CN111132297B - Beam forming optimization method and device for minimizing transmission power of ultra-dense network - Google Patents

Beam forming optimization method and device for minimizing transmission power of ultra-dense network Download PDF

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CN111132297B
CN111132297B CN201911314897.4A CN201911314897A CN111132297B CN 111132297 B CN111132297 B CN 111132297B CN 201911314897 A CN201911314897 A CN 201911314897A CN 111132297 B CN111132297 B CN 111132297B
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base station
small base
matrix
user
optimization
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CN111132297A (en
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沈弘
何振耀
许威
赵春明
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Southeast University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/265—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the quality of service QoS
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/02—Power saving arrangements
    • H04W52/0203—Power saving arrangements in the radio access network or backbone network of wireless communication networks
    • H04W52/0206—Power saving arrangements in the radio access network or backbone network of wireless communication networks in access points, e.g. base stations
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/267—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the information rate
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/38—TPC being performed in particular situations
    • H04W52/40—TPC being performed in particular situations during macro-diversity or soft handoff
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Quality & Reliability (AREA)
  • Power Engineering (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention discloses a method and a device for optimizing beam forming of ultra-dense network transmission power minimization, which consider an ultra-dense network with a macro base station and a plurality of small base stations, a user accesses a corresponding base station according to the position of the user, and the method jointly optimizes the transmission beam forming of the macro base station and all the small base stations by constructing an optimization problem which takes the QoS requirement of the user and the return trip rate limitation of the small base stations as constraints and minimizes the total transmission power of a system. The optimization process is that firstly, an intermediate variable is introduced, the optimization problem about the intermediate variable is solved in an iterative mode, an SDP problem needs to be solved in each iterative process, then based on the optimal intermediate variable, a series of transmitting beam forming meeting the constraint of the original problem is obtained by adopting Gaussian randomization and serves as alternative solutions, and a group of solutions with the minimum transmitting power is selected and serves as the optimal transmitting beam forming. Compared with the traditional zero-forcing transmission scheme, the invention can obviously reduce the total transmission power of the system.

Description

Beam forming optimization method and device for minimizing transmission power of ultra-dense network
Technical Field
The invention relates to an ultra-dense network, in particular to a beam forming optimization method and device for minimizing the transmitting power of the ultra-dense network.
Background
With the continuous development of communication systems, the demand of network information transmission rate is continuously increased, the traditional macro base station cellular system is difficult to deal with the challenge brought by the explosive increase of communication services, in order to meet the performance index requirements of high density and high rate demand in hot spot scenes, the base station distance is further reduced, and the macro base station and a large number of small base stations of various types form a macro-micro heterogeneous Ultra Dense Network (UDN).
However, with the large-scale deployment of small base stations, energy consumption and backhaul rate requirements are issues to be solved. On the one hand, as the number of base stations increases, the energy consumption and cost of the base stations will also rise sharply; on the other hand, since the small base stations are irregularly and densely arranged, some of the small base stations cannot access through the conventional wired network, and a wireless backhaul link between the small base stations and the macro base station is required to ensure the transmission of information. Therefore, it becomes crucial regarding the reduction of energy consumption and the presence of the backhaul link.
In an MIMO transceiving system, multiple antennas can bring space diversity and multiplexing, so that the reliability of data transmission and channel gain are improved, but the generation of interference among users can bring certain influence on the signal to interference plus noise ratio (SINR) of a receiving end, and the service quality is influenced. The pre-coding technology can pre-process the data to be transmitted in a baseband to generate signals with specific spatial domain distribution characteristics, so that the data transmitted by the base station can be more effectively transmitted to users in a cell, and the interference among the users is reduced.
Disclosure of Invention
The invention aims to: the invention aims to provide a beam forming optimization method and device for minimizing the transmission power of a super-dense network. The method can meet the requirement of the backhaul link rate of the small base station aiming at the user QoS requirement of the ultra-dense network, and jointly optimize the transmitting beam vectors of the macro base station and the small base station so as to realize the minimum transmitting power.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for optimizing beamforming for minimizing transmit power of an ultra-dense network, which minimizes the problem of optimizing transmit power of a system by constructing constraints such as QoS of users of the ultra-dense network and backhaul rate limitation of small base stations, and jointly optimizes beamforming of a macro base station and a plurality of small base stations, and specifically includes the following steps:
(1) Introducing intermediate variables
Figure BDA0002325584300000011
Obtaining an optimization problem about the intermediate variable; wherein
Figure BDA0002325584300000012
A beamforming vector used by the macro base station for the ith user accessing the macro base station,
Figure BDA0002325584300000013
for the nth small base station pair to access the baseThe beamforming vector used by the jth user of the station,
Figure BDA0002325584300000014
beamforming matrix for use by macro base station to nth small base station, (·) H Representing a matrix conjugate transpose;
(2) Iteratively solving the problem in the step (1) to obtain an optimal solution of intermediate variables
Figure BDA0002325584300000021
(3) Obtaining a group of feasible solutions meeting the original problem constraint by adopting a Gaussian randomization method, and using the feasible solutions as alternatives;
(4) And (4) repeating the step (3) until the preset randomization times are reached, and selecting the solution with the minimum power from all the alternative solutions as the optimal solution.
Preferably, step (1) constructs the following optimization problem for intermediate variables:
the optimization target is as follows: minimization
Figure BDA0002325584300000022
The constraint conditions are as follows:
Figure BDA0002325584300000023
Figure BDA0002325584300000024
Figure BDA0002325584300000025
Figure BDA0002325584300000026
Figure BDA0002325584300000027
wherein log 2 (. DEG) represents a base-2 logarithmic function, | is a vector's two-norm, tr (. -) represents the trace of the matrix, (. DEG) -1 Representing the matrix inversion, det (-) representing the determinant of the matrix, rank (-) representing the rank of the matrix,
Figure BDA0002325584300000028
is N S ×N S Unit array of dimensions, N S The number of antennas of the small base station is,
Figure BDA0002325584300000029
for the channel between the macro base station to the ith user accessing the macro base station,
Figure BDA00023255843000000210
for the channel between the nth small base station to the jth user accessing the base station,
Figure BDA00023255843000000211
being a channel between the macro base station and the nth small base station,
Figure BDA00023255843000000212
a beamforming vector for use by the macro base station for the ith user accessing the macro base station,
Figure BDA00023255843000000213
a beamforming vector used by the nth small base station for the jth user accessing the base station,
Figure BDA00023255843000000214
beamforming matrix, γ, used by macro base station to nth small base station i The lowest SINR required for the ith user to access the macro base station,
Figure BDA00023255843000000215
minimum SINR, sigma, required for the jth user to access the nth small base station 2 Is the power of white gaussian noise and is,N n receiving a noise covariance matrix, U, for an nth small base station m Indicating a set of users, U, accessing a macro base station s,n Represents the user set accessed to the nth small base station, B represents the small base station set, X is more than or equal to 0 represents that the matrix X is a semi-positive definite matrix, rank (-) represents the rank of the matrix,
Figure BDA00023255843000000216
and the number of the parallel transmission data streams sent by the macro base station to each small base station is represented.
Preferably, the step (2) iteratively solves the above problem, and the following optimization problem is constructed in each iteration:
the optimization target is as follows: minimization of
Figure BDA0002325584300000031
The constraint conditions are as follows:
Figure BDA0002325584300000032
Figure BDA0002325584300000033
Figure BDA0002325584300000034
Figure BDA0002325584300000035
wherein
Figure BDA0002325584300000036
Figure BDA0002325584300000037
Represent
Figure BDA0002325584300000038
The flare point of the t-th iteration,
Figure BDA0002325584300000039
represent
Figure BDA00023255843000000310
The flare point of the t-th iteration,
Figure BDA00023255843000000311
to represent
Figure BDA00023255843000000312
The flare point of the t-th iteration. Using semi-definite relaxation (SDR) to eliminate the constraint on rank in step (1) and obtain the constraint on rank
Figure BDA00023255843000000313
Semi-definite planning (SDP) problem.
Preferably, the solution of step (2) is performed by using an interior point algorithm
Figure BDA00023255843000000314
Updating the iterative expansion point, repeating the above processes until the iterative convergence to obtain a group of optimal solutions
Figure BDA00023255843000000315
Preferably, step (3) obtains the candidate beamforming vector by gaussian randomization, and first, the optimal solution obtained in step (2) is obtained
Figure BDA00023255843000000316
Performing characteristic value decomposition (EVD) to obtain
Figure BDA00023255843000000317
Figure BDA00023255843000000318
Generating a set of beamforming vectors using gaussian randomization
Figure BDA00023255843000000319
And matrix
Figure BDA00023255843000000320
Namely that
Figure BDA00023255843000000321
Wherein
Figure BDA00023255843000000322
All obey a standard complex gaussian distribution.
Preferably, step (3) is based on the obtained set of beamforming vectors
Figure BDA00023255843000000323
And matrix
Figure BDA00023255843000000324
Iteratively solving the following for scaling coefficients
Figure BDA00023255843000000325
The optimization problem of (2):
the optimization target is as follows:
Figure BDA00023255843000000326
the constraint conditions are as follows:
Figure BDA0002325584300000041
Figure BDA0002325584300000042
Figure BDA0002325584300000043
Figure BDA0002325584300000044
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002325584300000045
Figure BDA0002325584300000046
p i, (t) represents p i, Expansion point, p, of the t-th iteration n, (t) Represents p n, The flare point of the t-th iteration,
Figure BDA0002325584300000047
represent
Figure BDA0002325584300000048
The flare point of the t-th iteration,
Figure BDA0002325584300000049
Figure BDA00023255843000000410
and updating the expansion point after the solution is completed, and iteratively solving until convergence. Obtaining the scaling coefficient corresponding to the group of beams after iterative convergence
Figure BDA00023255843000000411
And corresponding alternative beamforming satisfying the original problem constraints
Figure BDA00023255843000000412
Preferably, step (4) selects the alternative beamforming with the least power by repeating step (3) a plurality of times
Figure BDA00023255843000000413
As an optimal solution, the corresponding minimum transmit power is
Figure BDA00023255843000000414
Based on the same inventive concept, the invention discloses a beam forming optimization device for minimizing the transmission power of an ultra-dense network, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the computer program realizes the beam forming optimization method for minimizing the transmission power of the ultra-dense network when being loaded to the processor.
Has the beneficial effects that: compared with the prior art, the invention has the following advantages:
1. aiming at the user QoS requirement and the return trip rate constraint, the invention minimizes the transmission power of the system on the premise of meeting the user QoS constraint by performing joint optimization on the transmission beam forming of the macro base station and the small base station.
2. Compared with the traditional zero forcing transmission scheme, the invention can obviously reduce the total transmission power of the system.
3. The method has low calculation complexity and is beneficial to engineering realization.
Drawings
FIG. 1 is a flow chart of the optimization method of the present invention.
Fig. 2 is a graph of simulation experiment results.
Detailed Description
The invention will be described in detail below with reference to a preferred embodiment and with reference to the accompanying drawings.
The typical application scenario of the invention is in ultra-dense networking, the transmission beam forming of the macro base station and the small base station is jointly optimized, the return trip rate requirement of the small base station is considered on the premise of meeting the QoS constraint of a user, and the total transmission power of the system is minimized. As shown in fig. 1, in the beamforming optimization method for minimizing transmit power of an ultra-dense network disclosed in the embodiment of the present invention, the constructed initial optimization problem may be represented as:
the optimization target is as follows: minimization
Figure BDA0002325584300000051
The constraint conditions are as follows:
Figure BDA0002325584300000052
Figure BDA0002325584300000053
Figure BDA0002325584300000054
wherein log 2 (. H) represents a base-2 logarithmic function, | is a vector's second norm |) F Frobenius norm of matrix (.) H Representing the conjugate transpose of the matrix (.) -1 Representing the matrix inversion, det (-) represents the determinant of the matrix,
Figure BDA0002325584300000055
is N S ×N S Unit array of dimensions, N S The number of antennas of the small base station is,
Figure BDA0002325584300000056
for the channel between the macro base station to the ith user accessing the macro base station,
Figure BDA0002325584300000057
for the channel between the nth small cell to the jth user accessing the base station,
Figure BDA0002325584300000058
being a channel between the macro base station and the nth small base station,
Figure BDA0002325584300000059
the beamforming vectors used by the macro base station for the ith access user,
Figure BDA00023255843000000510
a beamforming vector used by the nth small base station for the jth user accessing the base station,
Figure BDA00023255843000000511
is macro radicalBeamforming matrix, gamma, used by the station for the nth small base station i The lowest SINR required for the ith user to access the macro base station,
Figure BDA00023255843000000512
minimum SINR, sigma, required by jth user for accessing nth small base station 2 Is Gaussian white noise power, N n Receiving a noise covariance matrix, U, for an nth small base station m Representing a set of users, U, accessing a macro base station s,n And B represents a small base station set.
The specific optimization solving steps of the problem are as follows:
(1) Introducing intermediate variables
Figure BDA0002325584300000061
Obtaining an optimization problem about the intermediate variable;
in this step, the constructed optimization problem is described as:
the optimization target is as follows: minimization
Figure BDA0002325584300000062
The constraint conditions are as follows:
Figure BDA0002325584300000063
Figure BDA0002325584300000064
Figure BDA0002325584300000065
Figure BDA0002325584300000066
Figure BDA0002325584300000067
wherein the content of the first and second substances,
Figure BDA0002325584300000068
Figure BDA0002325584300000069
tr (-) denotes the trace of the matrix, rank (-) denotes the rank of the matrix,
Figure BDA00023255843000000610
and the number of the parallel transmission data streams sent by the macro base station to each small base station is represented.
(2) Iteratively solving the problem in the step (1) to obtain an optimal solution of intermediate variables
Figure BDA00023255843000000611
In this step, the optimization variables are
Figure BDA00023255843000000612
The optimization problem solved for each iteration is described as:
the optimization target is as follows: minimization
Figure BDA00023255843000000613
The constraint conditions are as follows:
Figure BDA00023255843000000614
Figure BDA00023255843000000615
Figure BDA00023255843000000616
Figure BDA0002325584300000071
wherein
Figure BDA0002325584300000072
Figure BDA0002325584300000073
To represent
Figure BDA0002325584300000074
The flare point of the t-th iteration,
Figure BDA0002325584300000075
represent
Figure BDA0002325584300000076
The flare point of the t-th iteration,
Figure BDA0002325584300000077
to represent
Figure BDA0002325584300000078
The flare point for the t-th iteration. Applying semi-deterministic relaxation (SDR) rounds the constraints on rank in step (1). Obtaining the optimal solution of the problem after iterative convergence
Figure BDA0002325584300000079
(3) Obtaining a group of feasible solutions meeting the original problem constraint by adopting a Gaussian randomization method, and using the feasible solutions as alternatives;
in this step, the optimal solution obtained is first obtained
Figure BDA00023255843000000710
Decomposing the characteristic value to obtain
Figure BDA00023255843000000711
Figure BDA00023255843000000712
Generating a set of beamforming vectors using gaussian randomization
Figure BDA00023255843000000713
And matrix
Figure BDA00023255843000000714
Namely that
Figure BDA00023255843000000715
Figure BDA00023255843000000716
Wherein
Figure BDA00023255843000000717
All obey a standard complex gaussian distribution.
And then based on the obtained group of beam forming vectors
Figure BDA00023255843000000718
And matrix
Figure BDA00023255843000000719
Iterative solution on scaling coefficients
Figure BDA00023255843000000720
The constructed optimization problem is described as follows:
the optimization target is as follows:
Figure BDA00023255843000000721
the constraint conditions are as follows:
Figure BDA00023255843000000722
Figure BDA00023255843000000723
Figure BDA00023255843000000724
Figure BDA00023255843000000725
wherein the content of the first and second substances,
Figure BDA00023255843000000726
Figure BDA00023255843000000727
p i , (t) denotes pi, the expansion point of the t-th iteration, p n, (t) Denotes p n The expansion point of the t-th iteration,
Figure BDA0002325584300000081
represent
Figure BDA0002325584300000082
The flare point of the t-th iteration,
Figure BDA0002325584300000083
Figure BDA0002325584300000084
and updating the expansion point after the solution is completed, and iterating the solution until convergence. Obtaining the scaling coefficient corresponding to the group of beams after iterative convergence
Figure BDA0002325584300000085
And corresponding alternative beamforming satisfying the original problem constraints
Figure BDA0002325584300000086
(4) And (4) repeating the step (3) until the preset randomization times are reached, and selecting the solution with the minimum power from all the alternative solutions as the optimal solution.
Repeating the step (3), continuously generating alternative beam forming vectors, comparing the total power of the alternative beam forming vectors,selecting the candidate beam forming with the minimum power until the preset randomization times
Figure BDA0002325584300000087
As an optimal solution, the corresponding minimum transmit power is
Figure BDA0002325584300000088
Based on the same inventive concept, the embodiment of the present invention discloses a beamforming optimization apparatus for minimizing transmit power of an ultra-dense network, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the computer program is loaded into the processor, the beamforming optimization method for minimizing transmit power of an ultra-dense network is implemented.
In order to verify the effect of the invention, a simulation experiment was performed, the parameters involved in the simulation experiment are shown in the following table:
table 1 simulation experiment parameter table
Parameter(s) Value taking
Number of macro base station antennas 8
Number of antennas of small base station 2
Number of antennas received by user 1
Number of small base stations 2
Number of macro base station access users 2
The number of users accessing each small base station 2
Small-scale fading model Rayleigh fading
Path loss due to transmission distance d (m) (-30-3.2log 10 d)dB
Noise power at the receiving end -80dBm
Minimum spectral efficiency requirement for accessing macro base station user 1bps/Hz
Minimum spectral efficiency requirement for access small base station users 0.5bps/Hz
Fig. 2 is a comparison result of a simulation experiment, and the simulation result shows that: compared with the traditional zero-forcing transmission scheme, the beam forming optimization method provided by the invention can obviously reduce the total transmitting power of the system.
The above is only a preferred embodiment of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (2)

1. A beam forming optimization method for minimizing the transmission power of an ultra-dense network is characterized in that the method is based on an ultra-dense network structure, the optimization problem of the transmission power of a system is minimized by constructing an optimization problem which takes the limitation of user service quality and the backhaul rate of a small base station as constraints, and the beam forming of a macro base station and a plurality of small base stations is jointly optimized, and the method specifically comprises the following steps:
(1) Introducing intermediate variables
Figure FDA0003760900230000011
Obtaining an optimization problem about the intermediate variable; wherein
Figure FDA0003760900230000012
A beamforming vector used by the macro base station for the ith user accessing the macro base station,
Figure FDA0003760900230000013
a beamforming vector used by the nth small base station for the jth user accessing the base station,
Figure FDA0003760900230000014
beamforming matrix for macro base station to nth small base station, (-) H Representing a matrix conjugate transpose;
(2) Iteratively solving the problem in the step (1) to obtain an optimal solution of intermediate variables
Figure FDA0003760900230000015
(3) Obtaining a group of feasible solutions meeting the initial problem constraint by adopting a Gaussian randomization method, and using the feasible solutions as alternatives;
(4) Repeating the step (3) until the preset randomization times are reached, and selecting a solution with the minimum power from all the alternative solutions as an optimal solution;
the optimal beamforming is solved by constructing the following initial problem:
the optimization target is as follows: minimization
Figure FDA0003760900230000016
The constraint conditions are as follows:
Figure FDA0003760900230000017
Figure FDA0003760900230000018
Figure FDA0003760900230000019
wherein log 2 (. DEG) represents a logarithmic function with base 2, | | ·| | is the two-norm of the vector, | | ·| | purple sweet F Frobenius norm of matrix (.) -1 Representing the matrix inversion, det (-) represents the determinant of the matrix,
Figure FDA00037609002300000110
is N S ×N s Unit array of dimensions, N s The number of antennas of the small base station is,
Figure FDA00037609002300000111
for the channel between the macro base station to the ith user accessing the macro base station,
Figure FDA00037609002300000112
for the channel between the nth small base station to the jth user accessing the base station,
Figure FDA00037609002300000113
is the channel between the macro base station and the nth small base station, gamma i The lowest SINR required for the ith user to access the macro base station,
Figure FDA00037609002300000114
is connected toLowest SINR, sigma, required by the jth user entering the nth small base station 2 Is Gaussian white noise power, N n Receiving a noise covariance matrix, U, for an nth small base station m Indicating a set of users, U, accessing a macro base station s,n Representing a user set accessed to the nth small base station, and B representing a small base station set; i belongs to U m Represents U m The ith user, i' e (U) m -i) represents U m Removing the users of the ith user; n belongs to B and represents the nth small base station in B, and n belongs to (B-n) and represents the base station except the nth small base station in B; j is as large as U s,n Represents U s,n User j' e (U) of the j-th user s,n -j) represents U s,n Removing the user of the jth user;
the initial problem was converted to the following form:
the optimization target is as follows: minimization
Figure FDA0003760900230000021
The constraint conditions are as follows:
Figure FDA0003760900230000022
Figure FDA0003760900230000023
Figure FDA0003760900230000024
Figure FDA0003760900230000025
Figure FDA0003760900230000026
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003760900230000027
tr (-) denotes the trace of the matrix,
Figure FDA0003760900230000028
the expression matrix X is a semi-positive definite matrix, rank (-) represents the rank of the matrix,
Figure FDA0003760900230000029
representing the number of parallel transmission data streams sent by the macro base station to each small base station;
step (2) the following problem is solved in each iteration:
the optimization target is as follows: minimization
Figure FDA00037609002300000210
The constraint conditions are as follows:
Figure FDA00037609002300000211
Figure FDA00037609002300000212
Figure FDA00037609002300000213
Figure FDA0003760900230000031
wherein
Figure FDA0003760900230000032
Figure FDA0003760900230000033
Represent
Figure FDA0003760900230000034
The flare point of the t-th iteration,
Figure FDA0003760900230000035
represent
Figure FDA0003760900230000036
The flare point of the t-th iteration,
Figure FDA0003760900230000037
represent
Figure FDA0003760900230000038
The flare point for the t-th iteration; using semi-definite relaxation to round off the constraint on rank in step (1) to obtain the constraint on rank
Figure FDA0003760900230000039
Solving the semi-definite programming problem and updating the iterative expansion point until the iterative convergence to obtain the optimal solution
Figure FDA00037609002300000310
Solving for problems about using interior point algorithm
Figure FDA00037609002300000311
The semi-fixed planning problem of (2);
step (3) is to obtain the optimal solution
Figure FDA00037609002300000312
Decomposing the eigenvalue to obtain
Figure FDA00037609002300000313
Figure FDA00037609002300000314
Generating a set of beamforming vectors using gaussian randomization
Figure FDA00037609002300000315
And matrix
Figure FDA00037609002300000316
Namely that
Figure FDA00037609002300000317
Wherein
Figure FDA00037609002300000318
Figure FDA00037609002300000319
All obey a standard complex Gaussian distribution;
based on the obtained group of beam forming vectors in the step (3)
Figure FDA00037609002300000320
And matrix
Figure FDA00037609002300000321
Iteratively solving the following for scaling coefficients
Figure FDA00037609002300000322
The problems of (2):
the optimization target is as follows:
Figure FDA00037609002300000323
the constraint conditions are as follows:
Figure FDA00037609002300000324
Figure FDA00037609002300000325
Figure FDA00037609002300000326
Figure FDA00037609002300000327
wherein the content of the first and second substances,
Figure FDA00037609002300000328
Figure FDA0003760900230000041
p i (t) represents p i Expansion point, p, of the t-th iteration n’ (t) Represents p n’ The flare point of the t-th iteration,
Figure FDA0003760900230000042
represent
Figure FDA0003760900230000043
The flare point of the t-th iteration,
Figure FDA0003760900230000044
Figure FDA0003760900230000045
after the solution is completed, updating the expansion point, and iterating until convergence; obtaining a scaling coefficient corresponding to the wave beam after iterative convergence
Figure FDA0003760900230000046
And corresponding alternative beamforming satisfying initial problem constraints
Figure FDA0003760900230000047
And (4) repeating the process of the step (3) until the preset times are reached, selecting a group of alternative wave beam forming with the minimum transmitting power as the optimal solution of the initial problem, and recording the optimal solution as the optimal solution of the initial problem
Figure FDA0003760900230000048
Optimal transmit beamforming to satisfy constraints
Figure FDA0003760900230000049
Corresponding minimum transmit power of
Figure FDA00037609002300000410
2. A beamforming optimization apparatus for ultra-dense network transmit power minimization, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the computer program, when loaded into the processor, implements the beamforming optimization method for ultra-dense network transmit power minimization according to claim 1.
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