CN108599831A - A kind of robust beam forming design method of cloud wireless access network - Google Patents
A kind of robust beam forming design method of cloud wireless access network Download PDFInfo
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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
- H04B7/06—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
Abstract
The invention discloses a kind of robust beam forming design methods of cloud wireless access network.There is step 1 including step:It determines model, increases by two restrictive conditions, Optimized model；Step 2：It converts two norm problems in former problem to linear problem using SDP methods；Step 3：Pass through l0The approximate method of norm eliminates reluctant l0Norm problem；Step 4：The probabilistic influence of signal is eliminated using Markov inequality；Step 5：It is a series of convex optimization problems convenient for solving that complicated beam forming, which is designed subproblem abbreviation, using MM algorithms；Step 6：Each subproblem is solved using ADMM algorithms.In the application, the maximum available transmission energy consumption of required communication quality and each base station of user need to only be set, it is i.e. uncertain to each user progress beam forming design in channel state information using algorithm proposed by the present invention, while so that meeting base station energy consumption constraint, most users meet Signal to Interference plus Noise Ratio constraint.
Description
Technical field
The present invention relates to wireless communication and signal processing methods, more particularly to a kind of to be suitable for channel information uncertain environment
Under wireless communications method.
Background technology
Cloud wireless access network is a kind of emerging network architecture, has while improving the availability of frequency spectrum and capacity usage ratio
Double benefit.In cloud wireless access network, base station is all to be connected to central processing unit by digital backhaul link, to realize across
The joint data processing and precoding stood.In order to improve capacity usage ratio, cloud wireless access network framework uses following three kinds of sides
Formula saves energy consumption：First, under cloud wireless access planar network architecture, most of base band signal process function in traditional base station can be with
Move to cloud computing center so that the high-power base station of high cost in traditional network framework can be by the wireless of inexpensive low-power
Electric long-range head (RRH) substitutes.Second, the presence of central processing unit can also provide the function of user message joint precoding to subtract
Few interference.Since the interference of generation is less, the transmission power of base station can be reduced.Third, in general (especially
It is in the off-peak hours), most of Internet resources may be idle, and central processing unit can execute joint money between the base stations
Source is distributed, and realizes distribution according to need resource, and it is energy saving that idle base station entered sleep pattern.
Although cloud wireless access network has huge power savings advantages, due to introducing central processing unit so that there is big energy
It is lost on backhaul link between base station and central processing unit.Most of beam forming to cloud wireless access network designs at present
It is all based on ideal communication channel progress, but due to wirelessly communicating the communication environment of time-varying so that it is obtained according to pilot signal
The beam forming design done of channel information, how can not ensure the communication quality of user under the channel circumstance after time-varying
In the case where channel circumstance has error, ensure the communication quality of user, at the same can also substantially reduce system energy consumption as cloud without
The a great problem of line access development.
Invention content
The purpose of the present invention is to solve the above problem, provide one kind be suitable for channel circumstance it is uncertain in the case of it is real
The cloud wireless access network beam forming design method that existing energy consumption is minimum, transmission is stable, including：By establish probability channel model come
The influence that channel errors are brought to communication quality is eliminated, the robustness of system is improved；Activation and the dormant state for introducing base station, with
Reduce energy consumption；Consider that the energy consumption of downlink medium cloud wireless transmission net is mainly derived from following three aspects：Shape residing for base station
State (activation, sleep), the backhaul link energy loss between the transmitting energy consumption of base station and central processing unit and base station is established and is closed
Suitable energy consumption model ensures that network energy consumption is minimum.
Specifically, the present invention is realized using technical solution below,
A kind of robust beam forming design method of cloud wireless access network, which is characterized in that use following steps：
Step 1, model is determined：
The total consumption power P of cloud wireless access network is characterized as
The service quality of further user is constrained with base station energy consumption, increases by two restrictive conditions, the model is after optimization
min P
s.t.SINRk≥γk
Step 2：It converts two norm problems in former problem to linear problem using SDP methods；
Step 3：Pass through l0The approximate method of norm eliminates reluctant l0Norm problem；
Step 4：The probabilistic influence of signal is eliminated using Markov inequality；
Step 5：Complicated beam forming design subproblem abbreviation is convenient for the convex excellent of solution to be a series of using MM algorithms
Change problem；
Step 6：Each subproblem is solved using ADMM algorithms.
The step 2)：It enablesIt can obtain：The order of Tr () representing matrix.WhereinFor distinguishing different base stations, whereinIndicate diagonal element
ForDiagonal matrix.At this point, optimization problem can be written to：
Step 3) passes through l0The approximate method of norm eliminates reluctant l0Norm problem:
For containing l0The problem of norm, is solved using the method for log approximations to function, as θ → 0, definitionSuch approximation：
By this approximation, object function is by an intermittent l0Norm function is approximately a continuous ln function.
The step 4)：The probabilistic influence of signal is eliminated using Markov inequality:
Signal to Interference plus Noise Ratio constraint is write as：Pr{SINRk≥γk}≥pk
Wherein, Pr{ A } indicates the probability that event A occurs, pkIndicate that goal satisfaction constrains ratio；
By Markov inequality, above-mentioned probability constraints are rewritten as：
Wherein E [SINRk] it is SINRkExpectation；
Due to
Wherein,It converts probability constraints to：
So far, probability Signal to Interference plus Noise Ratio can be converted into above-mentioned convex constraint.
The step 5)：The use of MM algorithms by complicated beam forming design subproblem abbreviation is a series of convenient for solving
Convex optimization problem, specifically comprises the following steps:
(a) initial problem, the starting point as iteration are solved.Concave function part in object function is removed, is directly translated into
Convex optimization problem is as initial problem.Then the initial problem of optimization problem is written to：
(b) Taylor expansion of selection target function is as the upper limit function in MM algorithms.At some with J (x) for mesh
In the optimization problem of scalar functions, for each iteration in MM algorithms, its upper limit function need to be built and the upper limit function need to be easy to
Optimization.For the new upper limit object function G of n times iteration structuren(x), G need to be met at the optimization point that upper primary iteration generatesn
(xn-1)=J (xn).So a Taylor expansion can meet above-mentioned structure requirement, the recess portion of object function is primary with it
Taylor expansion builds new object function, and Taylor expansion is as follows：
Wherein,WithFor two constants, exist for ln functionsLocate the constant term of Taylor expansion.Institute
The iterative problem that a series of convex problem is constituted can be converted by MM algorithms with former non-convex optimization problem, wherein n-th changes
It can be expressed as problem：
The step 6) solves each subproblem using ADMM algorithms, includes the following steps：
Step 6.1) is firstly introduced into two intermediate variables to use ADMM algorithms：
Γk,j=Tr (HkWj),Πl,k=Tr (BlWk)
Above-mentioned optimization problem can be write as again at this time：
s.t.Γk,j-Tr(HkWj)=0
Πl,k-Tr(BlWk)=0
Wherein,Thus three instructions are defined
Function IC,ID,IGIf Γ belongs to feasible zoneThen IC=0, otherwise IC=+∞；If
Π belongs to feasible zoneThen ID=0, otherwise ID=+∞；If WkBelong to feasible zoneThen IG=0, it is no
Then IG=+∞.Then its Augmented Lagrangian Functions can be written as：
Wherein,μl,kAnd λk,jFor Lagrange coefficient, ρ ＞ 0 indicate augmentation
The penalty coefficient of Lagrangian.
After step 6.2) is due to above-mentioned introducing channel variable, problem form has met the flow of ADMM solutions, passes through
ADMM algorithms can convert former problem to three relatively simple subproblems.
(a) { Γ } updates
{ Γ } update can be by solving an optimization problem, and the optimization problem can be broken down into that K is independent small to be asked
Topic：
Although this problem is a convex optimization problem, but since K variable is interrelated and is limited to the same constraint
Among, its closed solutions cannot be found out, Subgradient Algorithm solution may be used, steps are as follows for the m times update：
The initial value of secondary algorithm may be configured as, Γk,k(m)=Γk,j(m)=0.Wherein Δm＞ 0 is subgradient step-length,For Lagrange coefficient.
(b) { Π } updates
{ Π } update can also be by solving an optimization problem, and can be broken down into K independent small for the optimization problem
Problem：
The closed solutions that above formula is found out using KKT conditions are one of the following：
(c){WkUpdate
With { Γ } update and { Π } update, { WkUpdate be also required to one optimization problem of solution, and the optimization problem can be with
It is broken down into K independent minor issues：
s.t.Wk≥0
This problem is solved using Projected descent method, the result of gradient descent method each time is projected among feasible zone
It is updated iteration, iterative formula is as follows：
Wherein Proj { } expressions project to feasible zone Wk>=0, s are step-length, are a positive real numbers.For target letter
After several the t times iterationThe gradient at place.
The robust beam forming design method of the above cloud wireless access network, which is characterized in that minimize energy consumption as target,
Total energy consumption model, including transmitting energy consumption, backhaul link transmission energy consumption and base are established using the transmission characteristic of cloud wireless access network
Three parts of energy consumption of standing.The transmitting energy consumption is related with the beam forming design of base station, backhaul link energy consumption and ownership goal
Transmission rate is related, and base station energy consumption is related with the suspend mode attribute of base station.
The robust beam forming design method of cloud wireless access network, which is characterized in that the target, in conjunction with actual nothing
Line communications system properties establish total beam forming design problem.For reduce energy consumption, introducing can suspend mode base station model, in base station
When being in idle condition, it is controlled by the central processing unit of cloud wireless access network and enters dormant state；According to actual communication
System considers that the energy consumption of base station is limited, and then introduces base station energy consumption constraint；User's received signal need to meet centainly simultaneously
Signal to Interference plus Noise Ratio require just to can guarantee the reliability of communication, thus introduce user's Signal to Interference plus Noise Ratio and constrain.
The robust beam forming design method of the cloud wireless access network, which is characterized in that described problem, channel status
What information was not to determine.In wireless communication, channel state information is usually obtained by pilot signal, due to the presence of random noise
Radio channel estimation error is caused to be difficult to avoid that with the time-varying characteristics of wireless channel, so the channel state information cannot be complete
It obtains, detection channel state information can only be obtained to replace real channel status information.The beam forming design scheme utilizes
Channel state information is detected, real channel status information and detection channel state information is considered, passes through Markov inequality
Method ensures user in the uncertain wireless access network of channel, also meets user's ratio of Signal to Interference plus Noise Ratio requirement higher than setting
Ratio ensures the robustness of system.
The robust beam forming design method of the cloud wireless access network, which is characterized in that the problem utilizes
SDP、l0The modes such as norm approximation and MM algorithms convert problem to a series of relatively simple problems.It will using SDP methods
The quadratic term that beam forming designs in described problem is converted into first order；Utilize l0Norm approximation by described problem by l0Norm
Caused discontinuous object function is converted into continuous object function；The single optimization problem after conversion is turned using MM algorithms
Turn to a series of convex optimization problems convenient for solving.
The robust beam forming design method of the cloud wireless access network, which is characterized in that the problem solves one
Complexity convex optimization problem of the series comprising positive semidefinite constraint.It proposes the optimization method based on ADMM algorithms, is by former problem reduction
Three be easy to solve the problem of, be utilized respectively subgradient descent method, KKT conditions and Projected descent method solving-optimizing problem.
Actual cloud wireless access network need to meet base station energy consumption and constrain, and in the case of user communication quality, consider detection letter
In the state that road is imperfect, beam forming design is carried out to it, realizes that the energy consumption of whole network is minimum.
In the cloud wireless access network, benefit is transmitted to improve, the base station is multi-antenna base station.Base station is worked as in consideration
When having data to need to send, base station is active, and base station needs to consume larger energy at this time；When there is no data on base station
It needing to send, then base station enters sleep state, and base station, which needs to consume a small amount of energy, at this time carrys out monitoring users demand, once area under one's jurisdiction
When inside there are data to need to send, it is transferred to state of activation at once.
The described base station energy consumption constraint refer to the transmission power of base station be it is limited, in a cloud Radio Access Network, respectively
The transmission power of a base station is all no more than its defined upper limit of emission power.
The QoS requirement of each user refers to each user in order to realize normal communication, the letter received
It number has to meet respective Signal to Interference plus Noise Ratio requirement.In cloud wireless access network, in order to provide better communication service, a cell
In may include multiple base stations, user by that can receive the communication service of multiple base stations to realize the optimal of communication quality simultaneously
Change.The signal interference that more base stations and multi-user in one cell cause between user information is unavoidable, each user
Interference be no longer only limitted to traditional interchannel noise, further include the signal interference of other users.So user described in this system
Communication quality demand refers to considering the Signal to Interference plus Noise Ratio after signal interference.
The channel state information is uncertain to refer to that the channel that signal transmission is passed through, status information are not to determine
's.In wireless communications, since the time-varying characteristics of the presence of random noise and wireless channel cause radio channel estimation error difficult
To avoid, it, can only be by pilot signal detection channel errors so the channel state information cannot obtain completely, and the detection
Channel state information is uncertain.
Beneficial effects of the present invention：
(1) present invention utilizes the characteristic of Cloud RAN systems (cloud wireless access network system), is assisted using multi-antenna multi-base station
Make the mode communicated, establishes rational cloud wireless access network energy consumption model, have for the energy consumption of actual cloud wireless access network
Preferable theoretical direction.
(2) present invention establishes the traffic model of channel errors using the relevant knowledge of probability theory.The probability letter of the present invention
Road model and its elimination accidental channel error approach are applicable not only to the elimination of the channel errors of Cloud RAN systems, for it
The channel status uncertain problem that his wireless system faces in practical applications has actual meaning.
(3) present invention uses SDP (Semi-Definite Programming), l0Norm approximation and MM algorithms
(Majorization-Minimization) etc. modes dexterously convert original non-convex problem to a series of relatively simple
Problem.These transform modes have good reference function for the conversion of other similar problems with solution.
(4) activation and the dormant state for introducing base station, when base station has data to need to send, base station is active,
Base station needs to consume larger energy at this time；When not having data to need to send on base station, then base station enters sleep state, at this time base
Station, which needs to consume a small amount of energy, carrys out monitoring users demand, when having data to need to send, is transferred at once sharp once local
State living.The energy loss of system can be significantly improved.
(5) seven submethods solved the problems, such as are disclosed in method for solving of the present invention：
1) the double optimization problem of vector is converted to the positive semidefinite relaxation method of a suboptimization problem of matrix；
2) it is uncertain to solve channel, by Markov inequality, ensures that the channel for meeting communicating requirement is higher than centainly
Than row.
3) l introduced due to standby energy of the base station caused by the working condition difference is different is solved0Approximation Problem.
4) a kind of gradually system reduces the beam forming design iteration optimization algorithm of energy loss.
5) a kind of beam forming design scheme based on ADMM algorithms converts challenge to relatively simple son and asks
Topic.
6) a kind of subgradient descent algorithm for solving hybrid optimization parameter.
7) Projected Gradient based on gradient algorithm can utilize sciagraphy, and gradient descent method, which is applied to solve, to be had
The optimization problem of constraint.
The present invention may be implemented under channel state information uncertain condition, ensure the communication quality of user and the energy consumption of base station
Limitation, and the beam forming design scheme of comprehensive energy consumption minimum can be obtained.It is highly suitable for energy consumption benefit and user's communication
The higher scene of quality requirement.This system can also be applied in the wireless access network of following 5G by future, further research.
Description of the drawings
Fig. 1 is the basic boom schematic diagram of the method for the present invention medium cloud wireless access network system
Fig. 2 is the flow diagram solved in the method for the present invention
Fig. 3 is the beam forming design flow diagram based on ADMM algorithms
Specific implementation mode
The present invention research the nonideal channel basis of channel on, theoretical modeling is carried out to it, from save energy consumption angle,
United beam forming design is carried out to different cloud wireless access networks, while optimization problem is analyzed, design is suitable
Optimization algorithm solves optimum beam molded design scheme so that the prioritization scheme of proposition not only has higher energy consumption benefit, also has
There are stronger noiseproof feature, the robustness of lifting system.
Below in conjunction with Figure of description, the present invention is described further.
It is the basic boom of cloud wireless access network system as shown in Figure 1
Assuming that in a cloud wireless access network system, there is L base station to provide data service for K user.Each base station
There is NtRoot antenna, and user only has an antenna.All base stations are all linked to the same CP (central processings by backhaul link
Device) on, and each user receives independent data flow from base station.The required information of user of hypothesis is from
CP, by being issued to each base station after CP Combined Treatments.We assume that CP can obtain channel information by pilot signal,
The channel information of acquisition and actual channel information be not very close to but being true channel information, we can will at this time
Channel information is modeled as：
Wherein, hkFor actual channel state information,For the channel state information that base station end detects, Δ hkFor channel
Status information error vector, for indicating the uncertainty of channel information, in practical communication system, Δ hkIt is to meet Gauss point
One accidental channel error of cloth, distribution are satisfied withWhereinIndicate that mean value is 0, variance isNormal distribution, I be unit matrix.
In cloud wireless transmission net, the total energy consumption of system depends on the energy consumption and backhaul link energy consumption of base station itself, base station
Itself include the basic energy consumption (activation/suspend mode) of base station transmitting power and base station, backhaul link energy consumption depends on base station will how many
Data send base station to by central processing unit.Next, we will be from the total energy consumption of system from the aspect of following two.
1) base station energy consumption model：In the present invention, the base station in off position is set to sleep state, at this time base
It stands and only consumes a small amount of energy for monitoring；And in running order base station, the gross energy of base station consumption should include base station
The energy of autophage is used to emit the transmission power of signal with base station, so the total energy consumption of base stationIt can be write as：
Wherein, Pl,txFor Base Transmitter energy consumption, and η1＞ 0 is the proportion that a constant indicates transmission power, Pl,activeFor
The energy that base station consumes under state of activation, Pl,sleepIndicate the power consumed under the sleep state of base station.In general, Pl,active
>Pl,sleep, thus for central processing unit, base stations more as possible is in sleep state and is conducive to save energy.
2) energy loss of backhaul link：The transmission rate that backhaul link loss is transmitted with central processing unit to base station has
It closes, and transmission rate is designed with beam forming and the operating mode of cloud wireless transmission net is related, so, it can be by backhaul chain
Path loss consumesIt is expressed as：
Wherein, ρlIt is a constant, it is related with the channel capacity of backhaul link,For the transmission rate of backhaul link.
3) total energy consumption of signal：Based on the above analysis, total energy consumption of system can be expressed as the energy consumption of each base station
In addition backhaul link energy consumption, the expression formula that can be written as：
Wherein, | | Pl,tx||0Indicate Pl,txL0Norm indicates the number of base station being active；Pl,Δ=
Pl,active-Pl,sleepIndicate that the energy consumption of state of activation and dormant state is poor.
Cloud wireless transmission net in, the signal that receiving terminal receives other than the signal and white Gaussian noise that itself is needed,
There is likely to be the interference between different user signal, such as user k to be likely to be received the signal needed for user j, for user k
For, the signal of user j is a kind of interference, so, in cloud wireless transmission net, the reception signal y of user kkIt can be expressed as：
Wherein, hkFor a Nt×NtMatrix, be expressed as true transmission channel matrix, ωkIt is a Nt* L × 1 to
Amount indicates the beam forming vector that base station is sent；ηk~CN (0, σ2) indicate the white Gaussian that signal is superimposed into transmission process
Noise, σ2It is noise variance.skIndicate the symbolic vector sent.Herein, it will be assumed that symbol energy 1.So first of base
The transmission power P to standl,txIt can be write as：
At this point it is possible to find out the Signal to Interference plus Noise Ratio SINR of user kkFor：
Meanwhile it can obtain, the intended recipient rate r of user kkFor：
Wherein, ΓmFor constant, generally according to actual application scenarios setup parameter.
Because of a shared K user in cloud wireless transmission net, total transmission on the backhaul link of central processing unit to base station
Rate is equal to total receiving velocity.Therefore, backhaul link transmission rateIt can be write as：
Wherein,Indicate whether user is receiving data, if whole launching beams are all 0, user does not receive number
According to if it is not all 0, then it represents that it is receiving data.
According to analysis above, the total consumption power P of cloud wireless access network can be written as：
In actual wireless access network, the energy for not requiring nothing more than consumption is minimum, it is also necessary to consider the service quality of user,
It is constrained with base station energy consumption.So the above problem can be described as to an optimization problem, object function is energy consumption function, simultaneously
It can be written as there are two restrictive condition：
min P
s.t.SINRk≥γk
Wherein γkFor the Signal to Interference plus Noise Ratio requirement of user k；PlFor the maximum transmission power of first of base station.Entire wave beam as a result,
Molded design problem has characterized.
Beam forming design problem is summarized as optimization problem by flow chart as shown in Figure 2 in above discussion
Form, it can be seen that above-mentioned optimization problem is non-convex problem, can not direct solution, so we utilize 5 steps shown in Fig. 2
Submethod is translated into solvable problem.
Details are as follows for process:
Step 1)：It converts two norm problems in former problem to linear problem using SDP methods
1)SDP：Enable Wk=ωkωk HAs long as the W that order is 1 can be found outk, W is surely decomposed into regard to onek=ωkωk H, to ask
Obtain ωk.If enabling Wk=ωkωk H, can obtain：The order of Tr () representing matrix.WhereinFor distinguishing different base stations, whereinIndicate diagonal element
ForDiagonal matrix.At this point, optimization problem can be written to：
The problem of analysis two formula above, optimization problem is not a convex optimization, main cause is from two aspects：1)
Contain l in object function0Norm function；2)ΔhkIt is a uncertain value.So next, we will consider from these two aspects,
To solve the problem.
Step 2)：Pass through l0The approximate method of norm eliminates reluctant l0Norm problem
2)l0Norm is approximate.For containing l0The problem of norm, the general method using log approximations to function solves, when θ → 0
When, definitionSuch approximation can be done：
By this approximation, object function is by an intermittent l0Norm function is approximately a continuous ln function, right
It is more significant in solution later.
Step 3)：The probabilistic influence of signal is eliminated using Markov inequality
3) Markov inequality
In optimization problem, due to there is uncertain Δ hkSo that solution becomes very difficult, by analyzing the present invention's
Actual demand is made an uproar it is recognised that the present invention claims the minimum Signal to Interference plus Noise Ratio demand that most of base station all meets user so letter is dry
It can be write as than constraint：
Pr{SINRk≥γk}≥pk
Wherein, Pr{ A } indicates the probability that event A occurs, pkIndicate that goal satisfaction constrains ratio.It can be seen that more than passing through
Constraint, we can ensure there is pkUser more than ratio disclosure satisfy that minimum Signal to Interference plus Noise Ratio demand.
By Markov inequality, above-mentioned probability constraints can be rewritten as：
Wherein, E [SINRk] it is SINRkExpectation, notice that the constraint of the above problem and probability Signal to Interference plus Noise Ratio is not equivalent,
Above-mentioned constraint is stringenter.Due to,
Wherein,Probability constraints can be converted into as a result,：
So far, probability Signal to Interference plus Noise Ratio can be converted into above-mentioned convex constraint.
Step 4)：Complicated beam forming design subproblem abbreviation is convenient for the convex excellent of solution to be a series of using MM algorithms
Change problem
4) so far, other than containing log functions in object function, remaining optimization problem all meets convex optimization problem, solution
The problem of certainly object function is concave function, and restrictive condition is convex function, we commonly use is iterated optimization with MM algorithms.
(a) initial problem, the starting point as iteration are solved.In the present invention, the concave function part in object function is removed,
Convex optimization problem is directly translated into as initial problem.Then the initial problem of optimization problem can be written to：
(b) Taylor expansion of selection target function is as the upper limit function in MM algorithms.At some with J (x) for mesh
In the optimization problem of scalar functions, for each iteration in MM algorithms, its upper limit function need to be built and the upper limit function need to be easy to
Optimization.For the new upper limit object function G of n times iteration structuren(x), G need to be met at the optimization point that upper primary iteration generatesn
(xn-1)=J (xn).So a Taylor expansion can meet above-mentioned structure requirement, the recess portion of object function is primary with it
Taylor expansion builds new object function, and Taylor expansion is as follows：
Wherein,WithIt is ln functions in W for two constantsk (n)Locate the constant term of Taylor expansion.Institute
The iterative problem that a series of convex problem is constituted can be converted by MM algorithms with former non-convex optimization problem, wherein n-th changes
It can be expressed as problem：
Step 5)：Solution is carried out to each subproblem using ADMM algorithms
5) in this algorithm, it is proposed that it is a kind of based on the beam forming design method of ADMM algorithms by answering after above-mentioned conversion
Miscellaneous convex optimization problem is converted into three relatively simple optimization problems.
In order to use ADMM algorithms, it is firstly introduced into two intermediate variables：
Γk,j=Tr (HkWj),Πl,k=Tr(BlWk)
Above-mentioned optimization problem can be write as again at this time：
s.t.Γk,j-Tr(HkWj)=0
Πl,k-Tr(BlWk)=0
Wherein,Thus three instructions are defined
Function IC,ID,IGIf Γ belongs to feasible zoneThen IC=0, otherwise IC=+∞；If
Π belongs to feasible zoneThen ID=0, otherwise ID=+∞；If WkBelong to feasible zoneThen IG=0, it is no
Then IG=+∞.Then its Augmented Lagrangian Functions can be written as：
Wherein,μl,kAnd λk,jFor Lagrange coefficient, ρ ＞ 0 indicate augmentation
The penalty coefficient of Lagrangian.
It is illustrated in figure 3 the beam forming algorithm pattern based on ADMM algorithms, after above-mentioned introducing channel variable, problem
The flow that form has met ADMM solutions can convert former problem to three relatively simple subproblems by ADMM algorithms.
(a) { Γ } updates
From figure 3, it can be seen that { Γ } update can be by solving an optimization problem, and the optimization problem can be decomposed
For K independent minor issues：
Although this problem is a convex optimization problem, but since K variable is interrelated and is limited to the same constraint
Among, its closed solutions cannot be found out, Subgradient Algorithm solution may be used, steps are as follows for the m times update：
The initial value of secondary algorithm may be configured as, Γk,k(m)=Γk,j(m)=0.Wherein Δm＞ 0 is subgradient step-length,For Lagrange coefficient.
(b) { Π } updates
From figure 3, it can be seen that { Π } update can also be by solving an optimization problem, and the optimization problem can be divided
Solution is K independent minor issues：
The closed solutions that above formula is found out using KKT conditions are one of the following：
(c){WkUpdate
With { Γ } update and { Π } update, { WkUpdate be also required to one optimization problem of solution, and the optimization problem can be with
It is broken down into K independent minor issues：
This problem is solved using Projected descent method in the present invention, the result of gradient descent method each time is projected to can
Iteration is updated among row domain, iterative formula is as follows：
Wherein Proj { } expressions project to feasible zone Wk>=0, s are step-length, are a positive real numbers.For target letter
After several the t times iterationThe gradient at place.
So far entirely the robust beam forming design of the cloud wireless access network based on ADMM algorithms derives and technical detail is public
Cloth finishes.
The basic principles and main features and advantage of the present invention have been shown and described above.The technical staff of the industry should
Understand, the present invention is not limited to the above embodiments, and the above embodiments and description only describe the originals of the present invention
Reason, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes and improvements
It all fall within the protetion scope of the claimed invention.The claimed scope of the invention is by appended claims and its equivalent
Boundary.
Claims (6)
1. a kind of robust beam forming design method of cloud wireless access network, which is characterized in that use following steps：
Step 1, model is determined：
The total consumption power P of cloud wireless access network is characterized as
The service quality of further user is constrained with base station energy consumption, increases by two restrictive conditions, the model is after optimization
min P
s.t. SINRk≥γk
Step 2：It converts two norm problems in former problem to linear problem using SDP methods；
Step 3：Pass through l0The approximate method of norm eliminates reluctant l0Norm problem；
Step 4：The probabilistic influence of signal is eliminated using Markov inequality；
Step 5：Complicated beam forming design subproblem abbreviation is asked for a series of convex optimizations convenient for solving using MM algorithms
Topic；
Step 6：Each subproblem is solved using ADMM algorithms.
2. a kind of robust beam forming design method of cloud wireless access network as described in claim 1, which is characterized in that described
Step 2)：
Enable Wk=ωkωk H, can obtain：The order of Tr () representing matrix.Wherein
For distinguishing different base stations, whereinIndicate that diagonal element isIt is diagonal
Battle array.At this point, optimization problem can be written to：
Wk＞=0.
3. a kind of robust beam forming design method of cloud wireless access network as described in claim 1, which is characterized in that described
Step 3) passes through l0The approximate method of norm eliminates reluctant l0Norm problem:
For containing l0The problem of norm, is solved using the method for log approximations to function, as θ → 0, definition
Such approximation：
By this approximation, object function is by an intermittent l0Norm function is approximately a continuous ln function.
4. a kind of robust beam forming design method of cloud wireless access network as described in claim 1, which is characterized in that described
Step 4)：The probabilistic influence of signal is eliminated using Markov inequality:
Signal to Interference plus Noise Ratio constraint is write as：Pr{SINRk≥γk}≥pk
Wherein, Pr{ A } indicates the probability that event A occurs, pkIndicate that goal satisfaction constrains ratio；
By Markov inequality, above-mentioned probability constraints are rewritten as：
Wherein E [SINRk] it is SINRkExpectation；
Due to
Wherein,It converts probability constraints to：
So far, probability Signal to Interference plus Noise Ratio can be converted into above-mentioned convex constraint.
5. a kind of robust beam forming design method of cloud wireless access network as described in claim 1, which is characterized in that described
Step 5)：It is a series of convex optimization problems convenient for solving that complicated beam forming, which is designed subproblem abbreviation, using MM algorithms,
Specifically comprise the following steps:
(a) initial problem, the starting point as iteration are solved.Concave function part in object function is removed, is directly translated into convex excellent
Change problem is as initial problem.Then the initial problem of optimization problem is written to：
Wk＞=0
(b) Taylor expansion of selection target function is as the upper limit function in MM algorithms.At some with J (x) for target letter
In several optimization problems, for each iteration in MM algorithms, its upper limit function need to be built and the upper limit function need to be easy to optimize.
For the new upper limit object function G of n times iteration structuren(x), G need to be met at the optimization point that upper primary iteration generatesn(xn-1)
=J (xn).So a Taylor expansion can meet above-mentioned structure requirement, by its Taylor's exhibition of the recess portion of object function
It opens and builds new object function, Taylor expansion is as follows：
Wherein,WithFor two constants, exist for ln functionsLocate the constant term of Taylor expansion.So former
Non-convex optimization problem can be converted into the iterative problem that a series of convex problem is constituted by MM algorithms, wherein nth iteration is asked
Topic can be expressed as：
Wk＞=0.
6. a kind of robust beam forming design method of cloud wireless access network as described in claim 1, which is characterized in that described
Step 6) solves each subproblem using ADMM algorithms, includes the following steps：
Step 6.1) is firstly introduced into two intermediate variables to use ADMM algorithms：
Γk,j=Tr (HkWj),Πl,k=Tr (BlWk)
Above-mentioned optimization problem can be write as again at this time：
s.t.Γk,j-Tr(HkWj)=0
Πl,k-Tr(BlWk)=0
Wk＞=0
Wherein,Thus three indicator functions are defined
IC,ID,IGIf Γ belongs to feasible zoneThen IC=0, otherwise IC=+∞；If Π belongs to
In feasible zoneThen ID=0, otherwise ID=+∞；If WkBelong to feasible zone Wk＞=0, then IG=0, otherwise IG=
+∞.Then its Augmented Lagrangian Functions can be written as：
Wherein,μl,kAnd λk,jFor Lagrange coefficient, ρ ＞ 0 indicate augmentation glug
The penalty coefficient of bright day function.
After step 6.2) is due to above-mentioned introducing channel variable, problem form has met the flow of ADMM solutions, is calculated by ADMM
Method can convert former problem to three relatively simple subproblems.
(a) { Γ } updates
{ Γ } update can be by solving an optimization problem, and the optimization problem can be broken down into K independent minor issues：
Although this problem is a convex optimization problem, but since K variable is interrelated and among being limited to the same constraint,
Its closed solutions cannot be found out, Subgradient Algorithm solution may be used, steps are as follows for the m times update：
The initial value of secondary algorithm may be configured as, Γk,k(m)=Γk,j(m)=0.Wherein Δm＞ 0 is subgradient step-length,For
Lagrange coefficient.
(b) { Π } updates
{ Π } update can also be by solving an optimization problem, and the optimization problem can be broken down into K independent minor issues：
The closed solutions that above formula is found out using KKT conditions are one of the following：
(c){WkUpdate
With { Γ } update and { Π } update, { WkUpdate be also required to one optimization problem of solution, and the optimization problem can be decomposed
For K independent minor issues：
s.t. Wk≥0
This problem is solved using Projected descent method, the result of gradient descent method each time is projected among feasible zone and is carried out
Iteration is updated, iterative formula is as follows：
Wherein Proj { } expressions project to feasible zone Wk>=0, s are step-length, are a positive real numbers.For object function
After t iterationThe gradient at place.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110895327A (en) * | 2019-11-08 | 2020-03-20 | 电子科技大学 | Robustness self-adaptive beam forming method based on direct convex optimization modeling |
| CN113747452A (en) * | 2021-07-16 | 2021-12-03 | 国网河北省电力有限公司雄安新区供电公司 | Communication cooperation beam forming design method and system for cloud wireless access network |
| WO2022036642A1 (en) * | 2020-08-20 | 2022-02-24 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and apparatus for beamforming |
| US20230261377A1 (en) * | 2019-05-07 | 2023-08-17 | Bao Tran | Cellular system |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101867462A (en) * | 2010-05-21 | 2010-10-20 | 清华大学 | Multi-base station cooperation linear precoding method based on minimum total bit error rate |
| US20110059705A1 (en) * | 2009-09-09 | 2011-03-10 | Nec Laboratories America, Inc. | Robust linear precoder designs for multi-cell downlink transmission |
| CN103245941A (en) * | 2013-04-16 | 2013-08-14 | 哈尔滨工程大学 | Robust beam forming method based on robust least-square |
| CN105188125A (en) * | 2015-08-05 | 2015-12-23 | 东南大学 | Power distribution method for integrally optimizing energy efficiency and spectrum efficiency of wireless network |
| CN107135544A (en) * | 2017-04-06 | 2017-09-05 | 杭州电子科技大学 | A kind of efficiency resource allocation methods updated based on interference dynamic |
-
2018
- 2018-03-01 CN CN201810171261.8A patent/CN108599831A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20110059705A1 (en) * | 2009-09-09 | 2011-03-10 | Nec Laboratories America, Inc. | Robust linear precoder designs for multi-cell downlink transmission |
| CN101867462A (en) * | 2010-05-21 | 2010-10-20 | 清华大学 | Multi-base station cooperation linear precoding method based on minimum total bit error rate |
| CN103245941A (en) * | 2013-04-16 | 2013-08-14 | 哈尔滨工程大学 | Robust beam forming method based on robust least-square |
| CN105188125A (en) * | 2015-08-05 | 2015-12-23 | 东南大学 | Power distribution method for integrally optimizing energy efficiency and spectrum efficiency of wireless network |
| CN107135544A (en) * | 2017-04-06 | 2017-09-05 | 杭州电子科技大学 | A kind of efficiency resource allocation methods updated based on interference dynamic |
Non-Patent Citations (2)
| Title |
|---|
| DONGLIANG YAN等: ""Robust Beamforming Designs for Downlink Cloud Radio Access Networks"", 《2017 9TH INTERNATIONAL CONFERENCE ON WIRELESS COMMUNICATIONS AND SIGNAL PROCESSING (WCSP)》 * |
| TSUNG-HUI CHANG等: ""A Proximal Dual Consensus ADMM Method for Multi-Agent Constrained Optimization"", 《IEEE TRANSACTIONS ON SIGNAL PROCESSING》 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20230261377A1 (en) * | 2019-05-07 | 2023-08-17 | Bao Tran | Cellular system |
| US11936120B2 (en) * | 2019-05-07 | 2024-03-19 | Bao Tran | Cellular system |
| CN110895327A (en) * | 2019-11-08 | 2020-03-20 | 电子科技大学 | Robustness self-adaptive beam forming method based on direct convex optimization modeling |
| WO2022036642A1 (en) * | 2020-08-20 | 2022-02-24 | Telefonaktiebolaget Lm Ericsson (Publ) | Method and apparatus for beamforming |
| CN113747452A (en) * | 2021-07-16 | 2021-12-03 | 国网河北省电力有限公司雄安新区供电公司 | Communication cooperation beam forming design method and system for cloud wireless access network |
| CN113747452B (en) * | 2021-07-16 | 2023-08-08 | 国网河北省电力有限公司雄安新区供电公司 | Cloud wireless access network communication cooperative beam forming design method and system |
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