CN111464216A - Mobile edge calculation time delay minimization method based on large-scale MIMO - Google Patents

Mobile edge calculation time delay minimization method based on large-scale MIMO Download PDF

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CN111464216A
CN111464216A CN202010154662.XA CN202010154662A CN111464216A CN 111464216 A CN111464216 A CN 111464216A CN 202010154662 A CN202010154662 A CN 202010154662A CN 111464216 A CN111464216 A CN 111464216A
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time delay
users
user
optimal solution
maximum
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CN111464216B (en
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孙钢灿
孙继威
郝万明
赵飞
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Zhengzhou University Industrial Research Institute Co ltd
Zhengzhou University
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Zhengzhou University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/50—Allocation or scheduling criteria for wireless resources
    • H04W72/54—Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/542—Allocation or scheduling criteria for wireless resources based on quality criteria using measured or perceived quality
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention discloses a mobile edge calculation time delay minimization method based on large-scale MIMO, which comprises the following steps: the method comprises the following steps: calculating the channel gain of each user according to the channel state information, and performing normalization processing to obtain a data migration rate; step two: in consideration of the maximum power and energy constraint existing in practice and the fairness among users, the practical maximum transmission power is obtained under the condition of meeting the maximum energy constraint, and then the optimal solution is obtained; step three: and according to the optimal solution, performing wireless resource allocation, and allocating each user to realize the same overall delay for all users. The invention can utilize limited computing resources to minimize time delay under the condition of maximum transmission power and energy consumption constraint by joint distribution of wireless and computing resources while carrying out a large amount of user task migration computation, and can also ensure stable migration rate and less signal overhead by using the invention.

Description

Mobile edge calculation time delay minimization method based on large-scale MIMO
Technical Field
The invention relates to the technical field of communication signal processing, in particular to a mobile edge calculation time delay minimization method based on large-scale MIMO.
Background
With the arrival of the big data era, the network requirements of low time delay and low energy consumption are more and more demanding, and Mobile Edge Computing (MEC) migrates the computing task of the Mobile device to an edge base station with strong computing capability, thereby greatly reducing the computing time delay, simultaneously reducing the power consumption of the Mobile device, and prolonging the service life of the Mobile device. In the conventional MEC system, since the computation delay and the energy consumption are usually contradictory, that is, the more the computation capability is, the higher the energy consumption is, in order to balance between the two, the wireless resources and the computation resources need to be jointly allocated. In the past, the single antenna is mainly considered to be arranged on a user and a base station, and the advantage of the MIMO technology in the migration efficiency is not researched, namely, the large-scale MIMO technology can support a large number of users to perform task migration simultaneously, and has high frequency spectrum efficiency and energy efficiency, so that the loading time delay and energy consumption are reduced. In addition, the inherent channel hardening characteristic of the massive MIMO system can ensure that a stable migration rate is maintained when the mobile device migrates a task, which is important for the delay analysis in the MEC. Therefore, the invention applies the large-scale MIMO technology to the multi-user MEC system and designs a combined optimization scheme of computing resources and wireless resources to realize the minimum computing time delay of the system.
Disclosure of Invention
The invention aims to provide a method for minimizing the time delay of mobile edge calculation based on large-scale MIMO, which solves the problems in the prior art.
In order to achieve the purpose, the invention provides the following technical scheme: a mobile edge calculation time delay minimization method based on large-scale MIMO comprises the following steps:
the method comprises the following steps: calculating the channel gain of each user according to the channel state information, and performing normalization processing to obtain a data migration rate;
step two: in consideration of the maximum power and energy constraint existing in practice and the fairness among users, the practical maximum transmission power is obtained under the condition of meeting the maximum energy constraint, and then the optimal solution is obtained;
step three: and according to the optimal solution, allocating wireless resources, and allocating each user to realize the same overall delay for all users, thereby completing the joint allocation of wireless and computing resources and finally obtaining the minimum delay time.
Compared with the prior art, the invention has the following beneficial effects: the invention has the advantages of clearly illustrating the advantages of applying the massive MIMO technology to the mobile edge calculation and simultaneously considering the resource allocation under the condition of different channel state information. The invention can utilize limited computing resources to minimize time delay under the condition of maximum transmission power and energy consumption constraint by joint allocation of wireless and computing resources while carrying out a large amount of user task migration computation, and can also ensure stable migration rate and less signal overhead by using the invention.
Drawings
FIG. 1 is a process flow of resource allocation under ideal CSI conditions according to the present invention;
FIG. 2 is a process flow of resource allocation under non-ideal CSI conditions according to the present invention;
FIG. 3 is a graph of time delay versus number of antennas when using the method of the present invention;
figure 4 is a graph of time delay versus transmit power when using the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention providesA technical scheme is provided: the MEC system considered by the invention is provided with a BS of a large-scale antenna array and supports a plurality of single-antenna users to perform migration calculation
Figure BDA0002403653950000021
A group of users is represented as a group of users,
Figure BDA0002403653950000022
representing antennas, each user
Figure BDA0002403653950000023
Will generate a computationally intensive task comprising two parameters, input data LkAnd a computational requirement WkThe computational task then goes through two phases: a migration phase and a calculation phase. User k sends its input data to the BS through the wireless channel, and when the BS receives the data, the BS needs to allocate the computing resources to the tasks and perform the computation, so the total delay time t for the task execution of user k is
Figure BDA0002403653950000031
In the above formula, TkRepresenting the time consumed by the migration phase, QkRepresenting the time consumed by the calculation phase, RkIndicating data migration rate, fkRepresenting the computing resources allocated to user k by the MEC server, and fkSatisfy the requirement of
Figure BDA0002403653950000037
F denotes the computing power of the MEC server.
Considering that a massive MIMO system has two cases of ideal and non-ideal Channel State Information (CSI), the present invention designs different joint resource allocation schemes for the two cases.
The method comprises the following specific steps:
for the case of an ideal CSI,
the method comprises the following steps: calculating the channel gain of each user according to the channel state information, and normalizing, and recording as hkSubstituting the formula (2) to obtain the data migration rate Rk；
Rk＝log2(1+Pkhk) (2)
Wherein
Figure BDA0002403653950000032
Which is indicative of the power of the transmission,
Figure BDA0002403653950000033
representing the maximum transmission power.
Step two: considering the maximum power and energy constraint existing in practice and the fairness among users, the maximum energy constraint is satisfied
Figure BDA0002403653950000034
When the intermediate sign of the formula (3) is satisfied, the actual maximum transmission power is obtained by algebraic operation as shown in the formula (4), and then the P is obtained by the formula (5)kOf (2) an optimal solution
Figure BDA0002403653950000035
Figure BDA0002403653950000036
Figure BDA0002403653950000041
Figure BDA0002403653950000042
Where W (x) represents the L ambert-W function.
Step three: according to PkOf (2) an optimal solution
Figure BDA0002403653950000043
For the ideal CSI, the wireless resource allocation is carried out, and f is allocated to each user according to the formula (6)kAll users can realize the same integral delay, thereby completing the ideal CSI situationMoreover, the minimum delay time is finally obtained by the formula (1) of the joint allocation of wireless and computing resources.
Figure BDA0002403653950000044
Wherein the delay time t is initialized to the lower limit t according to the expressions (7) and (8)lowAnd an upper limit tupAnd t is obtained by equation (9) of the bisection methodmid。
Figure BDA0002403653950000045
Figure BDA0002403653950000046
Figure BDA0002403653950000047
Substituting equation (9) into equation (6) to obtain fkAnd verify
Figure BDA0002403653950000048
And the size of F, if
Figure BDA0002403653950000049
Will tmidAn upper limit of tupThen f is obtained by the following formulae (6) and (9)kThe optimal solution of (2); if it is
Figure BDA00024036539500000410
Will tmidGiving a lower limit of tlowAnd the same treatment is carried out to obtain fkThe optimal solution of (3) is to complete the resource allocation scheme under the condition of ideal CSI through the steps.
For the case of non-ideal CSI,
the method comprises the following steps: considering that the CSI under this condition is complex and there is large-scale fading in the channel resources, the effective channel gains of the users are normalized and then recorded as hkAnd hi', are approximated by the formula (8)To RkComprises the following steps:
Figure BDA0002403653950000051
the following steps are similar to the design of the ideal CSI case (R)k，hkAnd hi' non-ideal CSI case satisfied), in turn, find PkAnd fkBut at the maximum energy constraint
Figure BDA0002403653950000052
And when the total delay time t is reached, the result obtained by the formulas (1) and (3) is non-convex, and an optimal solution cannot be obtained, so that the invention designs a continuous convex approximation method:
the method comprises the following steps: the problem (3) is equivalently transformed into (11), where ω iskIs an auxiliary variable and satisfies the formula (12).
Figure BDA0002403653950000053
Figure BDA0002403653950000054
Step two: the problem (12) is further subjected to an equivalent transformation to transform into a problem (13), wherein y is also an auxiliary variable and satisfies the expression (14).
ωky≤Pkhk(13)
Figure BDA0002403653950000055
By means of auxiliary variable ωkAnd y constrains the maximum energy
Figure BDA0002403653950000056
And the total delay time t is converted into a convex constraint.
Step three: substituting the equations (12) and (13) into the equation (15) to perform iterative operation to continuously update omegakAnd y until the above process converges, at which time ω is obtainedkAnd y.
Figure BDA0002403653950000057
Wherein y is[n]And
Figure BDA0002403653950000058
y and ω for the nth iteration, respectivelykThe value is obtained.
Step four: will omegakThe optimal solution is substituted into the formula (11) to obtain the energy consumed by the migration of the calculation task, and finally, the P is obtained through the formulas (4) and (5)kF is obtained by (6), (7), (8) and (9)kThereby completing the joint resource allocation scheme under the non-ideal CSI condition.
The invention has the advantages of clearly illustrating the advantages of applying the massive MIMO technology to the mobile edge calculation and simultaneously considering the resource allocation under the condition of different channel state information. The invention can utilize limited computing resources to minimize time delay under the condition of maximum transmission power and energy consumption constraint by joint distribution of wireless and computing resources while carrying out a large amount of user task migration computation, and can also ensure stable migration rate and less signal overhead by using the invention.
Referring to fig. 1 to 4 of the drawings,
fig. 1 is a processing flow for resource allocation under an ideal CSI condition according to the present invention, which first obtains a migration data rate according to the CSI, then obtains a corresponding power according to a maximum energy constraint condition, compares the corresponding power with a maximum power constraint condition to find a power optimal solution, and finally allocates corresponding calculation resources to each user according to the power optimal solution and a set initial total time delay, so as to ensure that the time delays of all users are the same. In addition, when the computing resources are distributed, the upper limit and the lower limit of the total time delay are firstly set, and then the initial total time delay is obtained according to the dichotomy. If the sum of the computing resources distributed by all the users does not exceed the specified computing resources, the initial total time delay is given to the upper limit of the total time delay, and the total time delay condition met by the computing resources required by the users is obtained by utilizing the dichotomy calculation again; and otherwise, endowing the initial total time delay to the lower limit of the total time delay, and so on to complete the design and allocation of the computing resources required by the user, thereby completing the design of the combined scheme of the wireless resources and the computing resources.
Fig. 2 is a processing flow for resource allocation under the condition of non-ideal CSI, the process of the processing flow is similar to that under the condition of ideal CSI, the only difference is that because the condition of non-ideal CSI is complex, and the constraint conditions do not satisfy convexity, the convex approximation technique is adopted to introduce auxiliary variables to convert the maximum energy constraint problem into the constraint conditions satisfying convexity, so as to obtain the optimal solution of power and the optimal solution of computational resources through iterative operation, thereby completing the design of the joint scheme of wireless resources and computational resources.
Fig. 3 is a graph of time delay versus number of antennas when using the method of the present invention. It can be seen from the figure that in both the ideal CSI and the non-ideal CSI, the delay decreases with the increase of the number of antennas, which indicates the effectiveness of the present invention in applying massive MIMO technology.
Figure 4 is a graph of time delay versus transmit power when using the method of the present invention. As can be seen from the figure, the latency of the proposed joint allocation scheme is reduced, so the invention can be used to optimize the moving edge calculation.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (1)

1. A mobile edge calculation time delay minimization method based on large-scale MIMO is characterized in that: the method comprises the following steps:
the method comprises the following steps: calculating the channel gain of each user according to the channel state information, and performing normalization processing to obtain a data migration rate;
step two: in consideration of the maximum power and energy constraint existing in practice and the fairness among users, the practical maximum transmission power is obtained under the condition of meeting the maximum energy constraint, and then the optimal solution is obtained;
step three: and according to the optimal solution, allocating wireless resources, and allocating each user to realize the same overall delay for all users, thereby completing the joint allocation of wireless and computing resources and finally obtaining the minimum delay time.
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