CN112929058A - MIMO network cache placement method based on interference alignment - Google Patents

MIMO network cache placement method based on interference alignment Download PDF

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CN112929058A
CN112929058A CN202110083286.4A CN202110083286A CN112929058A CN 112929058 A CN112929058 A CN 112929058A CN 202110083286 A CN202110083286 A CN 202110083286A CN 112929058 A CN112929058 A CN 112929058A
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user
base station
cluster
interference
mimo network
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CN112929058B (en
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刘伟
李凌冰
索宏泽
焦利彬
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Xidian University
CETC 54 Research Institute
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CETC 54 Research Institute
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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
    • 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
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/02—Traffic management, e.g. flow control or congestion control
    • H04W28/10—Flow control between communication endpoints
    • H04W28/14—Flow control between communication endpoints using intermediate storage

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Abstract

The invention provides an interference alignment-based MIMO network cache placement method, which aims to perform interference alignment on multiple users and multiple base stations, eliminate partial interference, improve the signal-to-interference ratio of a user side and finally improve the hit rate of an MIMO network, and comprises the following steps: setting parameters of an MIMO network comprising a plurality of base stations and a plurality of users, clustering the base stations and the users, associating the base stations with the users in each cluster, aligning interference between the base stations in each cluster and the users, designing a pre-coding vector of each base station and a decoding vector of each user, eliminating interference caused by other base stations in each cluster, then calculating the hit rate of the MIMO network, establishing and solving an optimization problem with the maximized hit rate as a target, obtaining the optimized cache placement probability of each file, and finally adjusting the files cached in the cache equipment by each base station according to the optimized cache placement probability.

Description

MIMO network cache placement method based on interference alignment
Technical Field
The invention belongs to the technical field of wireless communication, relates to a method for placing a MIMO network cache, in particular to a method for placing a MIMO network cache based on interference alignment, and can be used for determining a file cache placing scheme of a base station in an MIMO network.
Background
As the communication demand for content-oriented services increases, a large number of files are frequently requested repeatedly by users, and the base station needs to continuously download the same files from the core network and then send the files to the users, which results in increased backhaul link burden. To alleviate the heavy burden of the backhaul link, deploying a base station configured with a caching device has become a promising solution. The file is cached in the cache device of the base station in advance, when a user initiates a request, the base station can directly acquire the file from the cache device without downloading the file from a core network through a backhaul link, and therefore the burden of the backhaul link is reduced. The main index for measuring the effect of cache on the reduction of the load of the backhaul link is the hit rate. Factors that affect hit rate include the caching probability of the file and the transmission success rate of the file.
With the continuous evolution of wireless networks, the network densification becomes the direction of wireless network development. The cell area is continuously reduced, and the spatial multiplexing is enhanced, so that the interference among users becomes stronger. Stronger interference causes lower signal-to-interference ratio of the user side, the user is difficult to correctly receive information, the success rate of file transmission is too low, and the network hit rate is reduced.
Interference alignment is receiving increasing attention as an efficient interference management method. The main idea of interference alignment is to design a pre-coding matrix at the transmitting end and a decoding matrix at the receiving end, so that interference signals of signals received at the receiving end are overlapped in space, and thus the receiving end can eliminate overlapped interference to obtain interference-free received signals. By adopting the interference alignment technology, higher signal-to-interference ratio can be obtained, so that the success rate of file transmission is improved, and the network hit rate is further improved.
In order to improve the network hit rate, the requirements on the reliability and effectiveness of the wireless communication quality are higher and higher. In order to improve the reliability, effectiveness and network resource utilization rate of the network, the MIMO technology is receiving more and more attention. By configuring a plurality of antennas for a base station and a user respectively to construct an MIMO network, the frequency spectrum efficiency can be improved, the reliability of a communication link can be improved, the network capacity can be increased, and a high-speed and high-reliability wireless communication service can be provided for the user. Therefore, designing a MIMO network cache placement method based on interference management becomes an important approach for improving the hit rate of the wireless network.
However, the prior art does not consider a cache placement method that is efficient for MIMO network design. Xu and M.Tao published a paper named Modeling, Analysis, and Optimization of learning in Multi-Antenna Small-Cell Networks in 2019 on IEEE Transactions on Wireless Communications, and discloses a Small cellular network cache placement method based on zero forcing technology.
According to the above description, although the above method performs interference management by using the zero forcing technique, the signal-to-interference ratio of the ue is improved. However, when the prior art is applied to the MIMO network, interference eliminated by the zero forcing technology is less, which causes a problem that the signal-to-interference ratio of the user terminal is not strong enough, thereby causing a low hit rate.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a method for placing a buffer of a MIMO (multiple input multiple output) network based on interference alignment, which is used for solving the problem of low hit rate when the prior art is applied to the MIMO network.
In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:
(1) setting MIMO network parameters:
the structure comprises a plurality of base stations
Figure BDA0002910093900000021
Multiple users
Figure BDA0002910093900000022
And a MIMO network of databases,
Figure BDA0002910093900000023
is subject to a position distribution of intensity lambdaBHomogeneous poisson point process of phiB＝{di|i≥3}，
Figure BDA0002910093900000024
Is subject to a position distribution of intensity lambdaUHomogeneous poisson point process of
Figure BDA0002910093900000025
The database contains L files
Figure BDA0002910093900000026
Wherein, BiIndicating the configuration of a cache device capable of storing C files
Figure BDA0002910093900000027
And the ith base station of M antennas, C is more than or equal to 1, M is more than or equal to 2, diIs represented by BiPosition coordinates of (1), UjIndicating the j-th user configured with N antennas, N ≧ 2,
Figure BDA0002910093900000028
represents UjL is not less than C, FlIndicates a popularity of qlAnd a base station BiThe probability of buffering is plThe first file of (a) is stored,
Figure BDA0002910093900000029
gamma represents a zipff distribution parameter, gamma > 0,
Figure BDA00029100939000000210
sigma represents summation operation;
(2) clustering the MIMO network:
grouping K users in a MIMO network
Figure BDA0002910093900000031
And K base stations nearest to the K base stations
Figure BDA0002910093900000032
Division into clusters
Figure BDA0002910093900000033
Obtaining a cluster set
Figure BDA0002910093900000034
Wherein K is more than or equal to 3 and less than or equal to M + N-1,
Figure BDA0002910093900000035
(3) each cluster
Figure BDA0002910093900000036
Each user in
Figure BDA0002910093900000037
And a base station
Figure BDA0002910093900000038
And (3) performing association:
each cluster
Figure BDA0002910093900000039
Each user in
Figure BDA00029100939000000310
Phi and phisRecently cached with files
Figure BDA00029100939000000311
Base station of
Figure BDA00029100939000000312
An association is made, wherein,
Figure BDA00029100939000000313
(4) each cluster
Figure BDA00029100939000000314
For each user
Figure BDA00029100939000000315
With each base station
Figure BDA00029100939000000316
And (3) interference alignment is carried out:
(4a) design each cluster
Figure BDA00029100939000000317
Each base station in
Figure BDA00029100939000000318
Of a precoding vector
Figure BDA00029100939000000319
And each user
Figure BDA00029100939000000320
Decoded vector of
Figure BDA00029100939000000321
Figure BDA00029100939000000322
Figure BDA00029100939000000323
Figure BDA00029100939000000324
Figure BDA00029100939000000325
Wherein the content of the first and second substances,
Figure BDA00029100939000000326
representing the inverse interference noise covariance matrix,
Figure BDA00029100939000000327
representing the interference noise covariance matrix,
Figure BDA00029100939000000328
indicating a base station
Figure BDA00029100939000000329
To the user
Figure BDA00029100939000000330
I denotes an identity matrix, (-)-1Representing an inversion operation (·)HExpressing conjugate transposition operation, and expressing norm operation by | DEG |;
(4b) each cluster
Figure BDA00029100939000000331
Each base station in
Figure BDA00029100939000000332
To each user
Figure BDA00029100939000000333
Transmitting coded signals
Figure BDA00029100939000000334
Each cluster
Figure BDA00029100939000000335
Each base station in
Figure BDA00029100939000000336
To each user
Figure BDA00029100939000000337
Transmitting coded signals
Figure BDA00029100939000000338
Wherein the content of the first and second substances,
Figure BDA00029100939000000339
presentation document
Figure BDA00029100939000000340
The symbol of (1);
(4c) each cluster
Figure BDA0002910093900000041
Each user therein
Figure BDA0002910093900000042
Receiving a signal
Figure BDA0002910093900000043
Each cluster
Figure BDA0002910093900000044
Each user therein
Figure BDA0002910093900000045
Receiving associated base stations
Figure BDA0002910093900000046
Transmitted by
Figure BDA0002910093900000047
Coded signal after channel coding
Figure BDA0002910093900000048
Figure BDA0002910093900000049
Each base station in
Figure BDA00029100939000000410
Transmitted by
Figure BDA00029100939000000411
Channel coded signal
Figure BDA00029100939000000412
And other base stations BiTransmitted siCoded signal after channel coding
Figure BDA00029100939000000413
Superimposed signals
Figure BDA00029100939000000414
Figure BDA00029100939000000415
Wherein the content of the first and second substances,
Figure BDA00029100939000000416
representing a user
Figure BDA00029100939000000417
And a base station
Figure BDA00029100939000000418
The distance between the two, alpha represents the path fading, and \ represents the set difference set operation;
(4d) each cluster
Figure BDA00029100939000000419
Each user therein
Figure BDA00029100939000000420
By decoding the vector
Figure BDA00029100939000000421
To pair
Figure BDA00029100939000000422
Filtering to obtain decoded signal
Figure BDA00029100939000000423
Figure BDA00029100939000000424
Wherein, the base station
Figure BDA00029100939000000425
To the user
Figure BDA00029100939000000426
Equivalent channel parameters of
Figure BDA00029100939000000427
(5) Calculating hit ratio P for MIMO networkshit：
Hit ratio P of MIMO networkhitDefined as the probability that a file in the MIMO network is cached in the caching device of the base station and correctly sent to the associated user:
Figure BDA00029100939000000428
wherein theta represents the threshold value of signal-to-interference ratio of correctly received signal of user, and auxiliary function
Figure BDA00029100939000000429
(6) Building and solving to maximize hit ratio PhitOptimization problem for the target:
set up to maximize hit rate PhitAn optimization problem P is taken as a target, and the P is solved to obtain the optimized cache placement probability
Figure BDA00029100939000000430
Figure BDA0002910093900000051
Figure BDA0002910093900000052
Figure BDA0002910093900000053
Figure BDA0002910093900000054
Where u is the Lagrangian multiplier, wl(u) is the equation
Figure BDA0002910093900000055
Non-negative true roots of (1);
(7) each base station BiCaching each file Fl：
Each base station BiTo optimize cache placement probability
Figure BDA0002910093900000056
Each file FlBuffer to buffer device
Figure BDA0002910093900000057
In (1).
Compared with the prior art, the invention has the following advantages:
1. according to the invention, the K users and the K base stations closest to the K users are divided into a cluster, each base station and each user are subjected to interference alignment in each cluster, and the precoding vector of each base station and the decoding vector of each user are designed, so that interference signals caused by other K-1 base stations in the cluster can be eliminated at each user side through the filtering of the decoding vectors, the signal-to-interference ratio strength of each user side is improved, and the obtained network hit rate is higher.
2. According to the invention, each base station can cache different file sets in the cache equipment of different base stations according to the probability cache files placed by the optimized cache, so that the number of the files cached in the network exceeds the capacity limit of the cache equipment of a single base station, thereby ensuring that a user can obtain the requested files from the cache equipment of the base station to the maximum extent, and further improving the hit rate.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples:
referring to fig. 1, the present invention includes the steps of:
step 1) setting MIMO network parameters:
the MIMO network area is 4000 x 4000m2Comprising a plurality of base stations
Figure BDA0002910093900000058
Multiple users
Figure BDA0002910093900000061
And a MIMO network of databases,
Figure BDA0002910093900000062
is subject to a position distribution of intensity lambdaB＝2×10-5Homogeneous poisson point process of phiB＝{di|i≥3}，
Figure BDA0002910093900000063
Is subject to a position distribution of intensity lambdaU＝2×10-5Homogeneous poisson point process of
Figure BDA0002910093900000064
Compared with the traditional method that the position distribution of the base station and the user adopts the homogeneous Poisson point processThe regular hexagon distribution is more consistent with the actual distribution, and the database contains 100 files L
Figure BDA0002910093900000065
Wherein, BiIndicating that a cache device capable of storing 10 files, C, is configured
Figure BDA0002910093900000066
And the ith base station of 4 antennas, diIs represented by BiPosition coordinates of (1), UjRepresenting the jth user configured with N-2 antennas,
Figure BDA0002910093900000067
represents UjPosition coordinates of (1), FlIndicates a popularity of qlAnd a base station BiThe probability of buffering is plThe popularity distribution of the file conforms to the zipff law,
Figure BDA0002910093900000068
gamma represents the zipff distribution parameter, gamma is 1.5, the probability of the file being cached should satisfy the constraint of the capacity of the caching equipment of the base station,
Figure BDA0002910093900000069
Σ denotes a summation operation.
Step 2) clustering the MIMO network:
setting K to 5 users in MIMO network
Figure BDA00029100939000000610
And K base stations nearest to the K base stations
Figure BDA00029100939000000611
Division into clusters
Figure BDA00029100939000000612
Obtaining a cluster set
Figure BDA00029100939000000613
Wherein the content of the first and second substances,K＝M+N-1，
Figure BDA00029100939000000614
when cluster division is carried out, K base stations closest to K users can be determined by drawing a Voronoi diagram of K order on a plane.
Step 3) Each cluster
Figure BDA00029100939000000615
Each user in
Figure BDA00029100939000000616
And a base station
Figure BDA00029100939000000617
And (3) performing association:
in order to reduce the load of the backhaul link by using the buffer files and ensure that the signal strength of the signal transmitted by the base station to the user terminal is higher, the user selects the base station with the request file buffered most recently in the cluster for association, so that each cluster has a higher signal strength
Figure BDA00029100939000000618
Each user in
Figure BDA00029100939000000619
Phi and phisRecently cached with files
Figure BDA00029100939000000620
Base station of
Figure BDA00029100939000000621
An association is made, wherein,
Figure BDA00029100939000000622
step 4) Each cluster
Figure BDA00029100939000000623
For each user
Figure BDA00029100939000000624
With each base station
Figure BDA00029100939000000625
And (3) interference alignment is carried out:
considering each user
Figure BDA00029100939000000626
The multi-antenna configuration carries out interference alignment on each base station and each user in each cluster under the constraint that K is more than or equal to 3 and less than or equal to M + N-1, and can eliminate mutual interference of the base stations in the clusters, thereby improving the signal-to-interference ratio strength of each user side. In this embodiment, K + N-1-5.
Step 4a) design of each cluster
Figure BDA0002910093900000071
Each base station in
Figure BDA0002910093900000072
Of a precoding vector
Figure BDA0002910093900000073
And each user
Figure BDA0002910093900000074
Decoded vector of
Figure BDA0002910093900000075
Designing each base station
Figure BDA0002910093900000076
Of a precoding vector
Figure BDA0002910093900000077
Aligning the interfering signals into the same interfering signal space and making the interfering signal space orthogonal to the desired signal space, thereby designing each user
Figure BDA0002910093900000078
Decoding of(Vector)
Figure BDA0002910093900000079
The interference signal in the received signal can be eliminated, and the expected signal can be obtained. In this embodiment, each base station is designed by max-SINR method
Figure BDA00029100939000000710
Of a precoding vector
Figure BDA00029100939000000711
And each user
Figure BDA00029100939000000712
Decoded vector of
Figure BDA00029100939000000713
The method comprises the following steps:
step 4a1) set the maximum number of iteration steps Zmax5000, the current iteration step number z is 1, and an initial precoding vector is initialized randomly
Figure BDA00029100939000000714
And an initial decoded vector
Figure BDA00029100939000000715
Step 4a2) updating the interference noise covariance matrix
Figure BDA00029100939000000716
Sum-inverse interference noise covariance matrix
Figure BDA00029100939000000717
Figure BDA00029100939000000718
Figure BDA00029100939000000719
Wherein the content of the first and second substances,
Figure BDA00029100939000000720
indicating a base station
Figure BDA00029100939000000721
To the user
Figure BDA00029100939000000722
I denotes an identity matrix, (-)HRepresenting a conjugate transpose operation;
step 4a3) updating the base station
Figure BDA00029100939000000723
Of a precoding vector
Figure BDA00029100939000000724
Figure BDA00029100939000000725
Wherein the content of the first and second substances,
Figure BDA00029100939000000726
indicating a base station
Figure BDA00029100939000000727
To the user
Figure BDA00029100939000000728
Channel matrix between, (·)-1Expressing inversion operation, and expressing norm operation by | DEG |;
step 4a4) updating the user
Figure BDA00029100939000000729
Decoded vector of
Figure BDA00029100939000000730
Figure BDA0002910093900000081
Step 4a5) judgment
Figure BDA0002910093900000082
And
Figure BDA0002910093900000083
or Z ═ ZmaxIf true, obtaining a precoding vector
Figure BDA0002910093900000084
And decoding the vector
Figure BDA0002910093900000085
Otherwise, let z be z +1, and perform step (4a 2);
clusters are obtained by a max-SINR method
Figure BDA0002910093900000086
Each base station in
Figure BDA0002910093900000087
Of a precoding vector
Figure BDA0002910093900000088
And each user
Figure BDA0002910093900000089
Decoded vector of
Figure BDA00029100939000000810
Step 4b) Each Cluster
Figure BDA00029100939000000811
Each base station in
Figure BDA00029100939000000812
To each user
Figure BDA00029100939000000813
Transmitting coded signals
Figure BDA00029100939000000814
Each cluster
Figure BDA00029100939000000815
Each base station in
Figure BDA00029100939000000816
To each user
Figure BDA00029100939000000817
Transmitting coded signals
Figure BDA00029100939000000818
Wherein the content of the first and second substances,
Figure BDA00029100939000000819
presentation document
Figure BDA00029100939000000820
The symbol of (1); each base station
Figure BDA00029100939000000821
Using precoding vectors
Figure BDA00029100939000000822
The interfering signals caused to other users are aligned to the same signal space.
Step 4c) Each cluster
Figure BDA00029100939000000823
Each user therein
Figure BDA00029100939000000824
Receiving a signal
Figure BDA00029100939000000825
Each cluster
Figure BDA00029100939000000826
Each user therein
Figure BDA00029100939000000827
Receiving associated base stations
Figure BDA00029100939000000828
Transmitted by
Figure BDA00029100939000000829
Coded signal after channel coding
Figure BDA00029100939000000830
Figure BDA00029100939000000831
Each base station in
Figure BDA00029100939000000832
Transmitted by
Figure BDA00029100939000000833
Channel coded signal
Figure BDA00029100939000000834
And other base stations BiTransmitted siCoded signal after channel coding
Figure BDA00029100939000000835
Superimposed signals
Figure BDA00029100939000000836
Figure BDA00029100939000000837
Wherein the content of the first and second substances,
Figure BDA00029100939000000838
for indicatingHousehold
Figure BDA00029100939000000839
And a base station
Figure BDA00029100939000000840
The distance between the two, alpha represents the path fading, and \ represents the set difference set operation; first item
Figure BDA00029100939000000841
For associating base stations
Figure BDA00029100939000000842
Sent to the user
Figure BDA00029100939000000843
Of the desired signal, the second term
Figure BDA00029100939000000844
For other base stations in the cluster
Figure BDA00029100939000000845
The resulting interference signal, item three
Figure BDA00029100939000000846
For other base stations BiThe resulting interference signal; because the base station uses the precoding vector to carry out coding transmission, the base station enables the base station to use the precoding vector to carry out coding transmission
Figure BDA00029100939000000847
And
Figure BDA00029100939000000848
orthogonal in signal space.
Step 4d) Each cluster
Figure BDA00029100939000000849
Each user therein
Figure BDA00029100939000000850
By decoding the vector
Figure BDA00029100939000000851
To pair
Figure BDA00029100939000000852
Filtering to obtain decoded signal
Figure BDA0002910093900000091
Figure BDA0002910093900000092
Wherein, the base station
Figure BDA0002910093900000093
To the user
Figure BDA0002910093900000094
Equivalent channel parameters of
Figure BDA0002910093900000095
Each user
Figure BDA0002910093900000096
Using decoded vectors
Figure BDA0002910093900000097
Filtering elimination clusters
Figure BDA0002910093900000098
Interference signals caused by other base stations in the cell
Figure BDA0002910093900000099
And obtaining a decoded signal with partial interference eliminated.
K-1 interfering signals in a cluster can be cancelled using an interference alignment technique in each cluster. However, when the zero forcing technique is applied to the MIMO network, only M-1 interference signals can be eliminated. Thus, using interference alignment, N-1 more recent interfering signals can be cancelled than using zero-forcing techniques. This is because the interference alignment technology performs interference alignment design on K users and K base stations closest to the K users, and the zero forcing technology only considers a single user and M base stations. Therefore, compared with the zero forcing technology, the interference alignment technology is adopted to obtain less interference signal components in the decoded signals, the obtained user side signal-to-interference ratio is higher, and the success rate of correct file transmission is favorably improved.
Step 5) calculating the hit rate P of the MIMO networkhit：
Hit ratio P of MIMO networkhitDefined as the probability that a file in a MIMO network is cached in the caching device of the base station and correctly sent to the associated user. The hit rate of a MIMO network is related to two factors: the probability of the file being cached and the file transfer success rate.
Figure BDA00029100939000000910
Wherein the content of the first and second substances,
Figure BDA00029100939000000911
it is shown that the probability of occurrence of an event is calculated,
Figure BDA00029100939000000912
expressing the expected value of the calculation event, |, expressing the operation of taking the modulus value, the base station
Figure BDA0002910093900000101
To the user
Figure BDA0002910093900000102
Signal-to-interference ratio of terminal
Figure BDA0002910093900000103
Theta 15dB represents the threshold value of signal-to-interference ratio of correctly received signal of user
Figure BDA0002910093900000104
End interference signal strength
Figure BDA0002910093900000105
Auxiliary function
Figure BDA0002910093900000106
acot (·) represents an inverse cotangent function. p is a radical ofl(1-pl)k-1The file representing the request is cached in the caching device of the base station which is k-th closer to the user,
Figure BDA0002910093900000107
representing a user
Figure BDA0002910093900000108
Receiving base station
Figure BDA0002910093900000109
The probability that the signal-to-interference ratio of the signal at the user terminal is greater than the receiving threshold value is equivalent to the success rate of correct transmission of the file.
In this embodiment, the success rate of correct transmission of a file sent by a base station in a cluster to an associated user can be obtained: when the user is associated with the nearest base station, the base station sends the correct transmission success rate of the file: 0.994;
when the user is associated with the base station close to the 2 nd distance, the base station sends the correct transmission success rate of the file: 0.975;
when the user is associated with the base station close to the 3 rd base station, the base station sends the correct transmission success rate of the file: 0.946; when the user is associated with the base station close to the 4 th distance, the base station sends the correct transmission success rate of the file: 0.906; when the user is associated with the base station close to the 5 th distance, the base station sends the correct transmission success rate of the file: 0.857.
step 6) establishing and solving to maximize the hit rate PhitOptimization problem for the target:
the hit rate of the MIMO network reflects the effect of the cache scheme on reducing the load of the backhaul link, the higher the hit rate is, the more remarkable the effect of the cache scheme on reducing the load of the backhaul link is, and therefore the establishment is made to maximize the hit rate PhitOptimization problem for target P:
Figure BDA00029100939000001010
Figure BDA00029100939000001011
Figure BDA00029100939000001012
wherein the constraint condition 0 is not less than pl1 is a probability feature constraint, constraint condition, on cache placement probability
Figure BDA00029100939000001013
The constraint relation between the file cache placement probability and the capacity of the cache equipment of the base station is concerned, and the cache placement scheme is designed so that the file cache placement probability does not violate the capacity limit of the cache equipment of the base station. By adjusting the cache placement probability plDifferent MIMO network hit rates P can be obtainedhit. Solving the optimization problem P to obtain the optimized cache placement probability
Figure BDA0002910093900000111
Maximizing hit ratio P of MIMO networkhit。
(6a) Establishing a Lagrangian function:
since the optimization problem P is a convex problem, the lagrangian function is established:
Figure BDA0002910093900000112
wherein u is a Lagrangian multiplier;
(6b) determining a KKT condition:
for lagrange function
Figure BDA0002910093900000113
And performing first-order partial derivation to obtain a KKT condition:
Figure BDA0002910093900000114
Figure BDA0002910093900000115
(6c) computing optimized cache placement probabilities
Figure BDA0002910093900000116
Solving the optimal solution of the optimization problem P according to the KKT condition
Figure BDA0002910093900000117
Wherein, wl(u) is the non-negative real root of the KKT conditional equation.
In this embodiment, the lagrangian multiplier u obtained by calculation is 0.00917, and the optimal cache placement probability of the first 35 files in the MIMO network is obtained as follows:
0.946、0.745、0.663、0.605、0.559、0.519、0.485、0.454、0.425、0.399、0.374、0.351、0.330、0.309、0.289、0.270、0.252、0.235、0.218、0.202、0.186、0.171、0.157、0.142、0.128、0.115、0.101、0.089、0.076、0.064、0.051、0.040、0.028、0.017、0.005；
the optimized cache placement probability for the remaining 65 files is 0. When the optimized cache placement probability is adopted, the maximum hit rate of the MIMO network is as follows: 0.884.
step 7) Each base station BiCaching each file Fl：
Each base station BiTo optimize cache placement probability
Figure BDA0002910093900000118
Each file FlBuffer to buffer device
Figure BDA0002910093900000119
In (1).

Claims (5)

1. An MIMO network cache placement method based on interference alignment is characterized by comprising the following steps:
(1) setting MIMO network parameters:
the structure comprises a plurality of base stations
Figure FDA0002910093890000011
Multiple users
Figure FDA0002910093890000012
And a MIMO network of databases,
Figure FDA0002910093890000013
is subject to a position distribution of intensity lambdaBHomogeneous poisson point process of phiB＝{di|i≥3}，
Figure FDA0002910093890000014
Is subject to a position distribution of intensity lambdaUHomogeneous poisson point process of
Figure FDA0002910093890000015
The database contains L files
Figure FDA0002910093890000016
Wherein, BiIndicating the configuration of a cache device capable of storing C files
Figure FDA0002910093890000017
And the ith base station of M antennas, C is more than or equal to 1, M is more than or equal to 2, diIs represented by BiPosition coordinates of (1), UjIndicating the j-th user configured with N antennas, N ≧ 2,
Figure FDA0002910093890000018
represents UjL is not less than C, FlIndicates a popularity of qlQuilt baseStation BiThe probability of buffering is plThe first file of (a) is stored,
Figure FDA0002910093890000019
gamma represents a zipff distribution parameter, gamma > 0,
Figure FDA00029100938900000110
sigma represents summation operation;
(2) clustering the MIMO network:
grouping K users in a MIMO network
Figure FDA00029100938900000111
And K base stations nearest to the K base stations
Figure FDA00029100938900000112
Division into clusters
Figure FDA00029100938900000113
Obtaining a cluster set
Figure FDA00029100938900000132
Wherein K is more than or equal to 3 and less than or equal to M + N-1,
Figure FDA00029100938900000115
(3) each cluster CsEach user in
Figure FDA00029100938900000116
And a base station
Figure FDA00029100938900000117
And (3) performing association:
each cluster
Figure FDA00029100938900000118
Each user in
Figure FDA00029100938900000119
Phi and phisRecently cached with files
Figure FDA00029100938900000120
Base station of
Figure FDA00029100938900000121
An association is made, wherein,
Figure FDA00029100938900000122
(4) each cluster
Figure FDA00029100938900000123
For each user
Figure FDA00029100938900000124
With each base station
Figure FDA00029100938900000125
And (3) interference alignment is carried out:
(4a) design each cluster
Figure FDA00029100938900000126
Each base station in
Figure FDA00029100938900000127
Of a precoding vector
Figure FDA00029100938900000128
And each user
Figure FDA00029100938900000129
Decoded vector of
Figure FDA00029100938900000130
Figure FDA00029100938900000131
Figure FDA0002910093890000021
Figure FDA0002910093890000022
Figure FDA0002910093890000023
Wherein the content of the first and second substances,
Figure FDA0002910093890000024
representing the inverse interference noise covariance matrix,
Figure FDA0002910093890000025
representing the interference noise covariance matrix,
Figure FDA0002910093890000026
indicating a base station
Figure FDA0002910093890000027
To the user
Figure FDA0002910093890000028
I denotes an identity matrix, (-)-1Representing an inversion operation (·)HExpressing conjugate transposition operation, and expressing norm operation by | DEG |;
(4b) each cluster
Figure FDA0002910093890000029
Each base station in
Figure FDA00029100938900000210
To each user
Figure FDA00029100938900000211
Transmitting coded signals
Figure FDA00029100938900000212
Each cluster
Figure FDA00029100938900000213
Each base station in
Figure FDA00029100938900000214
To each user
Figure FDA00029100938900000215
Transmitting coded signals
Figure FDA00029100938900000216
Wherein the content of the first and second substances,
Figure FDA00029100938900000217
presentation document
Figure FDA00029100938900000218
The symbol of (1);
(4c) each cluster
Figure FDA00029100938900000219
Each user therein
Figure FDA00029100938900000220
Receiving a signal
Figure FDA00029100938900000221
Each cluster
Figure FDA00029100938900000222
Each user therein
Figure FDA00029100938900000223
Receiving associated base stations
Figure FDA00029100938900000224
Transmitted by
Figure FDA00029100938900000225
Coded signal after channel coding
Figure FDA00029100938900000226
Figure FDA00029100938900000227
Each base station in
Figure FDA00029100938900000228
Transmitted by
Figure FDA00029100938900000229
Channel coded signal
Figure FDA00029100938900000230
And other base stations BiTransmitted siCoded signal after channel coding
Figure FDA00029100938900000231
Superimposed signals
Figure FDA00029100938900000232
Figure FDA00029100938900000233
Wherein the content of the first and second substances,
Figure FDA00029100938900000234
representing a user
Figure FDA00029100938900000235
And a base station
Figure FDA00029100938900000236
The distance between the two, alpha represents the path fading, and \ represents the set difference set operation;
(4d) each cluster
Figure FDA00029100938900000237
Each user therein
Figure FDA00029100938900000238
By decoding the vector
Figure FDA00029100938900000239
To pair
Figure FDA00029100938900000240
Filtering to obtain decoded signal
Figure FDA00029100938900000241
Figure FDA00029100938900000242
Wherein, the base station
Figure FDA00029100938900000243
To the user
Figure FDA00029100938900000244
Equivalent channel parameters of
Figure FDA00029100938900000245
(5) Calculating hit ratio P for MIMO networkshit：
Hit ratio P of MIMO networkhitDefined as the probability that a file in the MIMO network is cached in the caching device of the base station and correctly sent to the associated user:
Figure FDA0002910093890000031
wherein theta represents the threshold value of signal-to-interference ratio of correctly received signal of user, and auxiliary function
Figure FDA0002910093890000032
(6) Building and solving to maximize hit ratio PhitOptimization problem for the target:
set up to maximize hit rate PhitAn optimization problem P is taken as a target, and the P is solved to obtain the optimized cache placement probability
Figure FDA0002910093890000033
Figure FDA0002910093890000034
Figure FDA0002910093890000035
Figure FDA0002910093890000036
Figure FDA0002910093890000037
Where u is the Lagrangian multiplier, wl(u) is the equation
Figure FDA0002910093890000038
Non-negative true roots of (1);
(7) each base station BiCaching each file Fl：
Each base station BiTo optimize cache placement probability
Figure FDA0002910093890000039
Each file FlBuffer to buffer device
Figure FDA00029100938900000310
In (1).
2. The method of claim 1, wherein the step (4a) of designing each cluster
Figure FDA00029100938900000311
Each base station in
Figure FDA00029100938900000312
Of a precoding vector
Figure FDA00029100938900000313
And each user
Figure FDA00029100938900000314
Decoded vector of
Figure FDA00029100938900000315
The method comprises the following implementation steps:
(4a1) setting the maximum number of iteration steps ZmaxRandomly initializing an initial precoding vector when the current iteration step number z is equal to 1
Figure FDA00029100938900000316
And an initial decoded vector
Figure FDA00029100938900000317
(4a2) Updating interference noise covariance matrix
Figure FDA0002910093890000041
Sum-inverse interference noise covariance matrix
Figure FDA0002910093890000042
Figure FDA0002910093890000043
Figure FDA0002910093890000044
Wherein the content of the first and second substances,
Figure FDA0002910093890000045
indicating a base station
Figure FDA0002910093890000046
To the user
Figure FDA0002910093890000047
I denotes an identity matrix, (-)HRepresenting a conjugate transpose operation;
(4a3) updating a base station
Figure FDA0002910093890000048
Of a precoding vector
Figure FDA0002910093890000049
Figure FDA00029100938900000410
Wherein the content of the first and second substances,
Figure FDA00029100938900000411
indicating a base station
Figure FDA00029100938900000412
To the user
Figure FDA00029100938900000413
Channel matrix between, (·)-1Representing an inversion operation;
(4a4) updating a user
Figure FDA00029100938900000414
Decoded vector of
Figure FDA00029100938900000415
Figure FDA00029100938900000416
(4a5) Judgment of
Figure FDA00029100938900000417
And
Figure FDA00029100938900000418
or Z ═ ZmaxIf true, obtaining a precoding vector
Figure FDA00029100938900000419
And decoding the vector
Figure FDA00029100938900000420
Otherwise, let z be z +1, and perform step (4a 2).
3. The method according to claim 1The MIMO network buffer placement method with interference alignment is characterized in that, each cluster in the step (4d)
Figure FDA00029100938900000421
Each user therein
Figure FDA00029100938900000422
By decoding the vector
Figure FDA00029100938900000423
To pair
Figure FDA00029100938900000424
Filtering is carried out, and the filtering formula is as follows:
Figure FDA00029100938900000425
wherein, the base station
Figure FDA0002910093890000051
To the user
Figure FDA0002910093890000052
Equivalent channel parameters of
Figure FDA0002910093890000053
4. The method according to claim 1, wherein the step (5) of calculating the hit ratio P of the MIMO networkhitThe calculation formula is as follows:
Figure FDA0002910093890000054
wherein the content of the first and second substances,
Figure FDA0002910093890000055
it is shown that the probability of occurrence of an event is calculated,
Figure FDA0002910093890000056
expressing the expected value of the calculation event, |, expressing the operation of taking the modulus value, the base station
Figure FDA0002910093890000057
To the user
Figure FDA0002910093890000058
Signal-to-interference ratio of terminal
Figure FDA0002910093890000059
Theta represents the signal-to-interference ratio threshold value of successful reception of the user, and the user
Figure FDA00029100938900000510
End interference signal strength
Figure FDA00029100938900000511
5. The method for placing the buffer of the MIMO network based on the interference alignment according to claim 1, wherein the step (6) of solving P is implemented as:
(6a) establishing a Lagrangian function:
Figure FDA00029100938900000512
wherein u is a Lagrangian multiplier;
(6b) determining a KKT condition:
Figure FDA00029100938900000513
Figure FDA00029100938900000514
(6c) computing optimized cache placement probabilities
Figure FDA00029100938900000515
Figure FDA0002910093890000061
Wherein, wl(u) is the non-negative real root of the KKT conditional equation.
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