CN106788621B - Tree-shaped heterogeneous network base station clustering and beam forming method with limited backhaul link capacity - Google Patents

Tree-shaped heterogeneous network base station clustering and beam forming method with limited backhaul link capacity Download PDF

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CN106788621B
CN106788621B CN201510822039.6A CN201510822039A CN106788621B CN 106788621 B CN106788621 B CN 106788621B CN 201510822039 A CN201510822039 A CN 201510822039A CN 106788621 B CN106788621 B CN 106788621B
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base station
user
backhaul link
kth
tree
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CN106788621A (en
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张茜
何晨
蒋铃鸽
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Shanghai Jiaotong 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
    • H04B7/022—Site diversity; Macro-diversity
    • H04B7/024—Co-operative use of antennas of several sites, e.g. in co-ordinated multipoint or co-operative multiple-input multiple-output [MIMO] systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
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Abstract

The invention provides a method for clustering and beamforming a tree-shaped heterogeneous network base station with limited backhaul link capacity.A central processing unit and the base station form a multilayer tree-shaped network, the speed of the worst user is taken as an optimization target, binary search is adopted for a target value, and a three-step algorithm is adopted for each subproblem to judge whether the operation is feasible. The invention can strictly ensure the capacity constraint of the backhaul link, obtain better user rate and require less calculation time.

Description

Tree-shaped heterogeneous network base station clustering and beam forming method with limited backhaul link capacity
Technical Field
The invention relates to the technical field of wireless communication, in particular to a clustering and beam forming method for a tree-shaped heterogeneous network base station with limited backhaul link capacity.
Background
In recent years, the number of users of wireless communication systems has increased dramatically, and along with the development of multimedia services, the demand for high data rates by users has become more urgent. In order to improve system performance and expand network coverage, a large number of new access points need to be added to a conventional network, and the cost of laying base stations is high, so that the concept of heterogeneous networks is proposed and has received a lot of attention from both academic and industrial fields. In a heterogeneous network, a large number of nodes with low transmission power are distributed in a conventional macro cell, and the base stations include a pico base station (pico BS), a home base station (femto BS), and the like. A user with poor channel conditions with a macro base station (macro BS) may select a low power base station with better access channel conditions. However, as the distribution density of low power nodes increases, the interference situation of the network becomes more complicated than that of the conventional macro cell, and the inter-cell interference becomes a main factor limiting the performance of the heterogeneous network.
The cooperative transmission of multiple base stations is an effective method for suppressing inter-cell interference, and generally includes two ways: coordinated Beamforming (CB) and Joint Processing (JP). CB requires each user to access only one base station, and JP provides services to users by combining all base stations in the network. JP has a good performance, but a large amount of user data needs to be interacted between base stations, and in an actual system, the capacity of a backhaul link (backhaul link) connecting the base stations is limited, so that the JP mode cannot be supported. Therefore, the base station clustering method considering the limited backhaul link capacity has important practical significance. The simple processing method is to select a fixed number of base stations for each user, and the selection criteria include channel gain, signal-to-noise ratio, and the like. The method can obtain better performance when the number of users is small, and when the number of users is large, the situation that the same base station serves a plurality of users occurs, and the backhaul link capacity of the base station can limit the system performance. Therefore, in the prior art, mostly, the system performance is taken as an optimization target, and an indefinite number of base stations are selected for each user to serve.
Documents of b.dai and w.yu, "Sparse beamforming for limited-backhaul network MIMO system weighted power minimization" of a limited backhaul link network MIMO system, "IEEE global communications Conference (global), dec.2013, are disclosed in the prior art, and considering that the total power of each user is minimized when a certain performance requirement is met, the number of serving base stations of each user is constructed as a beamforming vector 2-norm (l-norm)2Norm 0 (l) of norm0Norm) and as a penalty term for the objective function, an iterative reweighted 1-norm (reweighted l) is used1Norm) method, reducing the number of serving base stations while optimizing the power.
M. hong, R.Sun, H.Baligh, and Z. -Q. L uo, documents "Joint base station clustering and beamforming for partial coordinated transmission networks" IEEE Journal on Selected Areas in Communications, vol.31, No.2, pp.226-240, Feb.2013, and also constructs the number of serving base stations as l2/l0-norm objective function penalty term, using reweighted l1The norm method, which proposes base station clustering and beamforming algorithms that balance system weights and rates with the number of serving base stations.
However, neither of the above two methods directly considers backhaul link capacity, and thus the resulting clustering scheme does not necessarily satisfy practical system limitations. The document "Spars" of D.Bai and W.Yu is disclosed in the prior arte-beamforming for network MIMO system with per-base-station-backhaul link capacity constraint method of sparse beamforming method of network MIMO system, 'in IEEE International work on Signal Processing Advances in Wireless Communications (SPAWC)' Jun.2014, wherein the capacity constraint of each base station backhaul link is taken as a constraint condition, and reweighed l is adopted1Approximation of l by the norm method0Norm and fix the user rate in the constraints to the value of the last iteration, optimizing the clustering and beamforming vectors. Although this approach directly considers backhaul link capacity, the backhaul link capacity limit is still not strictly guaranteed due to the approximation used.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a tree-shaped heterogeneous network base station clustering and beam forming method with limited backhaul link capacity.
The invention provides a method for clustering and beamforming a tree-shaped heterogeneous network base station with limited backhaul link capacity, which comprises the following steps:
step 1: setting system parameters:
the number of base stations is N, and N is a positive integer;
the number of base station antennas is A, and A is a positive integer;
the power constraint of the nth base station is Pn；
The capacity of the nth base station flowing into the backhaul link is Cn；
The lower layer base station of the nth base station is set as
Figure BDA0000855286850000036
The number of the single antenna users is K, and K is a positive integer;
the covariance of the zero mean complex Gaussian additive noise at the kth single antenna user is
Figure BDA0000855286850000037
The channel vector from the nth base station to the kth single-antenna user with dimension 1 × A is hnk；
Wherein, N is 1, 1., N, K is 1, 1.,;
step 2:
constructing a channel vector h with the dimension of 1 × NA from all base stations to the kth single-antenna userk，hk＝[h1k,h2k,...,hNk]Definition of vnkFor the beam forming vector with the dimension of A × 1 of the kth single-antenna user of the nth base station, the beam forming vector v of all the base stations with the dimension of NA × 1 of the kth single-antenna user is constructedk，
Figure BDA0000855286850000031
The superscript H denotes the conjugate transpose, defining γkReceived signal to interference noise power ratio for the kth single antenna user;
Figure BDA0000855286850000032
wherein j is 1, a., K-1, K +1, a.
And step 3: definition of tnmIs a variable of 0-1 indicating whether the mth base station is a lower node of the nth base station, i.e.
Figure BDA0000855286850000033
Wherein: n, · 1;
definition of xnkIs a 0-1 variable that indicates whether the nth base station serves the kth single-antenna user or not, i.e.
Figure BDA0000855286850000034
And 4, step 4: defining R as minimum user rate, initializing lower bound R of RminUpper boundary RmaxUpper and lower bound convergence thresholds η;
and 5: setting R ═ Rmin+Rmax) And/2, judging whether the system can support all the single-antenna users to at least reach the speed R, namely solving a feasible problem
Figure BDA0000855286850000035
Step 6: if it is not
Figure BDA0000855286850000041
If feasible, update the lower bound RminR; if it is not
Figure BDA0000855286850000042
If it is not feasible, the upper bound R is updatedmax＝R；
And 7: checking the difference R between the upper and lower boundsmax-RminIf R ismax-Rmin>η, returning to the step 5, otherwise, outputting R,
Figure BDA0000855286850000043
wherein the content of the first and second substances,
Figure BDA0000855286850000044
is the solution.
Preferably, the feasibility problem in step 5 is
Figure BDA0000855286850000046
The method comprises the following steps:
Figure BDA0000855286850000047
s.t.γk≥2R-1,k＝1,...,K
∑kxnkR≤Cn,n＝1,...,N
∑k||vnk||2≤Pn,n＝1,...,N
||vnk||≤xnkPn,n＝1,...,N,k＝1,...,K
xnk≥tnmxmk,m,n＝1,...,N,k＝1,...,K
xnk∈{0,1},n＝1,...,N,k＝1,...,K
wherein: x is the number ofnk∈ {0,1} denotes xnkIs gotThe values belong to the set 0,1, i.e. xnkIs a 0-1 variable, the notation Find denotes the sought variable, the notation s.t. denotes constrained by, xmkA 0-1 variable indicating whether the mth base station serves the kth single-antenna user.
Preferably, in step 5, it is determined whether the system can support all the single-antenna users at least to reach the rate R through a three-step algorithm;
the three-step algorithm comprises the following steps:
i) solving a power minimization problem
Figure BDA0000855286850000048
Obtaining beamforming vectors
Figure BDA0000855286850000049
ii) solving a linear optimization problem
Figure BDA00008552868500000410
If x is foundnkIf the number of the users is 1, the nth base station is allocated to serve the kth user, otherwise, the nth base station does not serve the kth user;
iii) judging whether the system can support all single-antenna users to at least reach the rate R under the current base station clustering scheme, and solving the optimization problem
Figure BDA00008552868500000411
Obtaining target function value α, if α is less than or equal to 1, judging
Figure BDA00008552868500000412
Feasible if α>1, then judging
Figure BDA00008552868500000413
It is not feasible.
Preferably, the power minimization problem
Figure BDA00008552868500000414
The method comprises the following steps:
Figure BDA0000855286850000051
s.t.γk≥2R-1,k＝1,...,K。
∑k||vnk||2≤Pn,n＝1,...,N
preferably, the linear optimization problem
Figure BDA0000855286850000052
The method comprises the following steps:
Figure BDA0000855286850000053
s.t.xnk≥tnmxmk,m,n＝1,...,N,k＝1,...,K
Figure BDA0000855286850000054
0≤xnk≤1,n＝1,...,N,k＝1,...,K
wherein:
Figure BDA0000855286850000055
represents a round-down operation; q. q.snkThe importance factor of the kth single-antenna user is served to the nth base station.
Preferably, q isnkThe definition of (A) means:
Figure BDA0000855286850000056
wherein: v. ofnkIs composed of
Figure BDA0000855286850000057
N1, K1, a.
Preferably, the optimization problem
Figure BDA0000855286850000058
The method comprises the following steps:
Figure BDA0000855286850000059
s.t.γk≥2R-1,k＝1,...,K
∑k||vnk||2≤αPn,n＝1,...,N
vnk＝xnkvnk,n＝1,...,N,k＝1,...,K
wherein: x is the number ofnkIs composed of
Figure BDA00008552868500000510
N1, 1., N, K1.,; when x isnkWhen 0, the constraint condition vnk＝xnkvnkLimiting beamforming vectors vnkIs 0, and when x isnkWhen 1, the constraint vnk＝xnkvnkBecomes a redundant constraint and is removed.
Compared with the prior art, the invention has the following beneficial effects:
the method considers the worst user rate maximization, adopts a dichotomy combined with a three-step algorithm comprising power distribution, base station clustering determination and feasible judgment, can strictly ensure the capacity constraint of the backhaul link, and has low calculation complexity of each step and better system performance.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a schematic diagram of a multi-layered tree heterogeneous network;
fig. 2 is a diagram of a multi-layer heterogeneous network base station distribution and backhaul link connection scenario with N-20;
FIG. 3 is a diagram illustrating that the method of the embodiment and the reweighed l-based method in the prior art are respectively adopted in the scenario of FIG. 21-worst user rate comparison graph of norm's algorithm;
FIG. 4 is a diagram illustrating that the method of the embodiment and the reweighed l-based method in the prior art are respectively adopted in the scenario of FIG. 21Of normThe computation time of the algorithm is compared with the graph.
In fig. 2, macro BS denotes a macro base station, and pico BS denotes a micro base station.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
The invention provides a method for clustering and beam forming of a tree-shaped heterogeneous network base station with limited backhaul link capacity, which belongs to the technical field of wireless communication. And taking the speed of the worst user as an optimization target, adopting binary search for the target value, and judging whether the target value is feasible or not by adopting a three-step algorithm for each subproblem. The method can strictly ensure the capacity constraint of the backhaul link, obtain better user rate and require less calculation time.
Specifically, the method takes the worst user rate as an optimization target, adopts binary search for a target value, and adopts a three-step algorithm to judge whether the target value is feasible or not for each subproblem, so as to obtain a base station clustering and beam forming scheme which strictly meets the capacity constraint of a backhaul link and has better system performance. The base station clustering and beam forming optimization problem is as follows:
max R
s.t.R≤log2(1+γk),k＝1,...,K
∑kxnkR≤Cn,n＝1,...,N
∑k||vnk||2≤Pn,n＝1,...,N
||vnk||≤xnkPn,n＝1,...,N,k＝1,...,K
xnk≥tnmxmk,m,n＝1,...,N,k＝1,...,K
xnk∈{0,1},n＝1,...,N,k＝1,...,K
wherein:
Figure BDA0000855286850000071
wherein: gamma raykIs the received signal to interference noise power ratio of the kth user, is the covariance of the zero mean complex Gaussian additive noise of the kth user, hk＝[h1k,h2k,...,hNk]For all base stations to the k-th user's channel vector,
Figure BDA0000855286850000073
beamforming vectors for all base stations for the kth user, R being the worst user rate (i.e., minimum user rate), PnFor power constraints of the nth base station, CnCapacity, x, of backhaul link for the nth base stationnkA variable of 0-1, t, indicating whether the nth base station serves the kth usernmIs a 0-1 known variable indicating whether the mth base station is the nth base station lower node.
The design method comprises the following steps:
firstly, setting system parameters: number of base stations N, number of base station antennas A, power constraint P of nth base stationnCapacity C of the backhaul link into which the nth base station flowsnLower base station set of nth base station
Figure BDA0000855286850000074
Wherein: n1.. N, number of single antenna users K, covariance of zero-mean complex gaussian additive noise at kth user
Figure BDA0000855286850000075
K, channel vector h with dimension from nth base station to kth user being 1 × ankWherein: n1, N, K1, K;
in this embodiment, the simulation scenario is shown in fig. 2, where N is 20, a is 4,
Figure BDA0000855286850000076
the connection situation of the base stations in FIG. 2 shows that the 1 st, 5 th, 11 th and 17 th base stations are macro BS, and the rest base stations are pico BS and Pmacro＝46dBm，PpicoThe inflow backhaul link capacity of the macro BS is 100bps/Hz, the inflow backhaul link capacity of the pico BS connected to the macro BS is 50bps/Hz, and the inflow backhaul link capacity of the pico BS connected to the other pico BS is 30bps/Hz, which is 30 dBm. Wherein, PmacroDenotes the maximum transmit power, P, of the macro BSpicoRepresents the maximum transmit power of the pico BS;
in this embodiment, the noise variance is-169 dBm/Hz, the bandwidth is 10MHz, and the channel vector
Figure BDA0000855286850000077
Figure BDA0000855286850000078
Each term of (a) is a random variable, μ, subject to a complex gaussian distribution with a mean of 0 and a variance of 1nkFor the pathloss coefficient, μ for macro BSnk＝128.1+37.6log10(dnk) For pico BS,. mu.nk＝140.7+36.7log10(dnk) Wherein d isnkThe distance from the nth base station to the kth user is expressed in km, the base station positions are shown in figure 2, and the users are uniformly distributed in a square area of 2km × 2 km.
Secondly, constructing channel vectors h from all base stations to the kth user with the dimension of 1 × NAk＝[h1k,h2k,...,hNk]Wherein: k1, K, defines vnkAnd constructing a beamforming vector with the K user dimension of A × 1 for the nth base station, wherein N is 1, the right, N, K is 1, the right, and K, and constructing beamforming vectors with the K user dimension of NA × 1 for all base stations
Figure BDA0000855286850000081
Wherein: k1.. K, superscript H denotes the conjugate transpose, defining γkReceived signal to interference noise power ratio for the kth user
Figure BDA0000855286850000082
Wherein: k1., K;
thirdly, defining tnmIs a variable of 0-1 indicating whether the mth base station is a lower node of the nth base station, i.e.
Figure BDA0000855286850000083
Wherein: n1, N, m 1, N;
definition of xnkIs a 0-1 variable that indicates whether the nth base station serves the kth user or not, i.e.
Figure BDA0000855286850000084
Wherein: n1, N, K1, K;
fourthly, defining R as minimum user rate and initializing lower bound R of RminUpper bound RmaxAnd upper and lower bound convergence thresholds η;
in this example, Rmin＝0，Rmax＝400/K，η＝0.5。
The fifth step, set R ═ R (R)min+Rmax) And 2, judging whether the system can support all users to at least reach the rate R through a three-step algorithm, namely solving a feasible problem
Figure BDA0000855286850000085
The described feasibility problem
Figure BDA0000855286850000086
The method comprises the following steps:
Figure BDA0000855286850000087
s.t.γk≥2R-1,k＝1,...,K
∑kxnkR≤Cn,n＝1,...,N
∑k||vnk||2≤Pn,n＝1,...,N
||vnk||≤xnkPn,n＝1,...,N,k＝1,...,K
xnk≥tnmxmk,m,n＝1,...,N,k＝1,...,K
xnk∈{0,1},n＝1,...,N,k＝1,...,K
wherein: x is the number ofnk∈ {0,1} denotes xnkBelongs to the set 0,1, i.e. xnkIs a variable 0-1, N1., N, K1., K;
the three-step algorithm comprises the following steps:
i) solving a power minimization problem
Figure BDA0000855286850000091
Obtaining beamforming vectors
Figure BDA0000855286850000092
The power minimization problem
Figure BDA0000855286850000093
The method comprises the following steps:
Figure BDA0000855286850000094
s.t.γk≥2R-1,k＝1,...,K
∑k||vnk||2≤Pn,n＝1,...,N
ii) definition of qnkAn importance factor for serving the kth user to the nth base station, wherein: n1, N, K1, K, solving a linear optimization problem
Figure BDA0000855286850000095
Determining base station clustering scheme if x is foundnkIf 1, the nth base station is allocated to serve the kth user, otherwise, the nth base stationNot serving the kth user;
q is a number ofnkThe definition is as follows:
Figure BDA0000855286850000096
wherein: v. ofnkIs composed of
Figure BDA0000855286850000097
N1, 1., N, K1.,;
the linear optimization problem
Figure BDA0000855286850000098
The method comprises the following steps:
Figure BDA0000855286850000099
s.t.xnk≥tnmxmk,m,n＝1,...,N,k＝1,...,K
Figure BDA00008552868500000910
0≤xnk≤1，n＝1，...，N，k＝1，...，K
wherein:
Figure BDA00008552868500000911
represents a round-down operation;
iii) judging whether the system can support all users to at least reach the rate R under the current base station clustering scheme, and solving the optimization problem
Figure BDA00008552868500000912
Obtaining target function value α, if α is less than or equal to 1, judging
Figure BDA00008552868500000913
Feasible if α>1, then judging
Figure BDA00008552868500000914
Is not feasible;
the optimization problem
Figure BDA0000855286850000101
The method comprises the following steps:
Figure BDA0000855286850000102
s.t.γk≥2R-1,k＝1,...,K
∑k||vnk||2≤αPn,n＝1,...,N
vnk＝xnkvnk,n＝1,...,N,k＝1,...,K
wherein: x is the number ofnkIs composed of
Figure BDA0000855286850000103
N1, 1., N, K1.,;
sixth step, if
Figure BDA0000855286850000104
If feasible, update the lower bound RminR; if it is not
Figure BDA0000855286850000105
If it is not feasible, the upper bound R is updatedmax＝R；
Seventh, check the difference between the upper and lower limits, if Rmax-Rmin>η, return to step 5), otherwise the algorithm is cut off, output R,
Figure BDA0000855286850000106
FIG. 3 shows that the method provided by the present invention and the reweighedll-based method in the prior art are respectively adopted in the scenario of FIG. 21-worst user rate comparison graph for norm's algorithm.
FIG. 4 is a diagram illustrating a scenario in FIG. 2, in which the method provided by the present invention and the method based on reweighed l in the prior art are respectively adopted1-a comparison graph of the calculated times of the algorithm of norm.
As can be seen from FIGS. 3 and 4, the method provided by the present invention and the method based on reweighed l in the prior art1The norm algorithm can achieve a similar worst user rate but requires a significantly reduced computation time.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (5)

1. A method for clustering and beamforming a tree heterogeneous network base station with limited backhaul link capacity is characterized by comprising the following steps:
step 1: setting system parameters:
the number of base stations is N, and N is a positive integer;
the number of base station antennas is A, and A is a positive integer;
the power constraint of the nth base station is Pn；
The capacity of the nth base station flowing into the backhaul link is Cn；
The lower layer base station of the nth base station is set as
Figure FDA0002386466440000011
The number of the single antenna users is K, and K is a positive integer;
the covariance of the zero mean complex Gaussian additive noise at the kth single antenna user is
Figure FDA0002386466440000012
The channel vector from the nth base station to the kth single-antenna user with dimension 1 × A is hnk；
Wherein, N is 1, 1., N, K is 1, 1.,;
step 2:
for constructing all base stations to kth single antennaChannel vector h with dimension of 1 × NAk，hk＝[h1k,h2k,...,hNk]Definition of vnkFor the beam forming vector with the dimension of A × 1 of the kth single-antenna user of the nth base station, the beam forming vector v of all the base stations with the dimension of NA × 1 of the kth single-antenna user is constructedk，
Figure FDA0002386466440000013
The superscript H denotes the conjugate transpose, defining γkReceived signal to interference noise power ratio for the kth single antenna user;
Figure FDA0002386466440000014
wherein j is 1, a., K-1, K +1, a.
And step 3: definition of tnmIs a variable of 0-1 indicating whether the mth base station is a lower node of the nth base station, i.e.
Figure FDA0002386466440000015
Wherein: n, · 1;
definition of xnkIs a 0-1 variable that indicates whether the nth base station serves the kth single-antenna user or not, i.e.
Figure FDA0002386466440000021
And 4, step 4: defining R as minimum user rate, initializing lower bound R of RminUpper boundary RmaxUpper and lower bound convergence thresholds η;
and 5: setting R ═ Rmin+Rmax) And/2, judging whether the system can support all the single-antenna users to at least reach the speed R, namely solving a feasible problem
Figure FDA0002386466440000022
Step 6: if it is not
Figure FDA0002386466440000023
If feasible, update the lower bound RminR; if it is not
Figure FDA0002386466440000024
If it is not feasible, the upper bound R is updatedmax＝R；
And 7: checking the difference R between the upper and lower boundsmax-RminIf R ismax-RminIf the value is more than η, the step 5 is returned, otherwise, R is output,
Figure FDA0002386466440000025
wherein the content of the first and second substances,
Figure FDA0002386466440000026
is that
Figure FDA0002386466440000027
The solution of (1);
the feasibility problem in step 5
Figure FDA0002386466440000028
The method comprises the following steps:
Figure FDA0002386466440000029
s.t.γk≥2R-1,k＝1,...,K
∑kxnkR≤Cn,n＝1,...,N
∑k||vnk||2≤Pn,n＝1,...,N
||vnk||≤xnkPn,n＝1,...,N,k＝1,...,K
xnk≥tnmxmk,m,n＝1,...,N,k＝1,...,K
xnk∈{0,1},n＝1,...,N,k＝1,...,K
wherein: x is the number ofnk∈ {0,1} denotes xnkBelongs to the set 0,1, i.e. xnkIs a 0-1 variable, the notation Find denotes the sought variable, the notation s.t. denotes constrained by, xmkA 0-1 variable indicating whether the mth base station serves the kth single-antenna user;
in step 5, judging whether the system can support all single-antenna users to at least reach the rate R through a three-step algorithm;
the three-step algorithm comprises the following steps:
i) solving a power minimization problem
Figure FDA00023864664400000210
Obtaining beamforming vectors
Figure FDA00023864664400000211
ii) solving a linear optimization problem
Figure FDA00023864664400000212
If x is foundnkIf the number of the users is 1, the nth base station is allocated to serve the kth user, otherwise, the nth base station does not serve the kth user;
iii) judging whether the system can support all single-antenna users to at least reach the rate R under the current base station clustering scheme, and solving the optimization problem
Figure FDA0002386466440000031
Obtaining target function value α, if α is less than or equal to 1, judging
Figure FDA0002386466440000032
If α > 1, then a decision is made
Figure FDA0002386466440000033
It is not feasible.
2. The method of claim 1, wherein the method for clustering and beamforming tree heterogeneous base stations with limited backhaul link capacity is characterized byThe power minimization problem
Figure FDA0002386466440000034
The method comprises the following steps:
Figure FDA0002386466440000035
3. the method of claim 1, wherein the linear optimization problem is a tree-shaped heterogeneous network base station clustering and beamforming method with limited backhaul link capacity
Figure FDA0002386466440000036
The method comprises the following steps:
Figure FDA0002386466440000037
s.t.xnk≥tnmxmk,m,n＝1,...,N,k＝1,...,K
Figure FDA0002386466440000038
0≤xnk≤1,n＝1,...,N,k＝1,...,K
wherein:
Figure FDA0002386466440000039
represents a round-down operation; q. q.snkThe importance factor of the kth single-antenna user is served to the nth base station.
4. The method of claim 3, wherein q is q, q is a tree-shaped heterogeneous network base station clustering and beam forming method with limited backhaul link capacitynkThe definition of (A) means:
Figure FDA00023864664400000310
wherein：vnkIs composed of
Figure FDA00023864664400000311
N1, K1, a.
5. The method of claim 1, wherein the optimization problem is based on a tree-shaped heterogeneous network base station clustering and beamforming method with limited backhaul link capacity
Figure FDA00023864664400000312
The method comprises the following steps:
Figure FDA0002386466440000041
s.t.γk≥2R-1,k＝1,...,K
∑k||vnk||2≤αPn,n＝1,...,N
vnk＝xnkvnk,n＝1,...,N,k＝1,...,K
wherein: x is the number ofnkIs composed of
Figure FDA0002386466440000042
N1, 1., N, K1.,; when x isnkWhen 0, the constraint condition vnk＝xnkvnkLimiting beamforming vectors vnkIs 0, and when x isnkWhen 1, the constraint vnk＝xnkvnkBecomes a redundant constraint and is removed.
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