CN108834080B - Distributed cache and user association method based on multicast technology in heterogeneous network - Google Patents

Distributed cache and user association method based on multicast technology in heterogeneous network Download PDF

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CN108834080B
CN108834080B CN201810341885.XA CN201810341885A CN108834080B CN 108834080 B CN108834080 B CN 108834080B CN 201810341885 A CN201810341885 A CN 201810341885A CN 108834080 B CN108834080 B CN 108834080B
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base station
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strategy
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CN108834080A (en
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杨绿溪
张珊
陶文武
李春国
黄永明
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Southeast University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W4/00Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/06Selective distribution of broadcast services, e.g. multimedia broadcast multicast service [MBMS]; Services to user groups; One-way selective calling services
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B17/00Monitoring; Testing
    • H04B17/30Monitoring; Testing of propagation channels
    • H04B17/391Modelling the propagation channel
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W28/00Network traffic management; Network resource management
    • H04W28/02Traffic management, e.g. flow control or congestion control
    • H04W28/10Flow control between communication endpoints
    • H04W28/14Flow control between communication endpoints using intermediate storage
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W72/00Local resource management
    • H04W72/50Allocation or scheduling criteria for wireless resources
    • H04W72/53Allocation or scheduling criteria for wireless resources based on regulatory allocation policies

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Abstract

The invention discloses a distributed cache and user association method based on a multicast technology in a heterogeneous network, and belongs to the technical field of wireless communication. The invention provides a multicast cooperative cache algorithm for carrying out combined optimization on a user association strategy and a cache configuration strategy to minimize the total backhaul cost of a system by combining the advantages of multicast transmission and cooperative cache aiming at the problem of backhaul congestion caused by the sharp increase of mobile data flow and the intensive deployment of Small Cell Base stations (SBS) and on the premise of ensuring the service quality of all users. Compared with the prior art, the invention has lower system backhaul cost and power consumption.

Description

Distributed cache and user association method based on multicast technology in heterogeneous network
Technical Field
The invention relates to a wireless edge caching technology, in particular to a distributed caching and user association method based on a multicast technology in a heterogeneous network, and belongs to the technical field of wireless communication.
Background
With the ever-increasing mobile smart devices and the dramatic increase in mobile data traffic, the demand for emerging applications and services has also begun to grow explosively. The dense deployment of small base stations is a key technology for dealing with the increase of mobile data traffic, but this method will bring great pressure to the backhaul link and also increase the system energy consumption.
Multicast and wireless caching are seen as two promising technologies to address the above problems. Caching shifts traffic from peak hours (e.g., daytime) to off-peak hours (e.g., nighttime) by leveraging a periodic pattern of traffic, by caching portions of the file in advance in a base station or like device during off-peak hours while serving user requests during peak hours. Caching is effective for scenarios where there is a sufficient amount of content to be multiplexed. Multicasting is to use a point-to-multipoint rather than point-to-point transmission method to serve concurrent requests of users to the same file, thereby reducing communication traffic and reducing energy consumption and bandwidth consumption. Multicasting is very effective when many users concurrently make requests for the same file. Such a scenario is more common in crowd gathering events, as there are a large number of co-located people interested in the same content, e.g., in sporting events and concert events, often with thousands of participants. Many new services, such as social networking platforms and news services, also employ one-to-many communication paradigms, such as the updates of Tweeter, Facebook, etc., with the expectation that multicast techniques will be applied more frequently. Currently, both academic circles and industrial circles generally apply the two technologies to different scenes and aspects respectively. There is less literature research to combine wireless caching with multicasting.
Disclosure of Invention
The purpose of the invention is as follows: based on the defects of the prior art, the invention provides a distributed cache and user association method based on a multicast technology in a heterogeneous network by combining the advantages of the wireless cache technology and the multicast technology, and aims to reduce the total backhaul cost of a system and reduce the power consumption of the system to a certain extent.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme:
a distributed cache and user association method based on multicast technology in a heterogeneous network comprises the following steps:
(1) the method comprises the steps that (M +1) xK matrixes are used for representing a base station (including a macro base station and a small base station) and a user association strategy, the (M +1) xN matrixes are used for representing a cache configuration strategy of the base station, users requesting the same file in each time slot are set to form a multicast group, the users in the same group adopt a multicast mode to carry out file transmission, the user service quality is guaranteed, each user can be guaranteed to be served by only one base station in each time slot, and the combined optimization problem of the user association strategy and the cache configuration strategy is established by taking the sum of the maximum transmission rates of the users in each multicast group as a target under the constraint condition that the files cached in the base station cannot exceed the cache capacity of the base station; the base station comprises macro base stations and small base stations, M is the total number of the small base stations, the network further comprises 1 macro base station, N is the total number of files requested by all users within a period of time, and K is the total number of mobile users in the network;
(2) performing iterative optimization on the user association strategy and the cache configuration strategy to obtain the optimal user association strategy and the optimal cache configuration strategy, wherein each iterative optimization process comprises the following steps:
(2.1) solving a user association strategy by adopting a game theory method based on a given cache configuration strategy;
and (2.2) based on the given user association strategy, adopting a Lagrange relaxation algorithm to solve the cache configuration strategy.
Further, the joint optimization problem established in step (1) is described as follows:
Figure GDA0002883186310000021
s.t.C1:
Figure GDA0002883186310000022
C2:
Figure GDA0002883186310000023
C3:
Figure GDA0002883186310000024
C4:
Figure GDA0002883186310000025
C5:
Figure GDA0002883186310000026
wherein, tmkIndicates whether user k is served by base station m, xmnRepresenting the proportion of the cached file n, R, in the base station mmkRepresenting the file transfer rate, SINR, from base station m to user kmkRepresenting the SINR value, gamma, of user k associated to base station mkIndicating the received signal to interference plus noise ratio threshold, C, for user kmIndicates the buffer capacity of base station m, cnIndicating the size of file n.
Figure GDA0002883186310000027
Represents a set of base stations, where 0 represents a macro base station, {1, 2.., M } represents a set of small base stations,
Figure GDA0002883186310000028
representing the set of files requested by all users over a period of time,
Figure GDA0002883186310000029
on behalf of the set of mobile users in the network,
Figure GDA00028831863100000210
a multicast group formed on behalf of the user requesting file n.
Further, in the step (2.1), a game theory method is adopted to solve the user association policy, and the method comprises the following steps:
(2.1.1) setting the iteration number j to 0, and selecting the initial probability vector of each possible association strategy of each user as
Figure GDA00028831863100000211
Wherein
Figure GDA00028831863100000212
Represents all possible associated policy sets for user k;
(2.1.2) all users
Figure GDA00028831863100000213
According to probability
Figure GDA00028831863100000214
Selection of the b-thk(j) Performing base station association by using a base station association strategy;
(2.1.3) each user updates its utility function Uk(j) And its current normalized utility function
Figure GDA00028831863100000215
Then the users update their respective probability vectors, and the update rule is:
Figure GDA0002883186310000031
wherein, beta is more than 0 and less than 1, the learning parameter, and the utility function of the user k is defined as the total return cost of the base station which can serve the user k;
(2.1.4) if for
Figure GDA0002883186310000032
All exist
Figure GDA0002883186310000033
If the value is larger than the set threshold value, the algorithm is ended, otherwise, the step (2.1.2) is returned to continue the circulation until the circulation is ended.
Further, when the game theory method is adopted to solve the user association strategy in the step (2.1), the game theory method is used
Figure GDA0002883186310000034
To represent a game theory model of subscriber base station association strategies in which subscribers are aggregated
Figure GDA0002883186310000035
For the set of players in the game theory model, SkRepresenting a set of base station association policies, U, representing user kkA utility function representing user k; set of policies Sk={skTherein of
Figure GDA0002883186310000036
Base station for all usersThe association policy is expressed as a matrix
Figure GDA0002883186310000037
Wherein
Figure GDA0002883186310000038
Represents the joint policy space of all users, the base station association policy of all other users except user k is
Figure GDA0002883186310000039
Wherein
Figure GDA00028831863100000310
The utility function for user k is defined as the total backhaul cost for the base station that can serve user k, expressed as:
Figure GDA00028831863100000311
wherein the content of the first and second substances,
Figure GDA00028831863100000312
representing a set of base stations that can serve user k, the base stations in the set satisfying a constraint SINRmk≥γktmk
Further, the method for solving the cache configuration policy by adopting the lagrangian relaxation algorithm in the step (2.2) comprises the following steps:
variable x is configured for cache by adopting gradient descent methodmnAnd lagrange multiplier
Figure GDA00028831863100000313
And (3) carrying out iteration updating until convergence to obtain an optimal solution:
Figure GDA00028831863100000314
wherein the content of the first and second substances,
Figure GDA00028831863100000315
to updateCache configuration variable xmnThe step size of (a) is determined,
Figure GDA00028831863100000316
to update multipliers
Figure GDA00028831863100000317
The parameter j represents the jth iteration,
Figure GDA00028831863100000318
represents: when z is less than a, the value is a, when z is more than b, the value is b, otherwise, the value is itself [ z ]]+Max {0, z } represents: and when z is less than 0, the value is 0, otherwise, the value is itself.
Has the advantages that: aiming at the heterogeneous network, the invention combines the multicast and cache technologies under the premise of ensuring the QoS of all users, and establishes the combined optimization problem of the cache configuration strategy and the user association strategy by taking the total backhaul cost of the minimized system as the target. To solve the NP-hard problem, it is divided into two sub-problems, namely, a user association problem based on a given cache configuration policy and a problem of optimizing the cache configuration policy based on the given user association policy. The method of the invention fully utilizes the advantages of both the multicast technology and the cache technology, and compared with the existing unicast cache algorithm and multicast cache algorithm, the method not only can effectively reduce the return total cost of the system, but also has obvious advantages in the aspect of reducing energy consumption on the premise of ensuring the QoS of each user in the system.
Drawings
Fig. 1 is a system model diagram of a heterogeneous network.
FIG. 2 is a flow chart of the method of the present invention.
FIG. 3 is a simulation graph of the power consumption of the SBS memory space according to the present invention and the prior art.
Fig. 4-6 are simulation graphs showing the total backhaul cost of the system of the present invention and the prior art varying with the SBS memory size, the Zipf distribution parameter α, and the number of users in the system.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
As shown in fig. 1, the heterogeneous cache network based on the present invention is composed of 1 Macro Base Station (MBS), M Small Base Stations (SBS), and K users.
Figure GDA0002883186310000041
Represents a set of base stations, where 0 represents MBS, {1, 2.., M } represents a set of SBS,
Figure GDA0002883186310000042
representing a collection of mobile users. SBS is densely deployed, i.e., users can be within the coverage of multiple SBS. By means of matrices
Figure GDA0002883186310000043
Indicates the base station and user association condition, where tmkIndicates a transmission decision, when tmkWhen 1 indicates that user k is served by base station m, tmkWhen 0, it means that user k is not served by base station m, and each user can be served by only one base station at most.
Figure GDA0002883186310000044
The file set of all user requests in a period of time is represented, the total number of files is N, the size of each file is the same, and the files are normalized to be 1 for convenience. The macro base station and the small base station have cache capacity, and the cache space is
Figure GDA0002883186310000045
The invention adopts an MDS coding caching scheme, and when the total bit number of the file coding data packets received by a user in any sequence exceeds a threshold value 1, the original file can be recovered. The cache allocation strategy uses a matrix of (M +1) x N
Figure GDA0002883186310000046
Is shown in which
Figure GDA0002883186310000047
Representing the proportion of the cached file n in the base station m. If the base stationIf the ratio of the m cache file n is 1, the file can be directly obtained from the base station m, if the ratio of the m cache file n of the base station m is between 0 and 1, one part of the file n can be directly obtained from the base station m, and the other part of the file n needs to be obtained from the core network through the base station, and if the base station m does not cache the file n, the file needs to be completely obtained from the core network by the base station.
The heterogeneous network in the embodiment of the present invention includes 1 Macro Base Station (MBS), 15 Small Base Stations (SBS) and 100 users. The total number of files requested by all users in a period of time is N-100, each file has the same size, and for convenience, the files are normalized to 1. The macro base station and the small base station have cache capacity, the size of the MBS storage space is 15, and the size of the SBS storage space is 8. When the MBS or SBS caches the multicast group request file, it directly multicasts the requested file to the multicast group through wireless link, when the base station does not cache the multicast group request file, the base station first obtains the file from the core network through limited backhaul and then multicasts the file to the user.
As shown in fig. 2, a method for associating a distributed cache and a user based on a multicast technology in a heterogeneous network disclosed in an embodiment of the present invention specifically includes the following steps:
step 1: based on the heterogeneous cache network scene, a combined optimization problem of a user association strategy and a cache configuration strategy is established with the aim of minimizing the total backhaul cost of the system. The specific process is as follows:
first, multicast transmission principles are formulated.
In each time slot, users requesting the same file form a multicast group for
Figure GDA0002883186310000051
Is shown in the formula, wherein q isknIndicates whether user k requests file n, when qkn1 means that user k requests file n, otherwise user k does not request file n in the time slot. The same group of users adopt a multicast mode to transmit files; in this example it is assumed that the user requests a Zipf profile obeying a parameter of 0.5.
Then, calculating the signal-to-interference-and-noise ratio value of the signals received by the user from each base station, and determining the SINR threshold value.
In the transmission phase, each base station (including MBS) multiplexes the same frequency band spectrum. In a coverage area of a certain base station, the user groups requesting different contents use different frequency band frequency spectrums for staggering, namely, the same base station does not have interference among the user groups requesting different contents, but the users requesting the same contents use the same frequency band frequency spectrums, and because the multicast mode is adopted for transmission, the interference does not exist among the users. If it is assumed that the base station is
Figure GDA0002883186310000052
To the user
Figure GDA0002883186310000053
The inter-channel is a flat fading channel with a channel gain of hmkBase station transmitting power of pmThen the sir value for user k associated to base station m can be expressed as:
Figure GDA0002883186310000054
in this example, considering a (1000 × 1000) zone, where there is only one MBS, the MBS is located at the center of the zone, i.e. the MBS coordinates are (500), and SBS and users are scattered relatively randomly in the zone. The coverage radius of the MBS is 500m, and the coverage radius of each SBS is 300 m. The transmitting power of MBS and SBS is 33dBm and 23dBm respectively, the total bandwidth of system is 10MHz, and the noise power spectrum density is-174 dBm/Hz. For large scale fading, the path loss models for MBS and SBS are l respectively0k=128.1+37.6log10(d0k) And
Figure GDA0002883186310000055
wherein d ismkDefined as the distance (km) between user k and base station m. The shadowing fading is taken as a Log-normal (Log-normal) shadowing fading with a standard deviation of 8 dB. In addition, the received signal to interference and noise ratio threshold γ for each user is set to-5 dB.
Next, a system total backhaul cost expression is established.
From the perspective of user experience, in order to make the file obtaining delay of a user lower, when a base station obtains a certain file from a core network and multicasts the file to its scheduling user group, the file download rate needs to meet the transmission rate requirements of all users in the group, that is, the data rate of the base station obtaining the file from the core network needs to be at least as large as the file transmission rate, so that the system backhaul cost can be defined as the sum of the maximum transmission rates of the users in each multicast group, which can be specifically expressed as:
Figure GDA0002883186310000061
wherein, CBRepresents the total backhaul cost, R, of the systemmkRepresenting the file transfer rate, R, from base station m to user kmkIs specifically represented by Rmk=Bmklog(1+SINRmk) Wherein
Figure GDA0002883186310000062
W is the total bandwidth of the system;
and finally, establishing a joint optimization problem of a user association strategy and a cache configuration strategy by taking the minimization of the total backhaul cost of the system as a target. The optimization problem can be described as:
Figure GDA0002883186310000063
s.t.C1:
Figure GDA0002883186310000064
C2:
Figure GDA0002883186310000065
C3:
Figure GDA0002883186310000066
C4:
Figure GDA0002883186310000067
C5:
Figure GDA0002883186310000068
wherein, the C1 constraint ensures the Quality of Service (QoS) of the user, the C2 constraint ensures that each time slot of each user can only be served by one base station, and the C3 constraint ensures that the files cached in the base station do not exceed the cache capacity of the base station;
step 2: and iteratively optimizing the user association strategy and the cache configuration strategy based on a multicast cooperative cache algorithm to obtain the optimal user association strategy and the optimal cache configuration strategy. The optimization problem described above is an NP-hard problem. In order to solve the problem, the method is divided into two sub-problems, namely a user association problem based on a given cache configuration strategy and a problem of optimizing the cache configuration strategy based on the given user association strategy; the method specifically comprises the following steps:
step 2.1: and solving the user association strategy by adopting a game theory method based on the given cache configuration strategy. The details are as follows
First, a game theory model is established.
By using
Figure GDA0002883186310000069
To represent a game theory model of subscriber base station association strategies in which subscribers are aggregated
Figure GDA00028831863100000610
For the set of players in the game theory model, SkRepresenting a set of base station association policies, U, representing user kkRepresenting the utility function of user k. Set of policies Sk={skTherein of
Figure GDA00028831863100000611
Thus, the base station association strategy of all users can be expressed as a matrix
Figure GDA0002883186310000071
Wherein
Figure GDA0002883186310000072
Representing the joint policy space of all users. To satisfy constraint C2, only one element of each association policy vector for each user is 1, and the remaining elements are 0. It is also possible to define the base station association policy for all users other than user k as
Figure GDA0002883186310000073
Wherein
Figure GDA0002883186310000074
In addition, consider that when user k is both at the base station
Figure GDA0002883186310000075
In the coverage range and satisfies the C1 constraint SINR in the optimization problemmk≥γktmkIn time, user k may select base station m for association, i.e., user k may be served by base station m for use
Figure GDA0002883186310000076
Representing the set of base stations that can serve user k, the utility function for user k can be defined as the total backhaul cost of the base stations that can serve user k, i.e., the total backhaul cost
Figure GDA0002883186310000077
Defining a normalized utility function for player k as
Figure GDA0002883186310000078
Can be expressed as:
Figure GDA0002883186310000079
after the neighboring users of user k have associated with the base station, user k selects a suitable base station for association according to the association policy of these users to improve the utility function of the base station. In addition, the utility function of each user depends only on the user and the adjacent users, so that the game can perform local information exchange in a distributed mode;
the user association problem can be proved to be a potential game problem.
In this example, a user association Algorithm based on random Learning (SLA) is adopted, in which users adjust their behaviors through their dynamic feedback to approach nash equilibrium points gradually, so as to obtain an optimal solution to the user association problem.
In SLA-based user association algorithm, the method comprises the following steps
Figure GDA00028831863100000718
The extension is a hybrid strategy form of a game and the following definitions are given. First, let all possible association policies for user k be set as
Figure GDA00028831863100000710
Collection
Figure GDA00028831863100000711
Is of a size of
Figure GDA00028831863100000712
And all users may have associated policy space of
Figure GDA00028831863100000713
The size of the policy space is
Figure GDA00028831863100000714
Then, let P ═ P (P)1,p2,...,pK) To represent
Figure GDA00028831863100000715
I.e. the probability matrix from which each possible base station association policy of a user is selected, wherein
Figure GDA00028831863100000716
A probability vector representing each associated policy choice for user k,
Figure GDA00028831863100000717
the representation indicates that user k selects the b-thkThe probability of a kind of association policy.
The method specifically comprises the following substeps:
step 2.1.1: initialization: setting the iteration number j to be 0, and selecting each possible association strategy of each user as an initial probability vector
Figure GDA0002883186310000081
Step 2.1.2: distributing associated base stations for each user: all users
Figure GDA0002883186310000082
According to the present probability pk(j) Selection of the b-thk(j) Performing base station association by using a base station association strategy;
step 2.1.3: and (3) dynamically updating the strategy: each user updates its utility function Uk(j) And its current normalized utility function
Figure GDA0002883186310000083
Then the users update their respective probability vectors, and the update rule is:
Figure GDA0002883186310000084
wherein 0 < β < 1 is a learning parameter;
step 2.1.4: judging the end of the program or returning to the step 6.3.2: if for
Figure GDA0002883186310000085
All exist
Figure GDA0002883186310000086
Close to 1, i.e.
Figure GDA0002883186310000087
The algorithm is ended, otherwise, the step 6.3.2 is returned to continue the circulation until the circulation is ended;
step 2.2: and based on the given user association strategy, solving a cache configuration strategy by adopting a Lagrange relaxation algorithm. Variable x is configured for cache by adopting gradient descent methodmnAnd lagrange multiplier
Figure GDA0002883186310000088
Updating:
Figure GDA0002883186310000089
wherein
Figure GDA00028831863100000810
Configuring variable x for updating cachemnIs sufficiently small and a fixed step size,
Figure GDA00028831863100000811
to update multipliers
Figure GDA00028831863100000812
A sufficiently small and fixed step size. The parameter j represents the jth iteration.
Figure GDA00028831863100000813
Represents: and when z is smaller than a, the value is a, when z is larger than b, the value is b, otherwise, the value is itself. [ z ] is]+Max {0, z } represents: and when z is less than 0, the value is 0, otherwise, the value is itself. The multiplier iteration update process will converge to the optimal solution.
In step 2 of this embodiment, a multicast cooperative caching algorithm is used to iteratively optimize a user association policy and a caching configuration policy, so as to obtain an optimal user association policy and an optimal caching configuration policy. The method specifically comprises the following steps: firstly, initializing the iteration number j to 0, initializing the maximum iteration number T to 500, and taking a Lagrange multiplier as a multiplier
Figure GDA00028831863100000814
And cachingConfiguration policy X0And according to the initial X0Obtaining the user association strategy t by adopting a game theory method0(ii) a Then for each iteration, updating the cache configuration strategy XjAnd lagrange multiplier
Figure GDA00028831863100000815
Recalculating the user association strategy t by adopting a game theory methodjUntil the iteration ends.
Fig. 3 is a simulation graph showing the variation of the system power consumption of the scheme of the present invention and the scheme of the prior art along with the variation of the size of the SBS memory space, and the performance evaluation index is the system power consumption. Fig. 4-6 show simulation graphs of the total return cost of the system of the solution of the present invention and the solution of the prior art, which varies with the size of the SBS storage space, the Zipf distribution parameters, and the number of users in the system, and the performance evaluation index is the total return cost of the system. Therefore, the performance of the method is obviously superior to that of a unicast cooperative caching scheme, a unicast hottest caching scheme, a multicast-to-caching scheme and a multicast hottest caching scheme, the total backhaul cost of the system can be effectively reduced, the problem of backhaul congestion caused by the rapid increase of the mobile data volume and the intensive deployment of small base stations is solved, and the power consumption cost of the system can be reduced to a certain extent.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, but any modifications or equivalent variations made according to the technical spirit of the present invention are within the scope of the present invention as claimed.

Claims (4)

1. A distributed cache and user association method based on multicast technology in a heterogeneous network is characterized by comprising the following steps:
(1) the matrix of (M +1) xK represents a base station and a user association strategy, the matrix of (M +1) xN represents a cache configuration strategy of the base station, users requesting the same file in each time slot form a multicast group, users in the same group transmit files in a multicast mode, the combined optimization problem of the user association strategy and the cache configuration strategy is established by aiming at minimizing the sum of the maximum transmission rates of the users in each multicast group under the constraint condition that the service quality of the users is ensured, the service can be provided by only one base station in each time slot of each user and the files cached in the base station cannot exceed the cache capacity of the base station; the base station comprises macro base stations and small base stations, M is the total number of the small base stations, the network further comprises 1 macro base station, N is the total number of files requested by all users within a period of time, and K is the total number of mobile users in the network;
(2) performing iterative optimization on the user association strategy and the cache configuration strategy to obtain the optimal user association strategy and the optimal cache configuration strategy, wherein each iterative optimization process comprises the following steps:
(2.1) solving a user association strategy by adopting a game theory method based on a given cache configuration strategy;
(2.2) based on a given user association strategy, solving a cache configuration strategy by adopting a Lagrange relaxation algorithm;
the joint optimization problem established in step (1) is described as follows:
Figure FDA0002883186300000011
s.t.C1:SINRmk≥γktmk,
Figure FDA0002883186300000012
C2:
Figure FDA0002883186300000013
C3:
Figure FDA0002883186300000014
C4:xmn∈[0,1]
Figure FDA0002883186300000015
C5:tmk∈{0,1}
Figure FDA0002883186300000016
wherein, tmkIndicates whether user k is served by base station m, xmnRepresenting the proportion of the cached file n, R, in the base station mmkRepresenting the file transfer rate, SINR, from base station m to user kmkRepresenting the SINR value, gamma, of user k associated to base station mkIndicating the received signal to interference plus noise ratio threshold, C, for user kmIndicates the buffer capacity of base station m, cnWhich represents the size of the file n and,
Figure FDA0002883186300000017
represents a set of base stations, where 0 represents a macro base station, {1, 2.., M } represents a set of small base stations,
Figure FDA0002883186300000018
representing the set of files requested by all users over a period of time,
Figure FDA0002883186300000019
on behalf of the set of mobile users in the network,
Figure FDA00028831863000000110
a multicast group formed on behalf of the user requesting file n.
2. The method for distributed caching and user association based on multicast technology in the heterogeneous network according to claim 1, wherein the step (2.1) of solving the user association policy by using a game theory method comprises:
(2.1.1) setting the iteration number j to 0, and selecting the initial probability vector of each possible association strategy of each user as
Figure FDA0002883186300000021
Wherein
Figure FDA0002883186300000022
Represents all possible associated policy sets for user k;
(2.1.2) all users
Figure FDA0002883186300000023
According to probability
Figure FDA0002883186300000024
Selection of the b-thk(j) Performing base station association by using a base station association strategy;
(2.1.3) each user updates its utility function Uk(j) And its current normalized utility function
Figure FDA0002883186300000025
Then the users update their respective probability vectors, and the update rule is:
Figure FDA0002883186300000026
wherein, beta is more than 0 and less than 1, the learning parameter, and the utility function of the user k is defined as the total return cost of the base station which can serve the user k;
(2.1.4) if for
Figure FDA0002883186300000027
All exist
Figure FDA0002883186300000028
If the value is greater than the set threshold value 0.99, the algorithm is ended, otherwise, the step (2.1.2) is returned to continue the circulation until the circulation is ended.
3. The method for distributed caching and user association based on multicast technology in heterogeneous network according to claim 1, wherein the step (2.1) of solving the user association policy by using a game theory method is implemented
Figure FDA0002883186300000029
To represent a game theory model of subscriber base station association strategies in which subscribers are aggregated
Figure FDA00028831863000000210
For the set of players in the game theory model, SkRepresenting a set of base station association policies, U, representing user kkA utility function representing user k; set of policies Sk={skIn which s isk=(t0k,t1k,t2k,t3k,...,tMk)T,tmk∈{0,1},
Figure FDA00028831863000000211
Base station association strategy representation of all users as matrix
Figure FDA00028831863000000212
Wherein
Figure FDA00028831863000000213
Represents the joint policy space of all users, the base station association policy of all other users except user k is
Figure FDA00028831863000000214
Wherein
Figure FDA00028831863000000215
The utility function for user k is defined as the total backhaul cost for the base station that can serve user k, expressed as:
Figure FDA00028831863000000216
wherein the content of the first and second substances,
Figure FDA00028831863000000217
representing a set of base stations that can serve user k, the base stations in the set satisfying a constraint SINRmk≥γktmk
Figure FDA00028831863000000218
Indicating a multicast group formed by users requesting file n in each time slot, where qknIndicates whether user k requests file n, when qkn1 means that user k requests file n, otherwise user k does not request file n in the time slot.
4. The method according to claim 1, wherein the method for solving the cache configuration policy by using the lagrangian relaxation algorithm in step (2.2) comprises:
variable x is configured for cache by adopting gradient descent methodmnAnd lagrange multiplier
Figure FDA0002883186300000031
And (3) carrying out iteration updating until convergence to obtain an optimal solution:
Figure FDA0002883186300000032
wherein the content of the first and second substances,
Figure FDA0002883186300000033
configuring variable x for updating cachemnThe step size of (a) is determined,
Figure FDA0002883186300000034
for updating lagrange multipliers
Figure FDA0002883186300000035
The parameter j represents the jth iteration,
Figure FDA0002883186300000036
represents: when z is less than a, the value is a, when z is more than b, the value is b, otherwise, the value is itself [ z ]]+Max {0, z } represents: and when z is less than 0, the value is 0, otherwise, the value is itself.
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