CN109245812A - A kind of wave beam forming design method for Differentiated Services quality multiple groups multicast system - Google Patents
A kind of wave beam forming design method for Differentiated Services quality multiple groups multicast system 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
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/0413—MIMO systems
- H04B7/0426—Power distribution
- H04B7/043—Power distribution using best eigenmode, e.g. beam forming or beam steering
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Abstract
The invention discloses a kind of wave beam forming design methods for Differentiated Services quality multiple groups multicast system, this method can effectively improve the service quality level of high optimization level user in multiple groups multicast system, and the service quality level of low priority user is suppressed, differentiated service is provided for different users.The present invention is based on near-optimal thought, the feasibility of initial vector is first improved using the method for iterative search, it by non-convex optimization problem is approximately then convex optimization problem using convex approximation method during each iteration, finally the problem is solved using convex optimization tool, to realize the iteration optimization for sending wave beam forming vector.The present invention can effectively improve the service quality level of high optimization level user in multiple groups multicast system, and suppress the service quality level of low priority user, reduces and sends power, promote the efficiency for sending wave beam forming.
Description
Technical field
The invention belongs to the transmitting-receiving design method technical fields of broadband wireless and mobile communication, and in particular to one kind is used for area
Divide the wave beam forming design method of service quality multiple groups multicast system.
Background technique
Under the premise of based on known to transmitting terminal or part known channel state information, pass through the hair in wireless communication system
Sending end designs wave beam forming vector, optimization sends power in the distribution in space, is capable of the diversity gain of effective lifting system.It is existing
A large number of studies show that beamforming technique can be applied to all kinds of channels in wireless communication system, including access channel, unicast
Channel, multicast channel and broadcast channel.With the continuous expansion of upper layer multicast service, wave under single group multicast and multiple groups multicast scene
The design work of beam figuration is increasingly goed deep into.For multiple groups Multicast Channel, wave beam forming design method mainly has following a few classes:
1) it is designed with eliminating between multicast group interference as the wave beam forming of target.Its specific practice is to utilize zero-forcing technique, will
Interference between difference group user is eliminated, to degenerating multiple groups multicast problems for multiple single group multicast problems.The master of this method
It wants problem to be the less situation of number of users only in multicast group number and each group, just there are enough spatial degrees of freedom to carry out
Force zero, in the case of other, algorithm all can not achieve the target that elimination is interfered between multicast group.
2) it under the premise of guaranteeing each group user Signal to Interference plus Noise Ratio, is set using minimizing transmission power as the wave beam forming of target
Meter.Its specific practice is will to acquire intermediate solution using semi definite programming method after the non-convex order constraint relaxation in former optimization problem,
It then uses gaussian random algorithm or calculates the feasible solution of former problem using interference function as the iterative algorithm of target.This method
Main problem be only to constrain the minimum Signal to Interference plus Noise Ratio of each user, the practical letter that can not accurately control user is dry
It makes an uproar ratio；Meanwhile it not accounting for constraining the highest Signal to Interference plus Noise Ratio of certain customers yet.
3) under the premise of transmission general power is controlled, to maximize the minimum Signal to Interference plus Noise Ratio of all users in system as mesh
The design of target wave beam forming.Its specific practice is using the problem and under the premise of guaranteeing each group user Signal to Interference plus Noise Ratio, with minimum
Change the association sent between the problem of power is target, using two points of solutions by iterative method.The main problem of this method be to
Surely it sends under power condition, just for signal-to-noise ratio, worst user is optimized, and the practical letter that can not accurately control user dry is made an uproar
Than；Meanwhile it is similar with the 2nd kind of method, it does not account for constraining the highest Signal to Interference plus Noise Ratio of certain customers yet.
4) under the premise of guaranteeing high-priority users Signal to Interference plus Noise Ratio and suppressing low priority user Signal to Interference plus Noise Ratio, with most
Smallization sends the wave beam forming that power is target and designs.Its specific practice is similar with the 2nd kind of method, first with semi definite programming
Method acquires intermediate solution, and the feasible solution of former problem is then obtained using gaussian random algorithm.The main problem of this method is
When complexity is subjected to, sends power-performance and optimal lower bound gap is larger；To optimize performance as far as possible, then need to be arranged
One very big positive integer will introduce the algorithm complexity for being difficult to bear as randomization number.
Summary of the invention
The purpose of the present invention is to propose to a kind of iteration order -2 of Differentiated Services quality multiple groups multicast system (order -2 is attribute,
Order of looking like is 2, English rank-two) wave beam Shape design method is sent, guaranteeing high-priority users, compacting low priority
While user's Signal to Interference plus Noise Ratio, the transmission power-performance of optimization system.
The present invention the following steps are included:
Step 1: the Differentiated Services problem in construction multiple groups multicast system solves Differentiated Services problem using interior point method and passes through
The Semidefinite Programming obtained after relaxation, obtains semi-definite matrix group；
Step 2: the semi-definite matrix group that step 1 obtains being decomposed, extracted vector；
Step 3: whether the order for the semi-definite matrix group that judgment step 1 obtains all is not more than 2, if so, step 8 is executed, it is no
Then follow the steps 4；
Step 4: utilizing convex near-optimal, feasibility optimization is carried out to the vector decomposed in step 2, obtain feasible first
Beginning wave beam forming vector；
Step 5: carrying out feasibility optimization judgement if meeting condition and execute step 6, otherwise return step 4；
Step 6: being iterated power optimization；
Step 7: the judgement of power optimization the number of iterations；
Step 8: wave beam forming vector output: wave beam forming vector obtained in output step 3 or step 7.
Step 1 includes:
Step 1-1, if base station end has MtRoot transmitting antenna, high-priority users and low priority group user respectively match one
Receiving antenna；K high-priority users are shared in system, are respectively present in L high priority bank { Ω1,Ω2,...,ΩL, and
Each user is pertaining only to one of group, ΩLIndicate l-th high priority bank；Meanwhile having N number of low priority user in system,
Belong to low priority group χ；In transmitting terminal, the channel state information of all users be it is known,WithTable respectively
Show the channel vector and noise power of m-th of user in first of high priority bank, whereinIndicate that a line number is 1, column
Number is MtComplex field vector；WithRespectively indicate the channel vector and noise function of low priority group nth user
Rate；
Step 1-2, constructs the Differentiated Services problem in multiple groups multicast system, and the constraint condition of the problem is that high priority is used
Family Signal to Interference plus Noise Ratio is not more than certain value not less than certain value, low priority user Signal to Interference plus Noise Ratio, for example, generally can be by high priority
The Signal to Interference plus Noise Ratio value of user is limited to 1dB or more, and the Signal to Interference plus Noise Ratio value of low priority user is limited to 0.1dB or less.Optimize mesh
Mark is the transmission general power of system, and variable to be optimized is l grouping wave beam forming vectorAn and additivity wave beam
Figuration vectorWhereinIndicate that a line number is Mt, columns be 2 complex-field matrix；wlIndicate first of grouping wave
Beam figuration vector；Pass through definitionWithWherein,
WithIt respectively indicates to vector wl、hl,m、gnThe vector obtained after conjugate transposition operation is carried out with v,It is conjugate transposition symbol；Wl、
Hl,m、GnIt is for the intermediary matrix variable convenient for indicating definition with V.Former problem is converted into following form:
V≥0,rank(V)≤2
Wherein, Tr expression asks the mark of matrix to operate, and rank () expression asks rank of matrix to operate, γl,mWithIt respectively indicates
The Signal to Interference plus Noise Ratio constraint and its noise power of m-th of user, λ in first of high priority banknWithRespectively indicate low priority group
The Signal to Interference plus Noise Ratio constraint of middle nth user and its noise power；Order constraint is abandoned, half set pattern after relaxation is solved by interior point method
The problem of drawing, obtains semi-definite matrix Wl, l=1,2 ..., L and V.
Step 2 includes: to semi-definite matrix Wl, l=1,2 ..., L and V do Eigenvalues Decomposition:WithExtract two dimensional beam figuration vector:With
Wherein, matrix UlIt is to matrix WlThe left battle array obtained after Eigenvalues Decomposition is done, is a unitary matrice；Matrix ΣlIt is pair
Matrix WlThe intermediate battle array obtained after Eigenvalues Decomposition is done, is a diagonal matrix, diagonal element is the real number more than or equal to zero；
MatrixIt is matrix UlAssociate matrix；Matrix B is the left battle array obtained after doing Eigenvalues Decomposition to matrix V, is a tenth of the twelve Earthly Branches
Matrix；Matrix Λ is the intermediate battle array obtained after doing Eigenvalues Decomposition to matrix V, is a diagonal matrix, and diagonal element is big
In null real number；MatrixIt is the associate matrix of matrix B；MatrixIt is to matrix ΣlAfter carrying out evolution operation
Obtained matrix,It is to the matrix obtained after matrix Λ evolution；With v0Respectively indicate vector w to be optimizedlIt is initial with v
Value.
Step 3 includes: to pass through the number of nonzero element on diagonal matrix, judgement half based on the Eigenvalues Decomposition in step 2
Set matrix Wl, l=1, the order of 2 ..., L and V, if their order is no more than 2, then it represents that the vector extracted in step 2 is
Optimal solution leaps to step 8；Otherwise step 4 is continued to execute.
Step 4 includes: to optimize to the two dimensional beam figuration vector extracted in step 2, as initial vector, is made
Its constraint for meeting power optimization problem, the constraint include two classes, and the first kind is the constraint to high-priority users, is denoted as
Costraint 1 has following form:
Second class is the constraint to low priority user, is denoted as Costraint 2, there is following form:
WhereinIt indicates to matrixDirection matrix when optimizing,WithRespectively
It is its 1st column and the 2nd column；It indicates to matrix v0Direction matrix when optimizing,WithRespectively
It is its 1st column and the 2nd column；InWithIt is matrix respectivelyThe 1st column and the 2nd column；InWithRespectively indicate matrix v0The 1st column and the 2nd column；Expression takes real part to operate；
If the two dimensional beam figuration vector extracted in step 2 is unsatisfactory for constraints above, following optimization problem is solved,
Search for feasible initial vector:
Wherein tmaxIt is the variable of command deployment range,It is then the parameter that vector feasibility is indicated in i+1 time iteration；
ΔwlIt respectively indicates with Δ v to matrixAnd v0The direction matrix optimized.LHS and RHS is Left Hand Side respectively
The abbreviation of (left-hand side) and Right Hand Side (right-hand side), the left side and rear edge of the sign of inequality or equal sign in representation formula
Point.
Step 5 includes: to make decisions to the iteration feasibility optimization process in step 4, whenWhen, initial vector is
It can satisfy the constraint of power optimization problem, stop feasibility optimization, execute step 6；If by the feasible of fixed number of times
Property Optimized Iterative initial value does not still obtainAs a result, then increasing parameter tmax, return step 4 re-starts repeatedly
Generation.Under normal conditions, feasibility Optimized Iterative number is generally set to 5 times, still unmet after reaching the optimization numberAs a result, then by tmaxIncreasing is twice.
Step 6 includes: to send power-performance by iteratively solving following convex optimization problem optimization:
Wherein ti+1It is the system transmission power value after i+1 iteration；MatrixWith Δ viRespectively indicate i-th iteration
In to matrixThe direction matrix and v optimized0The direction matrix optimized.
Step 7 includes: to send power optimization process to the iteration in step 6 to make decisions, when the number of iterations reaches maximum
Preset value when, stop iteration.Under normal circumstances, maximum number of iterations is set as 10 times.
The wave beam forming initial value feasibility optimization method designed in the step 4, can preferably optimize original vector pair
The feasibility of problem to be optimized, this method should meet claimed below:
1) the wave beam forming initial value feasibility optimization problem is convex optimization problem, can use interior point method and quickly asks
Solution；
2) in the wave beam forming initial value feasibility optimization method, there are the variables of command deployment range；
3) in the wave beam forming initial value feasibility optimization method, there are the whether feasible labels of vector, search to work as
Stop iterative search procedures when rope is to feasible solution.
The wave beam forming vector that designs in the step 6 sends power optimization method, can rapid Optimum wave beam forming to
The transmission power-performance of amount, this method should meet claimed below:
1) the iteration wave beam forming is sent in power-performance optimization method, the convex about beam ratio primal problem of Approximation Problem
Non-convex constraint is more stringent, and every resulting solution of step iteration is all the feasible solution of former problem；
2) the iteration wave beam forming is sent in power-performance optimization method, and every step iteration solution obtained is monotone decreasing
, i.e., the alternative manner is determining convergent.
Compared with prior art, the present invention has the advantages that:
Wave beam forming design method proposed by the present invention, by being approximately convex problem iterative solution by original non-convex problem
Method optimizing wave beam forming performance.Firstly, improving initial target Vector Groups for problem to be optimized with the mode of iterative search
Feasibility；Then, theoretical based on near-optimal, by original non-convex problem step-by-step processing, and by its approximation in each step
For convex optimization problem；Then, using mature convex optimization tool Solve problems, iteration updates wave beam forming Vector Groups.This method
It can guarantee the Signal to Interference plus Noise Ratio of horizontal, the accurate limitation low priority user of the Signal to Interference plus Noise Ratio of high-priority users in system, simultaneously
Its send power-performance approach it is optimal, to provide Differentiated Services for different brackets user in multiple groups multicast system and providing one kind
Completely new effective solution is suitable for the new generation broadbands such as 802.11n, TD-LTE TD-LTE-Advanced and 5G
Wireless and mobile communication system.
Detailed description of the invention
The present invention is done with reference to the accompanying drawings and detailed description and is further illustrated, it is of the invention above-mentioned or
Otherwise advantage will become apparent.
Fig. 1 is multiple groups multicast beamforming method implementation flow chart proposed by the present invention；
Fig. 2 is multiple groups multicast beamforming method signal processing flow figure proposed by the present invention；
Fig. 3 is the transmission power-performance of beam form-endowing method proposed by the present invention with low priority user number variation diagram；
Fig. 4 is the transmission power-performance of beam form-endowing method proposed by the present invention with transmission antenna number variation diagram.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and embodiments.
(order -2 is attribute to the iteration order -2 of Differentiated Services quality multiple groups multicast system proposed by the present invention, and meaning order is 2
, English rank-two) implementing procedure of wave beam Shape design method is sent as shown in Figure 1, mainly including 8 steps: 1) it is sharp
The Semidefinite Programming obtained after relaxation with the former problem of interior point method solution, 2) obtained semi-definite matrix group is divided
Solution, extracted vector, 3) judge the order of semi-definite matrix group whether all for Isosorbide-5-Nitrae) and to wave beam forming initial value progress feasibility optimization, 5)
Feasibility optimization judgement, 6) optimization of wave beam forming vector power, 7) judgement of power optimization the number of iterations, 8) wave beam forming vector is defeated
Out.The implementation of each step is described in further detail below.
Step 1: solving the Semidefinite Programming that former problem obtains after relaxation using interior point method.
The Differentiated Services problem in multiple groups multicast system is constructed, the constraint condition of the problem, which is that high-priority users letter is dry, makes an uproar
Than not less than the little Mr. Yu's definite value of certain definite value, low priority user Signal to Interference plus Noise Ratio, optimization aim is the transmission general power of system, to
Optimized variable is l grouping wave beam forming vectorAn and additivity wave beam forming vectorBy fixed
JusticeWithFormer problem can be converted into following form:
V≥0,rank(V)≤2
Order constraint is abandoned, the Semidefinite Programming after relaxation is solved by interior point method.
Step 2: obtained semi-definite matrix group being decomposed, extracted vector.
Semidefinite Programming is being solved by step 1, is obtaining semi-definite matrix Wl, after l=1,2 ..., L and V, they are done
Eigenvalues Decomposition:WithThen, two dimensional beam figuration vector is extracted:
With
Step 3: judging the order of semi-definite matrix group whether all no more than 2.
Based on the Eigenvalues Decomposition in step 2, pass through the number of nonzero element on diagonal matrix, it can be determined that semi-definite matrix
Wl, l=1, the order of 2 ..., L and V.If their order no more than 2, illustrates that the vector extracted in step 2 is optimal solution,
Step 8 can be leapt to；Otherwise step 4 is continued to execute.
Step 4: feasibility optimization is carried out to wave beam forming initial value.
Using the two dimensional beam figuration vector extracted in step 2 as initial value, as step 6 wave beam forming vector function
Before the input of rate optimization, needing to optimize the initial vector makes it meet the constraint of power optimization problem.The constraint includes two classes,
The first kind is the constraint (Constraint 1) to high-priority users, there is following form:
Second class is then the constraint (Constraint 2) to low priority user, there is following form:
WhereinSuch as
Fruit initial vector is unsatisfactory for constraints above, then solves following optimization problem, searches for feasible initial vector:
Wherein tmaxIt is the variable of command deployment range,It is then the parameter that vector feasibility is indicated in i+1 time iteration.
LHS and RHS is the abbreviation of Left Hand Side (left-hand side) and Right Hand Side (right-hand side), representation formula respectively
The left side and rear rim portion of the middle sign of inequality or equal sign.
Step 5: feasibility optimization judgement.
Iteration feasibility optimization process in step 4 is made decisions, whenWhen, initial vector can expire
The constraint of sufficient power optimization problem, to stop feasibility optimization algorithm.On the other hand, if feasibility by fixed number of times
Optimized Iterative initial value does not still obtainAs a result, then increasing parameter tmax, re-start iteration.
Step 6: the optimization of wave beam forming vector power.
Under the conditions of initial vector is feasible, power-performance is sent by iteratively solving following convex optimization problem optimization:
Wherein ti+1It is the system transmission power value after i+1 iteration.
Step 7: the judgement of power optimization the number of iterations.
Power optimization process is sent to the iteration in step 6 to make decisions, when the number of iterations reaches maximum preset value,
Stop iteration.
Step 8: the output of wave beam forming vector.
Wave beam forming vector obtained in step 3 or step 7 is exported.
From embodiments above as can be seen that the present invention is by utilizing alternative manner to solve the convex approximation of original non-convex problem
Problem realizes the optimization to wave beam forming Vector Groups, effectively reduces to guarantee that high-priority users Signal to Interference plus Noise Ratio, compacting are low
System needed for this target of priority users Signal to Interference plus Noise Ratio sends power.
Fig. 2 gives the transmitting terminal signal processing flow of multiple groups multicast beamforming method proposed by the invention.Believing
In the generation module of source, the raw information of l groupIt is the independent identically distributed zero-mean gaussian signal of two-way, passes through
Alamouti Space Time Coding obtains encoded signal matrixThen, by being grouped wave beam forming module, each group signal becomesThen, each group signal is overlapped to obtainAnd pass through additivity wave beam forming module production hair
The number of delivering lettersIt is represented by according to the power of above-mentioned definition, the transmission signal
Finally, the transmission signal is sent by wireless signal.
In order to further examine the system performance obtained using the method for the present invention, next the present embodiment utilizes Monte Carlo
Emulation experiment, which obtains to apply the method for the present invention, sends power and low priority in the multiple groups multicast system of Differentiated Services quality
The relation curve of number of users, and the method for the present invention is applied and sends power in the multiple groups multicast system of Differentiated Services quality
With the relation curve of transmission antenna quantity.In emulation experiment, it is assumed that each high priority bank possesses the user of identical quantity, and
And the identical SINR constraint of each user sharing in these groups, i.e.,Assuming that for low
The user of priority group, SINR are restricted to the 1/10 of high priority bank SINR, i.e.,Feasibility Optimized Iterative
Number is set as 5, sends power optimization the number of iterations and is set as 10, every Monte Carlo simulation experiment carries out 5000 times.
Fig. 3 give by the method for the present invention apply in the multiple groups multicast system of Differentiated Services quality send power with it is low excellent
The relation curve of first grade number of users, system parameter setting L=2, K=8, Mt=8 and γ=4dB.Meanwhile selection is " a
People's indoor mobile communication International Year in 2015 can collection of thesis " (in Proc.PIMRC, Hong Kong, China, 2015) " be based on
- 2 wave beam forming of Differentiated Services multiple groups multicast system order of Alamouti Space Time Coding designs " (Rank-two beamforming
for QoS-DiffServ multi-group multicast system based on Alamouti space-time
Coding the transmission power-performance based on gaussian random method that) proposes in a text, the present invention are under -1 degenerative conditions of order
The multiple groups multicast system for sending power-performance and Differentiated Services quality sends lower power bound as a comparison.As can be seen from Figure 3, not
Under same low priority user said conditions, power-performance A3 is sent using the multiple groups multicast system that the method for the present invention obtains and is distinguished
The transmission power-performance lower bound A4 for servicing multiple groups multicast system is very close；Relative to using the hair based on gaussian random method
The gain for sending power-performance A2 to have about 0.1~0.4dB；The opposite transmission power-performance A1 with the present invention under -1 degenerative conditions of order
There is the gain of 0.3~0.5dB, gain increases with the increase of low priority user number.
Fig. 4 gives to apply the method for the present invention and sends power in the multiple groups multicast system of Differentiated Services quality and send
The relation curve of antenna amount, system parameter setting L=2, K=8, N=2 and γ=4dB.Figure 4, it is seen that
Under different transmission antenna said conditions, power-performance B3 is sent using the multiple groups multicast system that the method for the present invention obtains and distinguishes clothes
The transmission power-performance lower bound B4 of business multiple groups multicast system is very close；Meanwhile slightly better than using based on gaussian random method
Transmission power-performance B2, have the gain of about 0.1~0.2dB；Relative to transmission power of the present invention under -1 degenerative conditions of order
Performance B1 has a gain of 0.2dB, and its performance gain is held essentially constant with the increase of antenna number.To sum up, to practical system
For system, the method for the present invention can effectively improve the transmission power-performance of the multiple groups multicast system of Differentiated Services quality.
It is specific real the present invention provides a kind of wave beam forming design method for Differentiated Services quality multiple groups multicast system
Now there are many method of the technical solution and approach, the above is only a preferred embodiment of the present invention, it is noted that for this
For the those of ordinary skill of technical field, without departing from the principle of the present invention, several improvement and profit can also be made
Decorations, these modifications and embellishments should also be considered as the scope of protection of the present invention.Each component part being not known in the present embodiment is available
The prior art is realized.
Claims (8)
1. a kind of wave beam forming design method for Differentiated Services quality multiple groups multicast system, which is characterized in that including following
Step:
Step 1: the Differentiated Services problem in construction multiple groups multicast system solves Differentiated Services problem by relaxation using interior point method
The Semidefinite Programming obtained later obtains semi-definite matrix group；
Step 2: the semi-definite matrix group that step 1 obtains being decomposed, extracted vector；
Step 3: whether the order for the semi-definite matrix group that judgment step 1 obtains all is not more than 2, if so, executing step 8, otherwise holds
Row step 4；
Step 4: utilizing convex near-optimal, feasibility optimization is carried out to the vector decomposed in step 2, obtains feasible primary wave
Beam figuration vector；
Step 5: carrying out feasibility optimization judgement if meeting condition and execute step 6, otherwise return step 4；
Step 6: being iterated power optimization；
Step 7: the judgement of power optimization the number of iterations；
Step 8: wave beam forming vector output: wave beam forming vector obtained in output step 3 or step 7.
2. the method according to claim 1, wherein step 1 includes:
Step 1-1, if base station end has MtRoot transmitting antenna, high-priority users and low priority group user respectively receive with a piece-root grafting
Antenna；K high-priority users are shared in system, are respectively present in L high priority bank { Ω1,Ω2,...,ΩL, and it is each
User is pertaining only to one of group, ΩLIndicate l-th high priority bank；Meanwhile having N number of low priority user in system, belong to
Low priority group χ；In transmitting terminal, the channel state information of all users be it is known,WithRespectively indicate l
The channel vector and noise power of m-th of user in a high priority bank, whereinIndicate that a line number is 1, columns Mt
Complex field vector；WithRespectively indicate the channel vector and noise power of low priority group nth user；
Step 1-2, constructs the Differentiated Services problem in multiple groups multicast system, and the constraint condition of the problem is high-priority users letter
It is dry to make an uproar than not less than certain value, low priority user Signal to Interference plus Noise Ratio, no more than certain value, optimization aim is the transmission total work of system
Rate, variable to be optimized are l grouping wave beam forming vectorsAn and additivity wave beam forming vectorIts
InIndicate that a line number is Mt, columns be 2 complex-field matrix；wlIndicate first of grouping wave beam forming vector；By fixed
JusticeWithWherein, WithIt respectively indicates to vector
wl、hl,m、gnThe vector obtained after conjugate transposition operation is carried out with v；Former problem is converted into following form:
V≥0,rank(V)≤2
Wherein, Tr expression asks the mark of matrix to operate, and rank () expression asks rank of matrix to operate, γl,mWithIt respectively indicates first
The Signal to Interference plus Noise Ratio constraint and its noise power of m-th of user, λ in high priority banknWithIt respectively indicates n-th in low priority group
The Signal to Interference plus Noise Ratio constraint of a user and its noise power；Order constraint is abandoned, is asked by the Semidefinite Programming that interior point method solves after relaxation
Topic, obtains semi-definite matrix Wl, l=1,2 ..., L and V.
3. according to the method described in claim 2, it is characterized in that, step 2 includes: to semi-definite matrix Wl, l=1,2 ..., L with
And V does Eigenvalues Decomposition:WithExtract two dimensional beam figuration vector:
With
Wherein, matrix UlIt is to matrix WlThe left battle array obtained after Eigenvalues Decomposition is done, is a unitary matrice；Matrix ΣlIt is to matrix
WlThe intermediate battle array obtained after Eigenvalues Decomposition is done, is a diagonal matrix, diagonal element is the real number more than or equal to zero；MatrixIt is matrix UlAssociate matrix；Matrix B is the left battle array obtained after doing Eigenvalues Decomposition to matrix V, is a unitary matrice；
Matrix Λ is the intermediate battle array obtained after doing Eigenvalues Decomposition to matrix V, is a diagonal matrix, and diagonal element is to be more than or equal to
Zero real number；MatrixIt is the associate matrix of matrix B；MatrixIt is to matrix ΣlCarry out the square obtained after evolution operation
Battle array,It is to the matrix obtained after matrix Λ evolution；With v0Respectively indicate vector w to be optimizedlWith the initial value of v.
4. according to the method described in claim 3, it is characterized in that, step 3 includes: to be led to based on the Eigenvalues Decomposition in step 2
The number for crossing nonzero element on diagonal matrix judges semi-definite matrix Wl, l=1, the order of 2 ..., L and V, if their order is equal
No more than 2, then it represents that the vector extracted in step 2 is optimal solution, leaps to step 8；Otherwise step 4 is continued to execute.
5. according to the method described in claim 4, it is characterized in that, step 4 includes: to assign to the two dimensional beam extracted in step 2
Shape vector optimizes, and as initial vector, it is made to meet the constraint of power optimization problem, which includes two classes, the
One kind is the constraint to high-priority users, is denoted as Costraint 1, there is following form:
Second class is the constraint to low priority user, is denoted as Costraint 2, there is following form:
WhereinIt indicates to matrixDirection matrix when optimizing,WithIt is it respectively
1st column and the 2nd column；It indicates to matrix v0Direction matrix when optimizing,WithIt is it respectively
1st column and the 2nd column；InWithIt is matrix respectivelyThe 1st column and the 2nd column；InWithRespectively indicate matrix v0The 1st column and the 2nd column；Expression takes real part to operate；
If the two dimensional beam figuration vector extracted in step 2 is unsatisfactory for constraints above, following optimization problem is solved, is searched for
Feasible initial vector:
Wherein tmaxIt is the variable of command deployment range,It is then the parameter that vector feasibility is indicated in i+1 time iteration；Δwl
It respectively indicates with Δ v to matrixAnd v0The direction matrix optimized.
6. according to the method described in claim 5, it is characterized in that, step 5 includes: to the iteration feasibility optimization in step 4
Process makes decisions, whenWhen, initial vector has been able to the constraint for meeting power optimization problem, and it is excellent to stop feasibility
Change, executes step 6；If the feasibility Optimized Iterative initial value by fixed number of times does not still obtainAs a result,
Then increase parameter tmax, return step 4 re-starts iteration.
7. according to the method described in claim 6, it is characterized in that, step 6 includes: by iteratively solving following convex optimization problem
Optimization sends power-performance:
Wherein ti+1It is the system transmission power value after i+1 iteration；MatrixWith Δ viIt is right in i-th iteration to respectively indicate
MatrixThe direction matrix and v optimized0The direction matrix optimized.
8. the method according to the description of claim 7 is characterized in that step 7 includes: excellent to the iteration transmission power in step 6
Change process makes decisions, and when the number of iterations reaches maximum preset value, stops iteration.
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