CN112073978A - Method for optimizing computing efficiency in multi-carrier NOMA mobile edge computing system - Google Patents

Method for optimizing computing efficiency in multi-carrier NOMA mobile edge computing system Download PDF

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CN112073978A
CN112073978A CN202010799592.3A CN202010799592A CN112073978A CN 112073978 A CN112073978 A CN 112073978A CN 202010799592 A CN202010799592 A CN 202010799592A CN 112073978 A CN112073978 A CN 112073978A
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CN112073978B (en
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许方铖
虞湘宾
蔡嘉丽
王光英
党小宇
朱秋明
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Nanjing University of Aeronautics and Astronautics
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    • H—ELECTRICITY
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    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
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    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
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    • H—ELECTRICITY
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    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
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    • H04W28/0215—Traffic management, e.g. flow control or congestion control based on user or device properties, e.g. MTC-capable devices
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Abstract

The invention discloses a method for optimizing the computational efficiency in a mobile edge computing system of multi-carrier NOMA (non-orthogonal multiple access), which jointly optimizes the computing resources and the transmitting power of users and the sub-channel scheduling of the system to ensure the fairness among the users based on the maximum-minimum fairness principle, provides an effective computational efficiency optimization algorithm based on a Big-M (Big-matrix) method, punishment sequence convex programming and generalized fractal programming, can start iteration from any initial point and finally converge on a feasible suboptimal solution, and can enable the system to achieve higher computational efficiency with polynomial time complexity.

Description

Method for optimizing computing efficiency in multi-carrier NOMA mobile edge computing system
The technical field is as follows:
the invention belongs to the field of mobile communication, relates to a resource allocation method of a mobile communication system, and particularly relates to a calculation efficiency optimization method in a mobile edge calculation system of multi-carrier NOMA.
Background art:
the rapid growth of mobile communication services has prompted tremendous advances in wireless communication and networking technologies over the past decade, which has led to mobile cloud computing. However, users are often far from the cloud data center, which may result in lengthy data exchange times between them. Therefore, mobile cloud computing has difficulty meeting the computing service requirements of various real-time mobile applications. Compared with the traditional Mobile cloud Computing, the Mobile Edge Computing (MEC) has a wide application prospect in the Internet of things as an emerging technology. The core idea of the MEC is to disperse the computing servers to the edge of the wireless network close to the user, thereby improving the computing power of the user and reducing the task delay and energy consumption.
Non-Orthogonal Multiple Access (NOMA) is considered a promising Multiple Access scheme in future wireless communication systems. The basic concept of NOMA is to provide access services to multiple users simultaneously in one orthogonal resource block by using superposition coding and multi-user detection techniques. This is very different from Orthogonal Multiple Access schemes, such as Orthogonal Frequency Division Multiple Access (OFDMA), which serves at most one user in one Frequency domain resource block. However, if multiple users are multiplexed in one orthogonal resource block, the system complexity and decoding delay will become very high. Therefore, a multi-carrier NOMA technology, namely a combination of NOMA and OFDMA, can be adopted to meet the requirement of large-scale connectivity of the MEC system and improve the transmission efficiency. In a multi-carrier NOMA based MEC system, all users are divided into several NOMA groups, one NOMA group may occupy one frequency domain resource block, i.e. different frequency domain resource blocks are OFDMA, the same frequency domain resource block is NOMA. Research has shown that the application of multi-carrier NOMA in MEC system can greatly improve the system performance compared with orthogonal multiple access. In the existing literature, latency minimization, energy consumption minimization and computation bit maximization are the main concerns of the MEC system resource allocation. However, with the rapid growth of communication services, the communication industry is becoming a major energy consumption field. In such a context, it is important to consider green communication in future MEC systems, especially an index of computational efficiency, i.e. the computational power per joule of energy. Based on the above discussion, the invention researches a calculation efficiency optimization method in a multi-carrier NOMA mobile edge calculation system, and the method is oriented to large-scale connection and green communication with high calculation efficiency in a future MEC system.
The invention content is as follows:
aiming at a mobile edge computing system of multi-carrier NOMA, in order to improve the computing efficiency of the system and ensure the fairness of users, the invention maximizes the minimum value of the computing efficiency of all users based on the maximum-minimum fairness principle, jointly optimizes the sub-channel scheduling, the local CPU frequency of the users and the transmitting power of the users, provides a computing efficiency optimization method in the mobile edge computing system of multi-carrier NOMA, and can obtain a better computing efficiency optimization scheme with polynomial time complexity.
The technical scheme adopted by the invention is as follows: a method for optimizing the calculation efficiency in a multi-carrier NOMA mobile edge calculation system comprises the following steps:
step S1: establishing a multi-carrier non-orthogonal multiple access (NOMA) -based Mobile Edge Computing (MEC) system, which consists of K users and a wireless access node (AP) connected with an MEC server, wherein all the users only have one transmitting antenna and a base station of a single receiving antenna to establish a communication link, and the bandwidth W used by the system is divided into N mutually-orthogonal subchannels, and the set of the subchannels is defined as
Figure BDA0002626894370000021
Then it is first
Figure BDA0002626894370000022
The bandwidth used by the sub-channel is WnSatisfy the following requirements
Figure BDA0002626894370000023
Each subchannel is modeled as a frequency-flat block fading channel, i.e. a channelThe variation is in time block units, the sub-channel in each time block is kept unchanged, a plurality of users share the same sub-channel through an uplink NOMA protocol, meanwhile, a calculation task is uploaded to an MEC server of the wireless access node, and the calculation efficiency of the users is defined as the ratio of the local calculation of the users and the total data amount (bits) uploaded to the MEC server to the consumed energy;
step S2: in order to ensure user fairness, a calculation efficiency optimization problem based on a maximum-minimum fairness principle is established, the optimization target is the minimum value of the calculation efficiency of all the users, the optimization variables are subchannel scheduling, local CPU frequency and transmitting power, and the optimization constraints are the minimum calculation bit number, the maximum power consumption, the maximum local CPU frequency, the maximum number of supported users of subchannels and the maximum number of accessible subchannels of the users;
s3, the optimization problem in the step S2 belongs to a non-convex mixed integer non-linear programming problem, a Big-M method is used for decomposing a product item of sub-channel scheduling and transmitting power, and then extra constraint is applied to equivalently convert the problem into a continuous optimization problem;
step S4: aiming at the optimization problem in the step S3, firstly, based on the sequence convex programming, a series of pseudo-convex optimization problems are obtained by using a first-order Taylor expansion, then each pseudo-convex optimization problem is iteratively solved by using a Dinkelbach iterative algorithm based on the generalized fractional programming theory, and simultaneously, an auxiliary variable is introduced to equivalently convert a non-smooth objective function into a smooth linear objective function;
step S5: aiming at the optimization problem in the step S4, a relaxation variable and a penalty factor are introduced, a calculation efficiency optimization algorithm of polynomial time complexity based on a Big-M method, a penalty sequence convex plan and a generalized fractional plan is provided, iteration is started from any initial point, and a feasible suboptimal solution is converged
Further, step S1 is specifically as follows:
for a time block of duration T, defining the set of all users as
Figure BDA0002626894370000031
The number of bits calculated by the kth user computing locally is then
Figure BDA0002626894370000032
And the energy consumed is
Figure BDA0002626894370000033
Wherein C iskIndicating the number of CPU cycles required by the user to calculate the amount of 1-bit task data, fkIndicates the local CPU frequency, gamma, of the userkThe coefficients are calculated for the respective CPUs. Order to
Figure BDA0002626894370000034
Denotes a subchannel scheduling variable, wherek,n1 denotes the part of the computation task that the kth user uploads using the nth subchannel, ρk,n0 means not used. According to the uplink NOMA protocol, all users using the nth sub-channel upload their respective partial computation tasks at the same time, and the received signal of the AP on the nth sub-channel may be represented as:
Figure BDA0002626894370000035
wherein h isk,nRepresents the channel fading coefficient of the k user on the n sub-channel, gk,nFor corresponding channel gain, sk,nIndicating the normalized signal transmitted by the kth user to the nth sub-channel
Figure BDA0002626894370000036
pk,nIs the corresponding transmission power, znIs white Gaussian noise on the nth sub-channel, subject to a complex Gaussian distribution, i.e.
Figure BDA0002626894370000037
n0Representing a single-sided power spectral density. On each sub-channel, AP adopts serial interference elimination technique, and decodes user signal in turn according to user channel gain, so that the k-th user is on the n-th sub-channelThe achievable rates are expressed as follows:
Figure BDA0002626894370000038
wherein the content of the first and second substances,
Figure BDA0002626894370000041
representing a set of users
Figure BDA0002626894370000042
All users having channel gains less than the channel gain of the k-th user. The bit number of the calculation task uploaded by the kth user on the nth sub-channel is
Figure BDA0002626894370000043
And corresponding energy consumption of
Figure BDA0002626894370000044
In which ξkRepresenting the power amplifier coefficient, p, of the k-th usercThe power consumption of the circuit is fixed. The computational efficiency η of the kth user in the above systemkDefined as the ratio of the total amount of data (bits) locally calculated and uploaded to the MEC server by the user in the first phase to the energy consumed, i.e.:
Figure BDA0002626894370000045
further, step S3 is specifically as follows: the optimization target is to maximize the minimum value of the computational efficiency of all users, the scheduling of sub-channels, the local CPU frequency and the transmission power of the users, and the specific optimization problem is expressed as follows:
Figure BDA0002626894370000046
therein, constraining
Figure BDA0002626894370000047
In (1)
Figure BDA0002626894370000048
Representing the minimum computation rate (bits per second) for the kth user, with constraints
Figure BDA0002626894370000049
In (1)
Figure BDA00026268943700000410
Represents the maximum power consumption of the kth user, constraint
Figure BDA00026268943700000411
Maximum local CPU frequency, constraint, representing the kth user
Figure BDA00026268943700000412
Representing the nth sub-channel to multiple support MnThe users upload the task and the discrete variable rho at the same timek,nAnd a continuous variable pk,nProduct term of (p)k,npk,nDecomposing the product term rho by using Big-M methodk,npk,nFirst, introducing an auxiliary variable
Figure BDA00026268943700000413
To replace all product terms ρ in (4)k,npk,nThen, there are:
Figure BDA00026268943700000414
wherein the content of the first and second substances,
Figure BDA0002626894370000051
the following constraints are then applied to (4):
Figure BDA0002626894370000052
further, restricting in (4)
Figure BDA0002626894370000053
And constraint
Figure BDA0002626894370000054
Equivalent transformation into:
Figure BDA0002626894370000055
then (4) can equivalently be translated into the following more easily solved continuous optimization problem:
Figure BDA0002626894370000056
wherein the content of the first and second substances,
Figure BDA0002626894370000057
further, step S5 is specifically as follows:
s5.1, initializing the maximum inner layer and outer layer iteration times I1And I2The outer layer iteration number t is 0, and the objective function value of (8)(0)Penalty factor τ(0)Increment factor mu, penalty factor upper bound taumaxSum of penalty factors
Figure BDA0002626894370000058
And penalty function value
Figure BDA0002626894370000059
Randomly generating an initiation point
Figure BDA00026268943700000510
S5.2, starting outer layer circulation;
S5.3，t＝t+1；
s5.4, setting the inner layer iteration sequence number q to be 0, and programming an iteration factor lambda in a generalized fractional manner(0)；
S5.5, starting inner layer circulation;
S5.6，q＝q+1；
s5.7, solving the optimal solution
Figure BDA00026268943700000511
S5.8, if
Figure BDA0002626894370000061
The inner layer convergence flag is set to true; if not, then,
Figure BDA0002626894370000062
s5.9, the inner layer circulates until the inner layer convergence mark is true or q is more than or equal to I2；
S5.10，
Figure BDA0002626894370000063
S5.11, if
Figure BDA0002626894370000064
And is
Figure BDA0002626894370000065
Setting an outer convergence flag to true; otherwise, according to theta(q)Updating
Figure BDA0002626894370000066
τ(t)＝min{μτ(t-1),τmax}；
S5.12, outer layer circulation is carried out until the outer layer convergence mark is true or t is more than or equal to I1；
S5.13, outputting a feasible suboptimal solution
Figure BDA0002626894370000067
The invention has the following beneficial effects: the method for optimizing the computing efficiency in the mobile edge computing system of the multi-carrier NOMA has polynomial time complexity, and can effectively improve the computing efficiency of the system and ensure the fairness among users. The method fully considers the internal structure of the original optimization problem, firstly, a Big-M method is used for equivalently converting the problem into a continuous optimization problem which is easier to solve, then, a non-smooth objective function and relaxed non-convex constraint are converted by introducing auxiliary variables, a calculation efficiency optimization algorithm based on the Big-M method, punishment sequence convex programming and generalized fractal programming is provided, iteration can be started from any initial point and convergence to a feasible suboptimal solution, and finally, an effective calculation efficiency optimization scheme is obtained.
Description of the drawings:
FIG. 1 is a flow chart of a system in an embodiment of the invention.
FIG. 2 is a diagram of a system in an embodiment of the invention.
Fig. 3 is a simulation graph of a partial unloading scheme proposed in an embodiment of the present invention and two other comparison schemes.
Fig. 4 is a simulation graph of the multi-carrier NOMA scheme proposed in the embodiment of the present invention and the conventional OFDMA scheme.
The specific implementation mode is as follows:
the invention will be further described with reference to the accompanying drawings.
First, system model
The system model involved in the computational efficiency optimization method in the multi-carrier NOMA mobile edge computing system of the present invention is shown in fig. 2, and the system is composed of K users and a wireless access node (AP) connected to the MEC server, where all users have only one transmitting antenna and a single receiving antenna base station to establish a communication link, and it is assumed that the AP can obtain complete information state information and the computation information of all users. The bandwidth W used by the system is divided into N mutually orthogonal subchannels, and the set of subchannels is defined as
Figure BDA0002626894370000071
Then it is first
Figure BDA0002626894370000072
The bandwidth used by the sub-channel is WnSatisfy the following requirements
Figure BDA0002626894370000073
And the different sub-channels do not interfere with each other. Each subchannel is modeled as a frequency-flat block fading channel, i.e. the channel variation is in time blocks, but the subchannels in each time block remain unchanged, wherein a time block can be divided into three stages as follows:
1) in the first stage, a multi-carrier NOMA protocol is adopted for uplink transmission between users and an AP, the K users are divided into N mutually exclusive user groups, different user groups access different sub-channels, all users in the same user group share one sub-channel through the uplink NOMA protocol, and simultaneously, tasks of the users are uploaded to an MEC server on the AP;
2) in the second stage, firstly, the AP adopts a serial interference elimination technology to decode the user signals superposed in each sub-channel, the decoding sequence of each sub-channel is the descending order of the user channel gain, and then the AP transfers the decoded user tasks to the MEC server for calculation;
3) in the third phase, the AP feeds back the calculation result of the MEC server to all users;
since the MEC server has a strong computing power and a small amount of data of the computing result, it can be considered that the ratio of the time occupied by the second stage and the third stage to one time block is almost 0. The computational efficiency of the system is therefore mainly determined by the first stage. In order to improve the computing efficiency of the user, the system adopts a partial unloading mode, namely the local computing of the user and the remote computing of the MEC server can be simultaneously carried out. For a time block of duration T, defining the set of all users as
Figure BDA0002626894370000074
The number of bits calculated by the kth user computing locally is then
Figure BDA0002626894370000075
And the energy consumed is
Figure BDA0002626894370000076
Wherein C iskIndicating the number of CPU cycles required by the user to calculate the amount of 1-bit task data, fkIndicates the local CPU frequency, gamma, of the userkThe coefficients are calculated for the respective CPUs. Since the system adopts the multi-carrier NOMA technology to carry out the task unloading of the user, the order is given
Figure BDA0002626894370000077
Denotes a subchannel scheduling variable, wherek,n1 denotes the part of the computation task that the kth user uploads using the nth subchannel, ρk,n0 means not used. According to the uplink NOMA protocol, all users using the nth sub-channel can upload their respective partial computation tasks at the same time, and the received signal of the AP on the nth sub-channel can be expressed as:
Figure BDA0002626894370000081
wherein h isk,nRepresents the channel fading coefficient of the k user on the n sub-channel, gk,nFor corresponding channel gain, sk,nIndicating the normalized signal transmitted by the kth user to the nth sub-channel
Figure BDA0002626894370000082
pk,nIs the corresponding transmission power, znIs white Gaussian noise on the nth sub-channel, subject to a complex Gaussian distribution, i.e.
Figure BDA0002626894370000083
N here0Representing a single-sided power spectral density. On each sub-channel, the AP uses the successive interference cancellation technique to decode the user signal in sequence according to the channel gain of the user, and the uploading reachable rate of the kth user on the nth sub-channel is represented as follows:
Figure BDA0002626894370000084
wherein the content of the first and second substances,
Figure BDA0002626894370000085
representing a set of users
Figure BDA0002626894370000086
All users having channel gains less than the channel gain of the k-th user. Therefore, the number of bits of the calculation task uploaded by the kth user on the nth sub-channel is equal to
Figure BDA0002626894370000087
And corresponding energy consumption of
Figure BDA0002626894370000088
In which ξkRepresenting the power amplifier coefficient, p, of the k-th usercThe power consumption of the circuit is fixed. The computational efficiency η of the kth user in the above systemkDefined as the ratio of the total amount of data (bits) locally calculated and uploaded to the MEC server by the user in the first phase to the energy consumed, i.e.:
Figure BDA0002626894370000089
second, maximum-minimum fairness principle-based calculation efficiency optimization problem modeling and solving process
In order to improve the computing efficiency of the system and ensure the fairness of the users, a computing efficiency optimization problem based on a maximum-minimum fairness principle is established, the optimization target is to maximize the minimum value in the computing efficiency of all the users, the scheduling of sub-channels, the local CPU frequency and the transmitting power of the users, and the specific optimization problem is expressed as follows:
Figure BDA0002626894370000091
therein, constraining
Figure BDA0002626894370000092
In (1)
Figure BDA0002626894370000093
Representing the minimum computation rate (bits per second) for the kth user, with constraints
Figure BDA0002626894370000094
In (1)
Figure BDA0002626894370000095
Represents the maximum power consumption of the kth user, constraint
Figure BDA0002626894370000096
Maximum local CPU frequency, constraint, representing the kth user
Figure BDA0002626894370000097
Representing the nth sub-channel to multiple support MnIndividual users upload tasks, constraints simultaneously
Figure BDA0002626894370000098
And constraint
Figure BDA0002626894370000099
It is ensured that a user can only upload its tasks on one sub-channel. It can be found that the optimization problem (4) belongs to a non-convex mixed integer nonlinear programming problem, and a global optimal solution is difficult to find in the polynomial time complexity, so that a polynomial time complexity calculation efficiency optimization algorithm is considered to be designed to obtain a better calculation efficiency optimization scheme. Due to the presence of the discrete variable ρ in (4)k,nAnd a continuous variable pk,nProduct term of (p)k,npk,nIt is conceivable to decompose the product term ρ by the Big-M methodk,npk,nFirst, introducing an auxiliary variable
Figure BDA00026268943700000910
To replace all product terms ρ in (4)k,npk,nThen, there are:
Figure BDA00026268943700000911
wherein the content of the first and second substances,
Figure BDA00026268943700000912
the following constraints are then applied to (4):
Figure BDA00026268943700000913
further, restricting in (4)
Figure BDA00026268943700000914
And constraint
Figure BDA00026268943700000915
Equivalent transformation into:
Figure BDA0002626894370000101
then (4) can equivalently be translated into the following more easily solved continuous optimization problem:
Figure BDA0002626894370000102
wherein the content of the first and second substances,
Figure BDA0002626894370000103
in order to solve the non-Convex maximum-minimum fractional Programming problem in (8), a method of jointly using Sequential Convex Programming (SCP) and generalized fractional Programming may be considered, which includes the following steps: in the first step, using the first order taylor expansion in SCP to obtain the concave lower bound form of the non-concave objective function and to approximate the non-convex constraints to the corresponding convex constraints, then at the tth SCP iteration, (8) can be approximated to the pseudo-convex optimization problem as follows:
Figure BDA0002626894370000104
wherein the content of the first and second substances,
Figure BDA0002626894370000105
Figure BDA0002626894370000106
Figure BDA0002626894370000107
and
Figure BDA0002626894370000108
are respectively as
Figure BDA0002626894370000109
And ρi,nValue at t-1 SCP iteration.
Because (9) conforms to the solving form of the generalized fractional programming, the optimal solution of (9) can be efficiently solved by adopting a generalized Dinkelbach iterative algorithm, and then the following problems need to be solved when the q-th generalized Dinkelbach iteration is performed:
Figure BDA00026268943700001010
wherein λ is(q-1)Is an iteration factor in the q-1 generalized Dinkelbach iteration. In the qth generalized Dinkelbach iteration, the solution at a given lambda needs to be solved(q-1)Optimal solution Θ of (12) below(q)Then updating the iteration factor needed by the next iteration
Figure BDA0002626894370000111
Introducing auxiliary variables
Figure BDA0002626894370000112
Equivalently converting a non-smooth objective function to a smooth linear objective function, the equivalent form of (10) can be written as:
Figure BDA0002626894370000113
based on the analysis, an iteration algorithm with an outer layer based on an SCP method and an inner layer based on a generalized Dinkelbach method can be adopted to obtain the feasible suboptimal solution of the step (8). However, the algorithm must require one feasible point of (8) as the initial point of the iteration, and feasible points other than the convex optimization problem are often difficult to find. To avoid the initial point requirement, we can consider using penalty SCP method, and then the optimization of the solution required for the t-th iteration of penalty SCP can be expressed as:
Figure BDA0002626894370000114
wherein, tau(t-1)Is the penalty factor for the t-1 th iteration. The update of the penalty factor is given by:
τ(t)＝min{μτ(t-1),τmax}, (29)
where μ is an increasing factor, τmaxIs an upper bound on the penalty factor. Further, (12) for the convex optimization problem, the existing convex optimization tools can be used to solve, such as CVX, CVXQUAD, YALMIP, and the like.
In summary, the invention provides a polynomial time complexity iterative algorithm based on a Big-M method, penalty sequence convex programming and generalized fractal programming, as shown in algorithm 1 in the following table.
Figure BDA0002626894370000121
Theorem 1: algorithm 1 may converge to a locally optimal solution of (8).
And (3) proving that: firstly, an iterative algorithm based on SCP and generalized fractional programming is proved and marked as an algorithm 2. Order to
Figure BDA0002626894370000122
And
Figure BDA0002626894370000123
respectively representing the optimal solution and the optimal objective function value of (9) at the t-th SCP iteration and simultaneously
Figure BDA0002626894370000124
The objective function value in (8) is expressed as
Figure BDA0002626894370000125
Then there are:
Figure BDA0002626894370000131
wherein (a) is true because
Figure BDA0002626894370000132
Is that
Figure BDA0002626894370000133
Is satisfied because the generalized Dinkelbach iterative algorithm ensures that the optimal solution of (9) can be obtained, and (c) is satisfied because the generalized Dinkelbach iterative algorithm uses
Figure BDA0002626894370000134
As the first order taylor expansion point. From (14), the objective function value of (8) is non-decreasing. And since the objective function value of (8) exists in the upper bound, the algorithm 2 can gradually converge to the local optimal solution of (8). Next, we can demonstrate the convergence of algorithm 1. If the penalty factor τ is large enough and the sum of the slack variables is very close to zero, (12) can be rewritten as (11), at which point algorithm 1 is equivalent to algorithm 2, indicating that algorithm 1 will converge to the locally optimal solution of (8).
The computational efficiency performance of the algorithm 1 proposed by the present invention is verified by the simulation of Matlab below. The users are randomly distributed in an area of 1km multiplied by 1km, the base station is positioned in the center and has the height of 100m, the channel model is a free space loss propagation model, and the gain of a reference channel at the position of 1m is-50 dB. To facilitate the numerical comparison, the unit of computational efficiency expressed in the simulation is "bits/Joule/Hz". It is not assumed that the maximum power consumption of all users is uniform, i.e.
Figure BDA0002626894370000135
Default parameter settings are as followsThe following are listed in the table:
Figure BDA0002626894370000136
Figure BDA0002626894370000141
fig. 3 compares the computational efficiency performance of the partial offload scheme proposed by the present invention with two other comparison schemes, where in the local computation scheme, all user input tasks are computed locally only, and are not uploaded to the MEC server for computation, and in the full offload scheme, all user input tasks are computed locally only on the MEC server, and are not computed locally. It can be seen from fig. 3 that the partial offload scheme clearly has a higher computational efficiency performance than the other two comparison schemes, especially when compared to the local-only computation scheme. This is because the partial offload scheme can flexibly adjust the resource allocation for task offloading and local computing. However, the local computation scheme performs local computation without considering channel conditions, while the all-offload scheme completely uploads the user's task to the UAV-MEC server even if the channel conditions are poor, both of which significantly reduce the computational efficiency performance of the system.
The computational efficiency performance of the proposed multi-carrier NOMA based partial offloading scheme of the present invention is compared to the OFDMA based partial offloading scheme in fig. 4. In the OFDMA scheme, each user can use at most one subchannel, each subchannel supports at most one user access, the number of subchannels in the OFDMA scheme is set to 8 in order to ensure a fair comparison, and other parameters are consistent with the multicarrier NOMA scheme. As can be seen from fig. 4, the multi-carrier NOMA scheme is clearly superior to the OFDMA scheme because the multi-carrier NOMA can simultaneously serve more users on one sub-channel compared to the OFDMA, thereby improving the computational efficiency performance of the system.
In conclusion, the computational efficiency optimization method provided by the invention can effectively improve the computational efficiency performance of the mobile edge computing system of the multi-carrier NOMA and ensure the fairness of users, and meanwhile, the method has the advantages of simple implementation steps, low polynomial time complexity and obvious effect. This fully demonstrates the effectiveness of the computational efficiency optimization method in the mobile edge computation of multi-carrier NOMA proposed by the present invention.
The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.

Claims (4)

1. A method for optimizing the computational efficiency in a multi-carrier NOMA mobile edge computing system is characterized in that: the method comprises the following steps:
step S1: establishing a multi-carrier non-orthogonal multiple access (NOMA) -based Mobile Edge Computing (MEC) system, which consists of K users and a wireless access node (AP) connected with an MEC server, wherein all the users only have one transmitting antenna and a base station of a single receiving antenna to establish a communication link, and the bandwidth W used by the system is divided into N mutually-orthogonal subchannels, and the set of the subchannels is defined as
Figure FDA0002626894360000011
Then it is first
Figure FDA0002626894360000012
The bandwidth used by the sub-channel is WnSatisfy the following requirements
Figure FDA0002626894360000013
Each subchannel is modeled as a frequency flat block fading channel, namely the channel variation is in time blocks, the subchannel in each time block is kept unchanged, a plurality of users share the same subchannel through an uplink NOMA protocol, meanwhile, a calculation task is uploaded to an MEC server of a wireless access node, and the calculation efficiency of the users is defined as the local calculation of the users and the total data amount (bits) and the consumed data amount (bits) uploaded to the MEC serverThe ratio of energy consumed;
step S2: in order to ensure user fairness, a calculation efficiency optimization problem based on a maximum-minimum fairness principle is established, the optimization target is the minimum value of the calculation efficiency of all the users, the optimization variables are subchannel scheduling, local CPU frequency and transmitting power, and the optimization constraints are the minimum calculation bit number, the maximum power consumption, the maximum local CPU frequency, the maximum number of supported users of subchannels and the maximum number of accessible subchannels of the users;
s3, the optimization problem in the step S2 belongs to a non-convex mixed integer non-linear programming problem, a Big-M method is used for decomposing a product item of sub-channel scheduling and transmitting power, and then extra constraint is applied to equivalently convert the problem into a continuous optimization problem;
step S4: aiming at the optimization problem in the step S3, firstly, based on the sequence convex programming, a series of pseudo-convex optimization problems are obtained by using a first-order Taylor expansion, then each pseudo-convex optimization problem is iteratively solved by using a Dinkelbach iterative algorithm based on the generalized fractional programming theory, and simultaneously, an auxiliary variable is introduced to equivalently convert a non-smooth objective function into a smooth linear objective function;
step S5: aiming at the optimization problem in the step S4, a relaxation variable and a penalty factor are introduced, a calculation efficiency optimization algorithm of polynomial time complexity based on a Big-M method, a penalty sequence convex plan and a generalized fractional plan is provided, iteration is started from any initial point, and a feasible suboptimal solution is converged.
2. A method of computational efficiency optimization in a multi-carrier NOMA mobile edge computing system according to claim 1, characterized by: step S1 is specifically as follows:
for a time block of duration T, defining the set of all users as
Figure FDA0002626894360000021
The number of bits calculated by the kth user computing locally is then
Figure FDA0002626894360000022
And the energy consumed is
Figure FDA0002626894360000023
Wherein C iskIndicating the number of CPU cycles required by the user to calculate the amount of 1-bit task data, fkIndicates the local CPU frequency, gamma, of the userkThe coefficients are calculated for the respective CPUs. Order to
Figure FDA0002626894360000024
Denotes a subchannel scheduling variable, wherek,n1 denotes the part of the computation task that the kth user uploads using the nth subchannel, ρk,n0 means not used. According to the uplink NOMA protocol, all users using the nth sub-channel upload their respective partial computation tasks at the same time, and the received signal of the AP on the nth sub-channel may be represented as:
Figure FDA0002626894360000025
wherein h isk,nRepresents the channel fading coefficient of the k user on the n sub-channel, gk,nFor corresponding channel gain, sk,nIndicating the normalized signal transmitted by the kth user to the nth sub-channel
Figure FDA0002626894360000026
pk,nIs the corresponding transmission power, znIs white Gaussian noise on the nth sub-channel, subject to a complex Gaussian distribution, i.e.
Figure FDA0002626894360000027
n0Representing a single-sided power spectral density. On each sub-channel, the AP uses the successive interference cancellation technique to decode the user signal in sequence according to the channel gain of the user, and the uploading reachable rate of the kth user on the nth sub-channel is represented as follows:
Figure FDA0002626894360000028
wherein the content of the first and second substances,
Figure FDA0002626894360000029
representing a set of users
Figure FDA00026268943600000210
All users having channel gains less than the channel gain of the k-th user. The bit number of the calculation task uploaded by the kth user on the nth sub-channel is
Figure FDA00026268943600000211
And corresponding energy consumption of
Figure FDA00026268943600000212
In which ξkRepresenting the power amplifier coefficient, p, of the k-th usercThe power consumption of the circuit is fixed. The computational efficiency η of the kth user in the above systemkDefined as the ratio of the total amount of data (bits) locally calculated and uploaded to the MEC server by the user in the first phase to the energy consumed, i.e.:
Figure FDA0002626894360000031
3. a method of computational efficiency optimization in a multi-carrier NOMA mobile edge computing system according to claim 1, characterized by: step S3 is specifically as follows: the optimization target is to maximize the minimum value of the computational efficiency of all users, the scheduling of sub-channels, the local CPU frequency and the transmission power of the users, and the specific optimization problem is expressed as follows:
Figure FDA0002626894360000032
therein, constraining
Figure FDA0002626894360000033
In (1)
Figure FDA0002626894360000034
Representing the minimum computation rate (bits per second) for the kth user, with constraints
Figure FDA0002626894360000035
In (1)
Figure FDA0002626894360000036
Represents the maximum power consumption of the kth user, constraint
Figure FDA0002626894360000037
Maximum local CPU frequency, constraint, representing the kth user
Figure FDA0002626894360000038
Representing the nth sub-channel to multiple support MnEach user uploads tasks at the same time. Due to the presence of a discrete variable ρk,nAnd a continuous variable pk,nProduct term of (p)k, npk,nDecomposing the product term rho by using Big-M methodk,npk,nFirst, introducing an auxiliary variable
Figure FDA0002626894360000039
To replace all product terms ρ in (4)k,npk,nThen, there are:
Figure FDA00026268943600000310
wherein the content of the first and second substances,
Figure FDA00026268943600000311
the following constraints are then applied to (4):
Figure FDA0002626894360000041
further, restricting in (4)
Figure FDA0002626894360000042
And constraint
Figure FDA0002626894360000043
Equivalent transformation into:
Figure FDA0002626894360000044
then (4) can equivalently be translated into the following more easily solved continuous optimization problem:
Figure FDA0002626894360000045
wherein the content of the first and second substances,
Figure FDA0002626894360000046
4. a method of computational efficiency optimization in a multi-carrier NOMA mobile edge computing system according to claim 1, characterized by: step S5 is specifically as follows:
s5.1, initializing the maximum inner layer and outer layer iteration times I1And I2The outer layer iteration number t is 0, and the objective function value of (8)(0)Penalty factor τ(0)Increment factor mu, penalty factor upper bound taumaxSum of penalty factors
Figure FDA0002626894360000047
And penalty function value
Figure FDA0002626894360000048
Randomly generating an initiation point
Figure FDA0002626894360000049
S5.2, starting outer layer circulation;
S5.3，t＝t+1；
s5.4, setting the inner layer iteration sequence number q to be 0, and programming an iteration factor lambda in a generalized fractional manner(0)；
S5.5, starting inner layer circulation;
S5.6，q＝q+1；
s5.7, solving the optimal solution
Figure FDA00026268943600000410
S5.8, if
Figure FDA00026268943600000411
The inner layer convergence flag is set to true; if not, then,
Figure FDA00026268943600000412
s5.9, the inner layer circulates until the inner layer convergence mark is true or q is more than or equal to I2；
S5.10，
Figure FDA0002626894360000051
S5.11, if
Figure FDA0002626894360000052
And is
Figure FDA0002626894360000053
Setting an outer convergence flag to true; otherwise, according to theta(q)Updating
Figure FDA0002626894360000054
τ(t)＝min{μτ(t-1),τmax}；
S5.12, outer layer circulation is carried out until the outer layer convergence mark is true or t is more than or equal to I1；
S5.13, outputting a feasible suboptimal solution
Figure FDA0002626894360000055
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