to communicate directly. In response to this situation, the literature "Xu, D.; Xu, D. Cooperative task offloading and resource allocation for UAV-enabled mobile edge computing systems. Computer Networks 2023, 223, 109574" and the literature "Zeng, S.; Huang, X.; Li, D. Joint Communication and Computation Cooperation in Wireless-Powered Mobile-Edge Computing Networks With NOMA. IEEE Internet of Things Journal 2023, 10, 9849-9862" and the literature "Zhang, G.; Wang, X.; Shan, M.; Ren, J.; Lu, W. Time allocation improvement method for UAV-based wireless energy transfer cooperative mobile edge. Physical Communication 2022, 55, 101861" provide us with valuable inspiration. The above-mentioned documents all adopt the user relay transmission method, dividing users into remote users and near-end users. Remote users cannot communicate directly with MEC nodes and need to rely on near-end users to upload tasks to MEC nodes.The document “Xu, D.; Xu, D. Cooperative task offloading and resource allocation for UAV-enabled mobile edge computing systems. Computer Networks 2023, 223, 109574” adopts the traditional communication method, while the document “Zeng, S.; Huang, X.; Li, D. Joint Communication and Computation Cooperation in Wireless-Powered Mobile-Edge Computing Networks With NOMA. IEEE Internet of Things Journal 2023, 10, 9849-9862” and the document “Zhang, G.; Wang, X.; Shan, M.; Ren, J.; Lu, W. Time allocation improvement method for UAV-based wireless energy transfer cooperative mobile edge. Physical Communication 2022, 55, 101861” adopt the NOMA communication method.In addition, to solve the energy load problem of UAVs, the literature "Hu, X.; Wong, K.-K.; Yang, K.; Zheng, Z. Task and bandwidth allocation for UAV-assisted mobile edge computing with trajectory design. In Proceedings of the 2019 IEEE Global Communications Conference (GLOBECOM), 2019; pp. 1-6" and the literature "Hu, X.; Wong, K.-K.; Yang, K.; Zheng, Z. UAV-assisted relaying and edge computing: Scheduling and trajectory optimization. IEEE Transactions on Wireless Communications 2019, 18, 4738-4752" and the literature "Liu, Z.; Qi, J.; Shen, Y.; Ma, K.; Guan, X. Maximizing energy efficiency in UAV-assisted NOMA-MEC networks. IEEE Internet of Things Journal 2023” explored the use of drones as relay nodes, relaying some of the computing tasks offloaded by users who cannot communicate directly with ground base stations to remote base stations for auxiliary computing.The literature “Hu, X.;Wong, K.-K.;Yang, K.;Zheng, Z.Task and bandwidth allocation for UAV-assisted mobileedge computing with trajectory design.In Proceedings of the 2019IEEE GlobalCommunications Conference(GLOBECOM),2019;pp.1-6” and the literature “Hu, X.;Wong, K.-K.;Yang, K.;Zheng, Z.UAV-assisted relaying and edge computing:Scheduling and trajectory optimization.IEEE Transactions on Wireless Communications 2019,18,4738-4752” use traditional communication methods, while the literature “Liu, Z.;Qi, J.;Shen, Y.;Ma, K.;Guan, X.Maximizingenergy efficiency in UAV-assisted NOMA-MEC networks.IEEE Internet of Things Journal 2023” uses the NOMA communication method. Summary of the invention

[0009] Through a systematic comparative analysis of the above-mentioned literature, in order to further optimize the system performance, a drone-assisted NOMA-MEC system based on user collaboration is invented. In the proposed system, there are two users, the remote user and the near-end user. The remote user cannot communicate with the drone and the base station, and part of the computing tasks need to be offloaded to the near-end user. NOMA is used for communication between the near-end user and the drone. The computing load of the drone is taken into consideration. Therefore, the drone can choose to offload part of the tasks to the ground base station for auxiliary calculation. The total energy consumption of the system is minimized by jointly optimizing the transmission power, the number of offloaded bits and the time allocation of each stage.

[0010] The specific research contents of the present invention are as follows:

[0011] (1) A user-cooperative drone-assisted NOMA-MEC four-node system energy consumption optimization model is proposed. Specifically, in the uplink computing offloading phase, in the partial offloading mode, users use NOMA and time division multiple access (TDMA) to offload their computing tasks, where near-end users collaborate and forward the computing tasks of remote users. The system energy consumption is minimized by jointly optimizing the number of user offloaded bits, the transmission power of users and drones, and the time allocation of each stage.

[0012] (2) Under the delay constraint, a task allocation algorithm based on the successive convex approximation method and the Lagrangian dual method is proposed. Specifically, the original non-convex problem is first transformed into an equivalent convex problem by using the variable substitution method, and then the successive convex approximation (SCA) method is used to solve the converted problem by iteratively solving a series of convex optimization problems. The Lagrangian dual method is used to derive the optimal transmission power, task allocation strategy, and time allocation of each stage in each iteration step.

[0013] (3) The simulation results show the effectiveness of the proposed scheme. Specifically, the algorithm has good convergence and can reach convergence in about three iterations. In addition, by comparing with the other three benchmark schemes, the proposed scheme of the present invention has achieved the best performance.

[0014] The technical solution adopted by the present invention is: a resource optimization method for minimizing energy consumption of a NOMA-MEC system based on user collaboration and drone assistance, including the following system models:

[0015] In a NOMA-MEC four-node system assisted by a user-cooperative drone, there is a remote user 1 and a near-end user 2, a fixed-position drone and a ground base station. Among them, user 1 has limited computing power and cannot communicate directly with the drone and the ground base station. It needs to rely on user 2 to relay the task to the drone for computing. This paper adopts a partial offloading method to complete its computing task, that is, the user's computing task can be arbitrarily divided into two parts, one part is completed by local computing, and the other part is completed by uplink computing offloading. For the offloading of uplink computing, a scheme based on NOMA and TDMA is adopted. Assuming that the computing task is constrained to complete the task in the time length T, user 1 offloads part of the task to user 2 in the first τ stage. In the second τ stage, user 2 offloads part of its own task and the task received from the remote user to the drone in a NOMA manner, where user 1 and user 2 can perform local computing in the entire time slot T. Considering that the user's experience quality and the drone's energy are limited, in the T-τ stage, the drone decodes the task uploaded by user 2 through the Successive Interference Cancellation (SIC) technology, and in the time slot t u The task of calculating the near-end user in time slot t r In this paper, the task of user 1 is offloaded to the ground base station for calculation. Since the calculation result is very small, the result return time of the downlink is ignored in this paper.

[0016] The transmission rate from user 1 to user 2 can be expressed as:

[0017]

[0018] where p 1,2 is the transmission power of user 1, h 1,2 is the channel gain between user 1 and user 2. B is the total channel bandwidth.

[0019] In this paper, it is assumed that user 2 uses power p 2,u Unload your own tasks to the drone, using power p 1,u Relay user 1's task to the drone. Assuming the drone decodes user 2's task first and then decodes user 1's task, the transmission rate of user 2 unloading his task to the drone is:

[0020]

[0021] The transmission rate from user 2 to the drone when the task unloaded from user 1 is:

[0022]

[0023] The transmission rate between the drone and the AP is:

[0024]

[0025] where p u,a is the transmission power from the UAV to the base station, h u,a is the channel gain between the UAV and the base station.

[0026] Since user 2 is used as a relay, the tasks offloaded by user 1 are subject to the following constraints:

[0027] L 1,tr ≤min{R 1,2 τ,R 1,u τ}(5)

[0028] The task that user 2 offloads has the following constraints:

[0029] L 2,tr ≤R 2,u τ(6)

[0030] The local computing of user 1 and user 2 has the following constraints:

[0031] (L1-L 1,tr )C1≤Tf1 max (7)

[0032]

[0033] Where T is the total delay, L1 and L2 are the total number of tasks to be calculated by user 1 and user 2 respectively.

[0034] The local computing energy consumption of user 1 and user 2 is:

[0035] E 1loc =(L1-L 1tr )C1p l (9)

[0036] E 2,loc =(L2-L 2,tr )C2p l (10)

[0037] Among them, L1 and L2 are the tasks to be processed by user 1 and user 2 respectively, C1 and C2 are the CPU clock cycles of user 1 and user 2 respectively, and p l The energy required by the CPU per cycle.

[0038] After user 2 offloads the task to the drone, considering the user experience quality and the limited energy of the drone, the drone chooses to offload user 1's task to the ground base station for calculation, and only calculates user 2's task.

[0039] The unloading time of the UAV is t r The following constraints exist:

[0040] t r R u,a ≥L 1,tr (11)

[0041] The calculation time of the UAV is t u The following constraints exist:

[0042]

[0043] in, is the maximum computing power of the UAV, C u is the CPU clock cycle.

[0044] In order to ensure that the task uploaded to the drone can be completed within a limited time, the following constraints are imposed.

[0045] max{t r ,t u}≤T-2τ(13)

[0046] In order to minimize the unloading energy consumption of the UAV, the transmission power of the UAV can be expressed as:

[0047]

[0048] The unloading energy consumption of the UAV can be expressed as:

[0049] E u,tr =p u,a t r (15)

[0050] The local computing energy consumption of the drone can be expressed as:

[0051]

[0052] Among them, ε u is the capacitance switching coefficient of the drone, Cu is the CPU clock cycle of the drone, Provides CPU computing power for drones.

[0053] In order to ensure that the task uploaded by user 2 to the drone is completed within the specified time slot, the following constraints exist:

[0054]

[0055] Among them, Cu is the CPU computing cycle of the drone.

[0056] The unloading energy consumption of user 1 and user 2 are:

[0057] E 1,tr =p 1,2 τ (18)

[0058] E 2,tr =p 2,u τ+p 1,u τ (19)

[0059] The energy consumption required by user 1 and user 2 in the system are:

[0060] E1=E 1,loc +E 1,tr (20)

[0061] E2=E 2,loc +E 2,tr (twenty one)

[0062] The energy consumption required in the UAV system is expressed as:

[0063] E u =E u,loc +E u,tr (twenty two)

[0064] The total energy consumption of the system is:

[0065] E=E1+E2+E u (twenty three)

[0066] This paper studies a drone-assisted NOMA-MEC network system by jointly optimizing the user's task allocation L = {L 1,tr ,L 2,tr}, time slot scheduling t = {τ, t r ,t u}, the transmission power of the user and the drone p = {p 12 ,p 2u ,p 1u}Minimize the total energy consumption of the system.

[0067] Therefore, the mathematical expression of the optimization problem P1 is as follows:

[0068]

[0069] Among them, C1 and C2 represent the constraints on the user's local computing power and experience quality within the time slot T; C3 indicates that the sum of the task delays in each time slot cannot exceed the length of T; C4 represents the local computing time slot constraint of the drone; C5 and C6 indicate that the user's task allocation constraints must meet the computing rate requirements; C7, C8, C9 and C10 indicate that the user's transmission power, offloaded data volume and task allocation delay must be positive and cannot exceed the maximum value.

[0070] It is observed that the objective function and the constraints C5 and C6 are coupled, so problem P1 is a non-convex optimization problem that is difficult to solve. In order to solve this non-convex problem, this paper introduces the auxiliary variable F = [F 1,2 ,F 1,u ,F 2,u ], where F 1,2 =p 1,2 τ, F 1,u =p 1,u τ, F 2,u =p 2,u τ. For C3 and C6, considering that the time length allocated to each stage is not greater than the total length of the time slot, it can be rewritten as:

[0071] 2τ+t r ≤T (25)

[0072] 2τ+t u ≤T (26)

[0073] L 1,tr ≤R 1,2 τ (27)

[0074] L 1,tr ≤R 1,u τ (28)

[0075] Then problem P1 can be transformed into P2:

[0076]

[0077] It can be seen that problem P2 is still a non-convex problem.

[0078] According to the characteristic of maintaining convexity in perspective operation, if the function P(x) (where x∈R n ) is convex or concave, then its perspective function will also be convex or concave. Since the function log2(1+x) is convex, when t>0, its perspective function is also convex. According to this theory, it can be judged that C7 and C8 in problem P2 are convex. However, due to the existence of C6, P2 is still a non-convex problem. To solve this problem, the formula in C6 is re-expressed as formula (30):

[0079]

[0080] Where r(F,τ) and v(F,τ) are both convex, and the expressions are as follows:

[0081]

[0082] By using the SCA scheme, we approximate v(F,τ) using a first-order Taylor expansion:

[0083]

[0084] Among them, F 1,u (n) ,τ (n) is any point of the nth iteration, Δv(F (n) ) and Δv(τ (n) ) is the value of v(F,τ) with respect to F at the nth iteration. 1,u The gradient of and τ is expressed as:

[0085]

[0086]

[0087] Then problem P2 can be rewritten as P3:

[0088]

[0089] Problem P3 is a convex problem concerning the optimization variables L, F and t.

[0090] In order to gain a deeper understanding of the P3 problem, this paper uses the Lagrangian dual method to solve it. The Lagrangian problem of P3 can be expressed as:

[0091]

[0092] where λ = {λ1, λ2, ...λ 10} is a non-negative Lagrange multiplier, then its dual function is expressed as follows:

[0093]

[0094] Then we can get the first-order derivative of the expression Ω(L,F,t,λ) with respect to L,F,t:

[0095]

[0096] According to KKT conditions, are all equal to 0, the optimal solution of the corresponding variable can be obtained. By observing formulas (40) and (43), we can see that the variable L 2,tr ,t u is linear, so this paper uses the interior point method to solve and obtain the optimal variable L 2,tr * ,t u * .

[0097] Let formula (39) and (44) equal to 0 to obtain L1,tr ,F 1,2 The optimal solution is:

[0098]

[0099] For the optimal variable τ * , t r * ,F 1,u * ,F 2,u * This can be obtained by setting formulas (41), (42), (45), and (46) equal to 0:

[0100]

[0101] This paper uses the equal division method to solve formulas (49), (50), (51), and (52). Then, according to formulas (53)-(62), the subgradient method is used to update the value of λ.

[0102] λ1(l+1)=[λ1(l)-Δλ1(l)((L1-L 1,tr )C1-Tf1 max )] + (53)

[0103]

[0104] λ3(l+1)=[λ3(l)-Δλ3(l)(2τ+t r -T)] + (55)

[0105] λ4(l+1)=[λ4(l)-Δλ4(2τ+t u -T)] + (56)

[0106]

[0107] Where [x] + represents max(0,x), l is the number of iterations, and Δλ is the iteration step size.

[0108] Because F 1,2 * =p 1,2 * τ * ,F 1,u * =p 1,u * τ * ,F 2,u * =p 2,u* τ * , therefore, we can further obtain the optimal solution of p {p 1,2 * ,p 1,u * ,p 2,u *}. The algorithm flow is as follows:

[0109]

[0110]

[0111] For problem P1, due to the high degree of coupling, it is a non-convex problem that is difficult to solve. In order to solve this problem, first, the auxiliary variable F is used to transform it into problem P2. At this time, P2 is still a non-convex problem. In order to solve this problem, this paper uses the SCA method to decouple it and obtain problem P3. By observation, P3 is a convex problem. In order to solve this convex problem, this paper uses the Lagrange dual method to solve and obtain the optimal variable {F * ,t *}, and further or the optimal variable p * .

[0112] The specific problem-solving steps are summarized in Algorithm 2:

[0113] BRIEF DESCRIPTION OF THE DRAWINGS

[0114] Figure 1 It is the system model diagram;

[0115] Figure 2 It is a time slot structure diagram;

[0116] Figure 3 System model of the considered scenario;

[0117] Figure 4 The relationship between the total energy consumption of the system and the number of iterations under different schemes;

[0118] Figure 5 Changes of total system energy consumption over time T under different schemes;

[0119] Figure 6 The total energy consumption of the system under different schemes varies with the user's computing tasks;

[0120] Figure 7 The relationship between the total system energy consumption and the distance between user 1 and user 2 under different schemes. DETAILED DESCRIPTION

[0121] In a NOMA-MEC four-node system assisted by a user-cooperative drone, there is a remote user 1 and a near-end user 2, a fixed-position drone and a ground base station. Among them, user 1 has limited computing power and cannot communicate directly with the drone and the ground base station. It needs to rely on user 2 to relay the task to the drone for computing. This paper adopts a partial offloading method to complete its computing task, that is, the user's computing task can be arbitrarily divided into two parts, one part is completed by local computing, and the other part is completed by uplink computing offloading. For the offloading of uplink computing, a scheme based on NOMA and TDMA is adopted. Assuming that the computing task is constrained to complete the task in the time length T, user 1 offloads part of the task to user 2 in the first τ stage. In the second τ stage, user 2 offloads part of its own task and the task received from the remote user to the drone in a NOMA manner, where user 1 and user 2 can perform local computing in the entire time slot T. Considering that the user's experience quality and the drone's energy are limited, in the T-τ stage, the drone decodes the task uploaded by user 2 through the Successive Interference Cancellation (SIC) technology, and in the time slot t u The task of computing the near-end user in time slot t r In this paper, the task of user 1 is offloaded to the ground base station for calculation. Since the calculation result is very small, the result return time of the downlink is ignored in this paper.

[0122] The transmission rate from user 1 to user 2 can be expressed as:

[0123]

[0124] where p 1,2 is the transmission power of user 1, h 1,2 is the channel gain between user 1 and user 2. B is the total channel bandwidth.

[0125] In this paper, it is assumed that user 2 uses power p 2,u Unload your own tasks to the drone, using power p 1,u Relay user 1's task to the drone. Assuming the drone decodes user 2's task first and then decodes user 1's task, the transmission rate of user 2 unloading his task to the drone is:

[0126]

[0127] The transmission rate from user 2 to the drone when the task unloaded from user 1 is:

[0128]

[0129] The transmission rate between the drone and the AP is:

[0130]

[0131] where p u,a is the transmission power from the UAV to the base station, h u,a is the channel gain between the UAV and the base station;

[0132] Since user 2 is used as a relay, the tasks offloaded by user 1 are subject to the following constraints:

[0133] L 1,tr ≤min{R 1,2 τ,R 1,u τ} (67)

[0134] The task that user 2 uninstalls has the following constraints:

[0135] L 2,tr ≤R 2,u τ (68)

[0136] The local computing of user 1 and user 2 has the following constraints:

[0137] (L1-L 1,tr )C1≤Tf1 max (69)

[0138]

[0139] Where T is the total delay, L1 and L2 are the total number of tasks to be calculated by user 1 and user 2 respectively.

[0140] The local computing energy consumption of user 1 and user 2 is:

[0141] E 1,loc =(L1-L 1,tr )C1p l (71)

[0142] E 2,loc =(L2-L 2,tr )C2p l (72)

[0143] Among them, L1 and L2 are the tasks to be processed by user 1 and user 2 respectively, C1 and C2 are the CPU clock cycles of user 1 and user 2 respectively, and p l The energy required by the CPU per cycle.

[0144] After user 2 offloads the task to the drone, considering the user experience quality and the limited energy of the drone, the drone chooses to offload user 1's task to the ground base station for calculation, and only calculates user 2's task.

[0145] The unloading time of the UAV is t r The following constraints exist:

[0146] t r R u,a ≥L 1,tr (73)

[0147] The calculation time of the UAV is t u The following constraints exist:

[0148]

[0149] Among them, f u max is the maximum computing power of the UAV, C u is the CPU clock cycle.

[0150] In order to ensure that the task uploaded to the drone can be completed within a limited time, the following constraints are imposed.

[0151] max{t r ,t u}≤T-2τ (75)

[0152] In order to minimize the unloading energy consumption of the UAV, the transmission power of the UAV can be expressed as:

[0153]

[0154] The unloading energy consumption of the UAV can be expressed as:

[0155] E u,tr =p u,a t r (77)

[0156] The local computing energy consumption of the drone can be expressed as:

[0157]

[0158] Among them, ε u is the capacitance switching coefficient of the drone, Cu is the CPU clock cycle of the drone, Provides CPU computing power for drones.

[0159] In order to ensure that the task uploaded by user 2 to the drone is completed within the specified time slot, the following constraints exist:

[0160]

[0161] Among them, Cu is the CPU computing cycle of the drone.

[0162] The unloading energy consumption of user 1 and user 2 are:

[0163] E 1,tr =p 1,2 τ (80)

[0164] E 2,tr =p 2,u τ+p 1,u τ (81)

[0165] The energy consumption required by user 1 and user 2 in the system are:

[0166] E1=E 1,loc +E 1,tr (82)

[0167] E2=E 2,loc +E 2,tr (83)

[0168] The energy consumption required in the UAV system is expressed as:

[0169] E u =E u,loc +E u,tr (84)

[0170] The total energy consumption of the system is:

[0171] E=E1+E2+E u (85)

[0172] This paper studies a drone-assisted NOMA-MEC network system by jointly optimizing the user's task allocation L = {L 1,tr ,L 2,tr}, time slot scheduling t = {τ, t r ,t u}, the transmission power of the user and the drone p = {p 12 ,p 2u ,p 1u}Minimize the total energy consumption of the system.

[0173] Therefore, the mathematical expression of the optimization problem P1 is as follows:

[0174]

[0175] Among them, C1 and C2 represent the constraints on the user's local computing power and experience quality within the time slot T; C3 indicates that the sum of the task delays in each time slot cannot exceed the length of T; C4 represents the local computing time slot constraint of the drone; C5 and C6 indicate that the user's task allocation constraints must meet the computing rate requirements; C7, C8, C9 and C10 indicate that the user's transmission power, offloaded data volume and task allocation delay must be positive and cannot exceed the maximum value.

[0176] It is observed that the objective function and the constraints C5 and C6 are coupled, so problem P1 is a non-convex optimization problem that is difficult to solve. In order to solve this non-convex problem, this paper introduces the auxiliary variable F = [F 1,2 ,F 1,u ,F 2,u ], where F 1,2 =p 1,2 τ, F 1,u =p 1,u τ, F 2,u =p 2,u τ. For C3 and C6, considering that the time length allocated to each stage is not greater than the total length of the time slot, it can be rewritten as:

[0177] 2τ+t r ≤T (87)

[0178] 2τ+t u ≤T (88)

[0179] L 1,tr ≤R 1,2 τ (89)

[0180] L 1,tr ≤R 1,u τ (90)

[0181] Then problem P1 can be transformed into P2:

[0182]

[0183] It can be seen that problem P2 is still a non-convex problem.

[0184] According to the characteristic of maintaining convexity in perspective operation, if the function P(x) (where x∈R n ) is convex or concave, then its perspective function will also be convex or concave. Since the function log2(1+x) is convex, when t>0, its perspective function is also convex. According to this theory, it can be judged that C7 and C8 in problem P2 are convex. However, due to the existence of C6, P2 is still a non-convex problem. To solve this problem, the formula in C6 is re-expressed as formula (30):

[0185]

[0186] Where r(F,τ) and v(F,τ) are both convex, and the expressions are as follows:

[0187]

[0188] By using the SCA scheme, we approximate v(F,τ) using a first-order Taylor expansion:

[0189]

[0190] Among them, F 1,u (n) ,τ (n) is any point of the nth iteration, Δv(F (n) ) and Δv(τ (n) ) is the value of v(F,τ) with respect to F at the nth iteration. 1,u The gradient of and τ is expressed as:

[0191]

[0192] Then problem P2 can be rewritten as P3:

[0193]

[0194] Problem P3 is a convex problem concerning the optimization variables L, F and t.

[0195] In order to gain a deeper understanding of the P3 problem, this paper uses the Lagrangian dual method to solve it. The Lagrangian problem of P3 can be expressed as:

[0196]

[0197] where λ = {λ1, λ2, ...λ 10} is a non-negative Lagrange multiplier, then its dual function is expressed as follows:

[0198]

[0199] Then we can get the first-order derivative of the expression Ω(L,F,t,λ) with respect to L,F,t:

[0200]

[0201] According to KKT conditions, are all equal to 0, the optimal solution of the corresponding variable can be obtained. By observing formulas (40) and (43), we can see that the variable L 2,tr ,t u is linear, so this paper uses the interior point method to solve and obtain the optimal variable L 2,tr * ,t u * .

[0202] Let formula (39) and (44) equal to 0 to obtain L 1,tr ,F 1,2 The optimal solution is:

[0203]

[0204] For the optimal variable τ * , t r * ,F 1,u * ,F 2,u * This can be obtained by setting formulas (41), (42), (45), and (46) equal to 0:

[0205]

[0206] This paper uses the equal division method to solve formulas (49), (50), (51), and (52). Then, according to formulas (53)-(62), the subgradient method is used to update the value of λ.

[0207] λ1(l+1)=[λ1(l)-Δλ1(l)((L1-L 1,tr )C1-Tf1 max )] + (115)

[0208]

[0209] λ3(l+1)=[λ3(l)-Δλ3(l)(2τ+t r -T)] + (117)

[0210] λ4(l+1)=[λ4(l)-Δλ4(2τ+t u -T)] + (118)

[0211]

[0212] Where [x] + represents max(0,x), l is the number of iterations, and Δλ is the iteration step size.

[0213] Because F 1,2 * =p 1,2 * τ * ,F 1,u * =p 1,u * τ * ,F 2,u * =p 2,u * τ *, therefore, we can further obtain the optimal solution of p {p 12 * ,p 1u * ,p 2u *}. The algorithm flow is as follows:

[0214]

[0215]

[0216] For problem P1, due to the high degree of coupling, it is a non-convex problem that is difficult to solve. In order to solve this problem, first, the auxiliary variable F is used to transform it into problem P2. At this time, P2 is still a non-convex problem. In order to solve this problem, this paper uses the SCA method to decouple it and obtain problem P3. By observation, P3 is a convex problem. In order to solve this convex problem, this paper uses the Lagrange dual method to solve and obtain the optimal variable {F * ,t *}, and further or the optimal variable p * The specific problem-solving steps are summarized in Algorithm 2:

[0217]

[0218] Experimental analysis:

[0219] The following is an analysis of the simulation results on the performance of the proposed algorithm and the impact of different parameters on system performance. The layout model of the considered scenario is as follows Figure 3 As shown, where d 1,2 d 2,u and d u,a They represent the distance between user 1 and user 2, the distance between user 2 and the UAV, and the distance between the UAV and the access point (AP). Considering the reciprocity of uplink and downlink, this paper assumes that the channel gain between user 1 and user 2 can be expressed as h 1,2 =10 -(4 / 2) (d 1,2 ) -α ,The channel gain between user 2 and UAV, and between UAV and AP can be expressed as h i,j =10 -(4 / 2) (d i,j ) -(α / 2) , where (i,j)∈{(2,u),(u,a)}(i,j)∈{(2,u),(u,a)}, α is the path loss index. The specific simulation parameters are shown in Table 1:

[0220]

[0221]

[0222] Figure 4 The comparison between the proposed solution and the other three base station solutions is given. Figure 4 As can be seen in the figure, the figure only shows the comparison of complete offloading, but not the comparison of all local calculations. This is because, due to the limited computing power of the user, if the user only chooses to perform calculations locally, the user cannot complete the calculation within the specified delay. Therefore, the figure does not have a convergence diagram for all local calculations. In addition, it can be seen from the figure that as the number of iterations changes, the scheme proposed in this paper is always better than the other three benchmark schemes. This is because this paper adopts a partial offloading scheme and also adds a ground base station as an auxiliary calculation. Therefore, the system can better balance task scheduling and make the system energy consumption smaller. At the same time, it can be seen that the algorithm begins to converge after about 3 iterations, which shows that the algorithm proposed in this paper has good convergence and high efficiency.

[0223] Figure 5 The relationship between the total energy consumption of the system and the time length T under different unloading schemes is compared in Figure 2. As can be seen from the figure, compared with the other three benchmark schemes, the proposed scheme can achieve the lowest energy consumption, which verifies the effectiveness of the scheme. This is because the scheme proposed in this article takes into account the collaboration of communication and computing at the same time, can fully exploit communication and computing resources, and achieves more efficient network resource utilization compared to other benchmark schemes. In addition, it can be seen that all schemes increase with the increase of time length T. The reason is that as T increases, the system can have more time for task scheduling, so there is more space to search for better optimization solutions, so the energy consumption is reduced.

[0224] Figure 6 The figure shows how the total energy consumption of the system changes with the input data size L1 under different schemes. L1 is the input data size of user 1. As can be seen from the figure, as the number of computing tasks increases, the total energy consumption of the system also increases. This is because when the system time length T is constant, as the number of computing tasks increases, the system needs to consume more energy to process computing tasks, resulting in an increase in the total energy consumption of the system. In addition, as the number of computing tasks increases, the scheme proposed in this paper is always better than the other three base station schemes, which once again shows the superiority and effectiveness of the scheme proposed in this paper.

[0225] exist Figure 7 In this paper, we further studied the impact of the change in the distance between users on the total energy consumption of the system. 2,u =60m,d u,a =60m, and d 1,2From 10m to 40m. As expected, as the distance between user 1 and user 2 increases, the system energy consumption of the proposed scheme and the other three benchmark schemes increases. This is because as the distance between users increases, the data offloading cost also increases, so the required energy consumption also increases. In addition, it can be seen from the figure that the system energy consumption of the proposed scheme and the base station participating in the calculation and completely offloading scheme is almost the same when the distance between users is 10m to 20m, and the energy consumption gap begins to gradually widen after 20m. The reason is that when the distance between user 1 and user 2 is too small, the channel gain between user 1 and user 2 becomes larger, so user 1 will be more greedy to offload more computing tasks to user 2. When the distance between users gradually increases, the channel gain between users also gradually increases. At this time, user 1 will become more sensitive to offloading energy consumption. Therefore, the computing tasks offloaded by user 1 to user 2 will become smaller, while the local computing tasks will increase, resulting in an increase in the total energy consumption of the system. For the scheme where the base station does not participate in auxiliary computing, the difference in system energy consumption between the full offloading and partial offloading schemes does not change significantly. This is because the computing resources of the drone are limited. Therefore, under the constraint of latency, user 1 always performs local computing with the most efficient task call.

[0226] This paper proposes a NOMA-MEC four-node system assisted by drones based on user collaboration, which minimizes the system energy consumption by jointly optimizing the number of user offloaded bits, the transmit power of users and drones, and the time allocation and task allocation of each stage. The SCA method and Lagrangian dual method are used to transform the non-convex problem into a convex problem, and the optimal transmit power, task allocation strategy and time allocation are solved through iterative optimization. The simulation results show that the algorithm has good convergence and shows the best performance when compared with other benchmark schemes.

Claims

1. The energy consumption minimization optimization algorithm of the NOMA-MEC four-node system assisted by drones based on user cooperation includes the following system models: (1) In a non-orthogonal multiple access (NOMA) mobile edge computing (MEC) four-node system assisted by a user-cooperative unmanned aerial vehicle (UAV), there is a remote user 1 and a near user 2, a fixed-position UAV and a ground base station (Access Point, AP). User 1 has limited computing power and cannot communicate directly with the drone and the ground base station. It needs to rely on user 2 to relay the task to the drone for computing. This paper adopts partial offloading to complete its computing task, that is, the user's computing task can be arbitrarily divided into two parts, one part is completed by local computing, and the other part is completed by uplink computing offloading; (2) For the offloading of uplink computing, a scheme based on NOMA and time division multiple access (TDMA) is adopted. Assuming that the computing task is constrained to complete the task within the time length T, user 1 offloads part of the task to user 2 in the first τ stage. In the second τ stage, user 2 offloads part of its own task and the task received from the remote user to the drone in a NOMA manner, where user 1 and user 2 can perform local computing in the entire time slot T. Considering that the user's experience quality and the energy of the drone are limited, in the T-τ stage, the drone decodes the task uploaded by user 2 through the successive interference cancellation (SIC) technology and sends it to the drone in time slot t. u The task of calculating the near-end user in time slot t r In this paper, the task of user 1 is offloaded to the ground base station for calculation. Since the calculation result is very small, the result return time of the downlink is ignored in this paper; (3) The transmission rate from user 1 to user 2 can be expressed as: where p 1,2 is the transmission power of user 1, h 1,2 is the channel gain between user 1 and user 2. B is the total channel bandwidth. In this paper, it is assumed that user 2 uses power p 2,u Unload your own tasks to the drone, using power p 1,u Relay user 1's task to the drone. Assuming the drone decodes user 2's task first and then decodes user 1's task, the transmission rate of user 2 unloading his task to the drone is: The transmission rate from user 2 to the drone when the task unloaded from user 1 is: The transmission rate between the drone and the AP is: where p u,a is the transmission power from the UAV to the base station, h u,a is the channel gain between the UAV and the base station. (4) Since user 2 is used as a relay, the task offloaded by user 1 is subject to the following constraints: L 1,tr ≤min{R 1,2 τ,R 1,u τ} (5) The task that user 2 offloads has the following constraints: L 2,tr ≤R 2,u t (6) The local computing of user 1 and user 2 has the following constraints: (L1-L 1,tr )C1≤Tf1 max (7)(L2-L 2,tr )C2≤Tf2 max (8) Where T is the total delay, L1 and L2 are the total number of tasks to be calculated by user 1 and user 2, respectively. The local computing energy consumption of user 1 and user 2 is: AND 1,loc =(L1-L 1,tr )C1p l (9) Yes 2,loc =(L2-L 2,tr )C2p l (10) Among them, L1 and L2 are the tasks to be processed by user 1 and user 2 respectively, C1 and C2 are the CPU clock cycles of user 1 and user 2 respectively, and p l The energy required per CPU cycle; (5) After user 2 offloads the task to the drone, considering the user experience quality and the limited energy of the drone, the drone chooses to offload user 1's task to the ground base station for calculation and only calculates user 2's task. The unloading time of the UAV is t r The following constraints exist: t r R u,a ≥L 1,tr (11) The calculation time of the UAV is t u The following constraints exist: Among them, f u max is the maximum computing power of the UAV, C u is the CPU clock cycle. In order to complete the task uploaded to the drone within a limited time, the following constraints are imposed: max{t r ,t u }≤T-2τ (13) In order to minimize the unloading energy consumption of the UAV, the transmission power of the UAV can be expressed as: The unloading energy consumption of the UAV can be expressed as: E u,tr =p u,a t r (15) The local computing energy consumption of the drone can be expressed as: E u,loc =ε u (f u max ) 3 t u (16) Among them, ε u is the capacitance switching coefficient of the drone, Cu is the CPU clock cycle of the drone, and f u max Provides CPU computing power for drones. In order to ensure that the task uploaded by user 2 to the drone is completed within the specified time slot, the following constraints exist: Among them, Cu is the CPU computing cycle of the drone; (6) The unloading energy consumption of user 1 and user 2 is: E 1,tr =p 1,2 t (18) E 2,tr =p 2,u t+p 1,u t (19) The energy consumption required by user 1 and user 2 in the system are E1=E 1,loc +E 1,tr (20) E2=E 2,loc +E 2,tr (21) The energy consumption required in the UAV system is expressed as: AND u =And u,loc +E u,tr (22) The total energy consumption of the system is: E1+E2+E u (23) (7) This paper studies a drone-assisted NOMA-MEC network system, which jointly optimizes the user's task allocation L = {L 1,tr ,L 2,tr }, time slot scheduling t = {τ, t r ,t u }, the transmission power of the user and the drone p = {p 12 ,p 2u ,p 1u }Minimize the total energy consumption of the system. Therefore, the mathematical expression of the optimization problem P1 is as follows: Among them, C1 and C2 represent the constraints on the user's local computing power and experience quality within the time slot T; C3 indicates that the sum of the task delays in each time slot cannot exceed the length of T; C4 represents the local computing time slot constraint of the drone; C5 and C6 indicate that the user's task allocation constraints must meet the computing rate requirements; C7, C8, C9 and C10 indicate that the user's transmission power, offloaded data volume and task allocation delay must be positive and cannot exceed the maximum value.

2. According to the user-cooperative drone-assisted NOMA-MEC four-node system energy consumption minimization optimization algorithm described in claim 1, the problem is solved: It is observed that the objective function and the constraints C5 and C6 are coupled, so problem P1 is a non-convex optimization problem that is difficult to solve. In order to solve this non-convex problem, this paper introduces the auxiliary variable F = [F 1,2 ,F 1,u ,F 2,u ],in, F 1,2 =p 1,2 τ, F 1,u =p 1,u τ, F 2,u =p 2,u τ. For C3 and C6, considering that the time length allocated to each stage is not greater than the total length of the time slot, it can be rewritten as: 2τ+t r ≤T (25) 2τ+t u ≤T (26) L 1,tr ≤R 1,2 t (27) L 1,tr ≤R 1,u t (28) Then problem P1 can be transformed into P2: It can be seen that problem P2 is still a non-convex problem. According to the characteristic of maintaining convexity in perspective operation, if the function P(x) (where x∈R n ) is convex or concave, then its perspective function will also be convex or concave. Since the function log2(1+x) is convex, when t>0, its perspective function is also convex. According to this theory, it can be judged that C7 and C8 in problem P2 are convex. However, due to the existence of C6, P2 is still a non-convex problem. To solve this problem, the formula in C6 is re-expressed as formula (30): Where r(F,τ) and v(F,τ) are both convex, and the expressions are as follows: By using the SCA scheme, we approximate v(F,τ) using a first-order Taylor expansion: where F 1,u (n) ,τ (n) is any point of the nth iteration, Δv(F (n) ) and Δv(τ (n) ) is the value of v(F,τ) with respect to F at the nth iteration. 1,u The gradient of and τ is expressed as: Then problem P2 can be rewritten as P3: Problem P3 is a convex problem concerning the optimization variables L, F and t. In order to gain a deeper understanding of the P3 problem, this paper uses the Lagrangian dual method to solve it. The Lagrangian problem of P3 can be expressed as: where λ = {λ1, λ2, ...λ 10 } is a non-negative Lagrange multiplier, then its dual function is expressed as follows: Then we can get the first-order derivative of the expression Ω(L,F,t,λ) with respect to L,F,t: According to KKT conditions, are all equal to 0, the optimal solution of the corresponding variable can be obtained. By observing formulas (40) and (43), we can see that the variable L 2,tr ,t u is linear, so this paper uses the interior point method to solve and obtain the optimal variable L 2,tr * ,t u * . Let formula (39) and (44) equal to 0 to obtain L 1,tr ,F 1,2 The optimal solution is: For the optimal variable τ * , t r * ,F 1,u * ,F 2,u * This can be obtained by setting formulas (41), (42), (45), and (46) equal to 0: This paper uses the equal division method to solve formulas (49), (50), (51), and (52). Then, according to formulas (53)-(62), the subgradient method is used to update the value of λ. λ1(l+1)=[λ1(l)-Δλ1(l)((L1-L 1,tr )C1-Tf1 max )] + (53) λ2(l+1)=[λ2(l)-Δλ2(l)((L2-L 2,tr )C2-Tf2 max )] + (54) λ3(l+1)=[λ3(l)-Δλ3(l)(2τ+t r -T)] + (55) λ4(l+1)=[λ4(l)-Δλ4(2τ+t u -T)] + (56) Where [x] + represents max(0,x), l is the number of iterations, and Δλ is the iteration step size. Because F 1,2 * =p 1,2 * τ * ,F 1,u * =p 1,u * τ * ,F 2,u * =p 2,u * τ * , therefore, we can further obtain the optimal solution of p The algorithm flow is as follows: For problem P1, due to the high degree of coupling, it is a non-convex problem that is difficult to solve. In order to solve this problem, first, the auxiliary variable F is used to transform it into problem P2. At this time, P2 is still a non-convex problem. In order to solve this problem, this paper uses the SCA method to decouple it and obtain problem P3. By observation, P3 is a convex problem. In order to solve this convex problem, this paper uses the Lagrange dual method to solve and obtain the optimal variable {F * ,t * }, and further or the optimal variable p * The specific problem-solving steps are summarized in Algorithm 2:

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