CN104039005B - The power distribution method of consideration user's request based on SLNR wave beam formings - Google Patents
The power distribution method of consideration user's request based on SLNR wave beam formings Download PDFInfo
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Abstract
The power distribution method of consideration user's request based on SLNR wave beam formings, the beamforming technique field belonged in wireless communication system.Current beam form-endowing method is solved when improving systematic function, the problem of depositing fairness and the low corresponding satisfaction of each user among different users.Feasible power initial value is obtained by initial point selection algorithm；The approximate convex optimization problem for the power optimization problem set up is solved, the power assignment value of user is obtained；Obtain temporary transient optimal power allocation value；Update SLNR beam form-endowing methods and obtain corresponding wave beam formed matrix, obtain optimal power allocation result.Or use suboptimization：Expression formula and matrixing using SINR, obtain the expression formula of the corresponding power distribution matrix when the SINR that user terminal is received is minimum essential requirement, obtain power distribution and are worth to final power distribution result.The fairness between systematic function, different user and the corresponding satisfaction of each user is set to reach optimal compromise.
Description
Technical field
It is more particularly to a kind of to be assigned based on SLNR wave beams the invention belongs to the beamforming technique field in wireless communication system
The power distribution method of the consideration user's request of shape.
Background technology
How the availability of frequency spectrum is improved while channel fading and interference is resisted, and while communication quality is ensured
Power system capacity is improved, is urgent problem to be solved in lte-a system.Multiuser MIMO and beamforming technique can reach enhancing
Desired signal simultaneously suppresses inter-user interference, improves the purpose of message capacity and quality, therefore, in LTE-A standards, multi-user
The technology such as MIMO and beam shaping has also obtained further development and application.In TD-LTE-A downlink, non-code book
Beam shaping method using the reciprocity of tdd mode lower channel due to that can reduce the signaling consumption of channel estimation in recent years
More to be paid close attention to.
Multi-user's multi-flow beam excipient is supported since after the 3GPP versions of Release 10, the non-code book wave beam of multi-user is assigned
Shape scheme is divided into the non-linear beamforming scheme by representative of dirty paper code, and linear arrangement, including block diagonalization, compels
0th, least mean-square error and SLNR (Signal-to-leakage-and-noise Ratio leak signal to noise ratio) algorithm.Dirty paper is compiled
Code algorithm can reach the channel capacity upper bound of multi-user MIMO system, but it realizes extremely complex, is difficult in actual hardware
Realize.And SLNR algorithms, the complexity of algorithm can be greatly reduced, and other lines are compared in the bit error rate and with the performance of capacity
Property pre-coding scheme is more preferable.In addition, by the way that the performance of wave beam forming, transmitting terminal pair can be improved with reference to suitable power distribution algorithm
User terminal carries out power distribution, enables to system to reach maximum capacity.Power distribution also disclosure satisfy that user for business
Demand for services, such as, the channel conditions of a certain user terminal are poor, but its service rate have minimum limit value, then this
When by distributing bigger power for it can be made to meet demand.There is scholar to propose to consider the water injection power distribution that capacity is optimal
Algorithm, the power that the bad user of channel condition is assigned to is just small, because water-filling algorithm pursues the capacity optimized, can abandon
The transmission of the particularly poor user of channel condition, this is irrational.There is scholar to propose the power distribution algorithm of channel self-adapting,
The fairness between the difference of the channel condition of user and user is considered, but does not reach the optimization of capacity, does not also consider to use
The business demand at family.
The content of the invention
The invention aims to solve current beam form-endowing method while systematic function is improved, also in the presence of not
The problem of with the fairness between user and the low corresponding satisfaction of each user, SLNR ripples are based on the invention provides one kind
The power distribution method of the consideration user's request of beam figuration.
The present invention adopts the technical scheme that to solve above-mentioned technical problem：
The power distribution method of the consideration user's request based on SLNR wave beam formings of the present invention, provides two kinds of technical sides
Case：
Technical scheme one：The power distribution method of optimization, is comprised the following steps：
Step one：Under conditions of constant power distribution, phase is obtained using the SLNR beam form-endowing methods for combining user power
The wave beam formed matrix answered；
Step 2：Under the wave beam formed matrix that step one is obtained, feasible power is obtained by initial point selection algorithm
Initial value；
Step 3：Under the power initial value that step 2 is obtained, the approximate convex optimization for solving the power optimization problem set up is asked
Topic, obtains the power assignment value of user；
Step 4：The power distribution result that step 3 is obtained repeats step 3 as the initial value of step 3, judges
Whether the difference of the front and rear power assignment value obtained twice is sufficiently small, and satisfaction then performs step 5, now, obtains temporary transient optimal work(
Rate apportioning cost；
Step 5：Under the optimal power allocation value that step 4 is obtained, using the SLNR wave beam formings for combining user power
Method obtains corresponding wave beam formed matrix, step 2 is performed to step 4, if the front and rear optimization aim (system obtained twice
And capacity) value difference it is sufficiently small, terminate algorithm, obtain final optimal power allocation result.
Technical scheme one is further qualified：
The SLNR beam form-endowing methods for combining user power are used to obtain corresponding wave beam formed matrix in the step one
Process be：
When the transmission power of user terminal configurations match filtering receiver and user has been normalized, user k SLNR
It is expressed as：
In formula, wkIt is user k wave beam formed matrix, NrIt is the reception antenna number of user terminal, NtIt is the transmitting of base station end
Number of antennas,Wherein K is the number of users that base station is serviced, HiIt is user i letter
Road matrix,WhereinFor NtThe unit matrix of dimension, pkThe performance number that user k distribution is obtained is represented, whereinTable
Show the Frobenius norms of matrix A, trace (A) is the mark of matrix A, σ2For user k noise power；
When SLNR is maximized, the user k of optimization wave beam formed matrix is：
The process of initial point selection algorithm is in step 2：
Step 2 one：By constant power apportioning cost initial value P the mostm, m=0, i-th of constraints of optimization problem is set to ci
(P)；
Step 2 two：Calculate non-effective collection J, setting J={ j:cj(Pk)>0 }, if Represent empty set, algorithm knot
Beam, obtains rational power initial vector；Otherwise, step 2 three is continued executing with；
Step 2 three：J ∈ J are taken, with PmFor initial value, following problem is solved using interior point method：
min cj(P) j∈J
Step 2 four：If the optimal solution P of this subproblemm+1Meet cj(Pm+1)≤0, then m=m+1, performs step 2 two.
The power optimization targets in step 3 are modeled as：
s.t.SINRi≥SINRimin
In formula,C (P) is is in power distribution matrix
During P and capacity, optimization aim is system and capacity is reached maximization, and top n constraints represents what user i was received
SINR value is greater than user i minimum SINR limit values SINRimin, last constraints, which is limited, distributes to the power of each user
The transmission power level maximum with must not exceed base station, wherein PTFor the general power of Base Transmitter antenna；One shared N+1 limitation
Condition；
For object function, maximizeIt is equal to maximizationDue to
SINRiMore than zero, therefore maximizeEquivalent to minimumObject function turns
Turn to：
In formula,U=1,2 ..., N }；It is approximately by F (P)：
In formula,L represents iterations, approximately
Function can approach original object function in certain iterations, obtain the new object function that can be solved；
The conversion of form is carried out for constraints, logarithm is removed to object function and constraints, is obtained described in step 2
Power optimization problem approximate convex optimization problem：
Above formula is the convex formula of geometric programming, and geometric programming can be solved using interior point method, obtain power assignment value.
It is described described in step 4 judge whether perform step 5 condition be：
In formula,Represent the power for the user i that the L times approximate iteration is obtained.
Condition that the evaluation algorithm described in step 5 terminates is：
|C(Pn)-C(Pn-1)|≤ε2；
In formula, PnRepresent that n-th repeats the step two in claim 2 to four obtained power distribution results, C
(Pn) represent that in power distribution matrix be PnWhen and capacity.
Technical scheme two：In order to reduce the power distribution method that complexity also proposed suboptimization, comprise the following steps：
Step one：Under conditions of constant power distribution, phase is obtained using the SLNR beam form-endowing methods for combining user power
The wave beam formed matrix answered；
Step 2：Expression formula and matrixing using SINR, the SINR for obtaining receiving when user terminal is minimum
During SINR demands, the expression formula of corresponding power distribution matrix under the wave beam formed matrix that step one is obtained, and then obtains firm
The power assignment value of user's request is met well.
Step 3：By remaining power, proportionally the factor is allocated, and obtains final power distribution result.
Technical scheme two is further qualified：
In the step 2 when the SINR that user terminal is received is minimum SINR demands, user power expression formula is obtained
For：
For simplified expression, matrix A and B are introduced, the method for obtaining A and B is：
User power expression formula is converted into expression matrix form：
In formula, P=[p1,p2,…,pN]T,It is that matrix is tieed up in N × 1；By simple matrixing, power
Allocation matrix is expressed as：
In formula, P(1)For the power distribution matrix when the SINR that user terminal is received is minimum SINR demands, I is N × N
Tie up unit matrix.
The formula that scale factor described in step 3 is obtained is：
The formula for obtaining final power distribution matrix is：
In formula, ρ=[ρ1,ρ2,…,ρK] it is equitable proportion factor matrix.
The invention has the advantages that：
Effect of the invention is that, optimal iterative power allocation algorithm being capable of lifting system and capacity, guarantee customer service
Demand and matched beam figuration matrix and power distribution matrix.Suboptimization algorithm drops significantly relative to optimum allocation algorithm
Low complex degree, and capacity only have 10% decline, can preferably meet user's request.In other words, the present invention is in the system of raising
While performance, the fairness and the corresponding satisfaction of each user between different user can be taken into account, makes systematic function, difference
Fairness and the corresponding satisfaction of each user between user reach optimal compromise.
The complexity of algorithm can be greatly reduced because SLNR beamforming algorithms have, and in the bit error rate and and capacity
Performance compare other more preferable advantages of linear predictive coding scheme, the present invention be based on this algorithm research power distribution algorithm, due to
The communication quality of the power of certain user not only influence itself is distributed to, and influences it to disturb others, such wave beam is assigned
The performance of shape can be got a promotion by the power distribution to user, good power distribution strategies be capable of lifting system and hold
Amount and the demand for ensureing user.
Optimal iterative algorithm in the present invention can maximize system on the premise of user's request is met and capacity, this
Outside, it is considered to which the result of power distribution can cause to devise renewal wave beam formed matrix in the change of wave beam formed matrix, the present invention
Iterative process so that wave beam formed matrix and power distribution matrix match.Meanwhile, in order to reduce the complexity in physical device
Degree, the present invention proposes suboptimization power distribution algorithm.
Brief description of the drawings
Fig. 1 is the principle schematic of the power distribution method based on SLNR wave beam formings described in embodiment one；
Fig. 2 be power distribution method of the present invention and existing power distribution algorithm and the signal of capacity comparison curve
Figure；
Fig. 3 is unsatisfied for the removal demand of power distribution method of the present invention and existing power distribution algorithm
User and capacity comparison curve synoptic diagram；
Fig. 4 is the average interrupt probability contrast song of power distribution method of the present invention and existing power distribution algorithm
Line schematic diagram；
The SINR's that Fig. 5 receives for the user of power distribution method of the present invention and existing power distribution algorithm
Contrast block diagram.
Embodiment
Embodiment one：Illustrate present embodiment with reference to Fig. 1, described in present embodiment based on SLNR wave beam formings
Consideration user's request power distribution method, wherein optimal iterative power distribution method comprises the following steps：
Step one：Under conditions of constant power distribution, phase is obtained using the SLNR beam form-endowing methods for combining user power
The wave beam formed matrix answered；
Step 2：Under the wave beam formed matrix that step one is obtained, feasible power is obtained by initial point selection algorithm
Initial value；
Step 3：Under the power initial value that step 2 is obtained, the approximate convex optimization for solving the power optimization problem set up is asked
Topic, obtains the power assignment value of user；
Step 4：The power distribution result that step 3 is obtained repeats step 3 as the initial value of step 3, judges
Whether the difference of the front and rear power assignment value obtained twice is sufficiently small, and satisfaction then performs step 5, now, obtains temporary transient optimal work(
Rate apportioning cost；
Step 5：Under the optimal power allocation value that step 4 is obtained, using the SLNR wave beam formings for combining user power
Method obtains corresponding wave beam formed matrix, step 2 is performed to step 4, if the front and rear optimization aim (system obtained twice
And capacity) value difference it is sufficiently small, terminate algorithm, obtain final optimal power allocation result.
Embodiment two：Present embodiment is to the examining based on SLNR wave beam formings described in embodiment one
Consider the SLNR wave beams of the combination user power used in the further restriction of the power distribution method of user's request, the step one
The method that shaping method obtains corresponding wave beam formed matrix is：
User k SLNR is expressed as：
In formula, wkIt is user k wave beam formed matrix, NrIt is the reception antenna number of user terminal, NtIt is the transmitting of base station end
Number of antennas,Wherein K is the number of users that base station is serviced, HiIt is user i letter
Road matrix,WhereinFor NtThe unit matrix of dimension, pkThe performance number that user k distribution is obtained is represented, whereinTable
Show the Frobenius norms of matrix A, trace (A) is the mark of matrix A, σ2For user k noise power；
When SLNR is maximized, the user k of optimization wave beam formed matrix is：
Embodiment three：Present embodiment be to described in embodiment one or two based on SLNR wave beam formings
Consideration user's request optimal iterative power distribution method further restriction,
It is the step of initial point system of selection in step 2：
Step 1：By constant power apportioning cost initial value P the mostm, m=0, i-th of constraints of optimization problem is set to ci(P)。
Step 2：Calculate non-effective collection J, setting J={ j:cj(Pk)>0 }, ifAlgorithm terminates, and obtains rational
Power initial vector.Otherwise, step 3 is continued executing with；
Step 3：J ∈ J are taken, with PmFor initial value, following problem is solved using interior point method：
min cj(P) j∈J
Step 4：If the optimal solution P of this subproblemm+1Meet cj(Pm+1)≤0, then m=m+1, performs step 2.
Embodiment four：Present embodiment be to described in embodiment one, two or three based on SLNR wave beams
The further restriction of the optimal iterative power distribution method of the consideration user's request of figuration, builds in the power optimization problem of step 3
Mould is：
s.t.SINRi≥SINRimin
In formula,Optimization aim is to make system and appearance
Amount reaches maximization, and top n constraints represents that the SINR value that user i is received is greater than user i minimum SINR limit values
SINRimin, last constraints, which is limited, distributes to the power of each user transmitting work(maximum with must not exceed base station
Rate value, wherein PTFor the general power of Base Transmitter antenna.One has N+1 restrictive condition.
Above-mentioned optimization problem is non-linear non-convex optimization problem, it is difficult to obtain globally optimal solution, therefore uses approximate side
Method is translated into convex optimization problem.
For object function, maximizeIt is equal to maximizationDue to
SINRiMore than zero, therefore maximizeEquivalent to minimumObject function turns
Turn to：
In formula,U=1,2 ..., N }.It is approximately by F (P)：
In formula,L represents iterations, approximately
Function can approach original object function in certain iterations, can thus obtain the new target that can be solved
Function.
The conversion of form is carried out for constraints, logarithm is removed to object function and constraints, is obtained described in step 2
Power optimization problem approximate convex optimization problem：
Above formula is the convex formula of geometric programming, and geometric programming can be solved using interior point method, obtain power assignment value.
Embodiment five：Present embodiment be to described in embodiment one, two, three or four based on SLNR ripples
The further restriction of the optimal iterative power distribution method of the consideration user's request of beam figuration, the judgement described in step 4 is
It is no perform step 5 condition be：
Embodiment six：Present embodiment be to described in embodiment one, two, three, four or five based on
The further restriction of the power distribution method of the consideration user's request of SLNR wave beam formings, the evaluation algorithm knot described in step 5
The condition of beam is：
|C(Pn)-C(Pn-1)|≤ε2
In formula, PnRepresent that n-th repeats the step two in embodiment one to four obtained power distribution results, C
(Pn) represent that in power distribution matrix be PnWhen and capacity.
Embodiment seven：Illustrate present embodiment with reference to Fig. 1, described in present embodiment based on SLNR wave beam formings
Consideration user's request power distribution method, wherein suboptimization power distribution method comprises the following steps：
Step one：Under conditions of constant power distribution, phase is obtained using the SLNR beam form-endowing methods for combining user power
The wave beam formed matrix answered；
Step 2：Expression formula and matrixing using SINR, the SINR for obtaining receiving when user terminal is minimum
During SINR demands, the expression formula of corresponding power distribution matrix under the wave beam formed matrix that step one is obtained, and then obtains firm
The power assignment value of user's request is met well.
Step 3：By remaining power, proportionally the factor is allocated, and obtains final power distribution result.
Embodiment eight：Present embodiment is to the examining based on SLNR wave beam formings described in embodiment seven
Consider in the further restriction of the power distribution second-rate optimization method of user's request, step 2 when the SINR that user terminal is received is minimum
During SINR demands, the method for obtaining user power expression formula is：
For simplified expression, matrix A and B are introduced, the method for obtaining A and B is：
So, the method that user power expression formula is converted into expression matrix form is：
In formula, P=[p1,p2,…,pN]T,It is that matrix is tieed up in N × 1.Power distribution matrix can be expressed as：
Embodiment nine：Present embodiment be to described in embodiment seven or eight based on SLNR wave beam formings
Consideration user's request power distribution second-rate optimization method further restriction, the method that scale factor described in step 3 is obtained
For：
The method for obtaining final power distribution matrix is：
In formula, ρ=[ρ1,ρ2,…,ρK]。
For the purpose of the present invention, technological means and advantage is more clearly understood, below in conjunction with accompanying drawing, the present invention is done into
One step is described in detail.
Embodiment：
In the principle schematic that Fig. 1 distributes for multiuser downstream wave beam forming joint Power, the present invention, channel status is set
Information (CSI, Channel State Information) is known at eNodeB ends, according to the result and CSI of wave beam forming
Carry out power distribution.Total number of users of system is set to K, and eNodeB transmitting antenna number is Nt, and UE reception antenna number is Nr.
At eNodeB ends, the data of all users are sent by serioparallel exchange module via beam shaping module and power distribution module
To UE.HkIt is the channel matrix between user k and eNodeB, when channel is the accidental channel of flat fading, its element obeys zero
Average, the distribution of the multiple Gauss of unit variance；wkIt is user k wave beam formed matrix, pkIt is allocated to family k performance number, nkIt is zero
Average, variance are σ2Additive white Gaussian noise；It is the transmission of the user k after power normalization
Signal, mkFor user k data fluxion..
Assume that transmission mode is single-stream transmission in the present invention, receiving terminal, user k reception signal is represented by：
As can be seen that receiving signal rkIn in addition to user k desired signal, also there are other users to user
K interference, if this interference can not be eliminated or reduced, can greatly reduce the Signal to Interference plus Noise Ratio of receiving terminal, so cause be
The decline for performance of uniting.First, using the corresponding wave beam formed matrix of SLNR beam form-endowing method primary Calculations.When the configuration of UE ends
During with filtering receiver, user k SLNR is represented by：
In formula, wkIt is user k wave beam formed matrix, NrIt is the reception antenna number of user terminal, NtIt is the transmitting of base station end
Number of antennas,Wherein K is the number of users that base station is serviced, HiIt is user i letter
Road matrix,WhereinFor NtThe unit matrix of dimension, pkThe performance number that user k distribution is obtained is represented, whereinTable
Show the Frobenius norms of matrix A, trace (A) is the mark of matrix A, σ2For user k noise power.SLNR wave beam formings are calculated
Method is to maximize above formula as target, i.e., wave beam formed matrix can be obtained by following formula：
By above formula it can be found that when using SLNR algorithms, the selection of user k optimal beam figuration matrix is only with it
The wave beam formed matrix of itself is relevant, and has no direct relation with the wave beam formed matrix of other users.Existing literature channel syndrome
Bright, wave beam formed matrix is solved to：
According to wave beam formed matrix and power distribution result, the SINR of each user is calculated, specific formula for calculation is as follows：
System and capacity calculation formula is as follows, and wherein B is system bandwidth：
Each user minimum SINR demands are equal in the emulation of Fig. 2,3,4, its arranges value such as institute of table 1 under unjust SNR
Show：
Table 1 is minimum SINR demands under different SNR
| SNR(dB) | 0 | 5 | 10 | 15 | 20 | 25 |
| SINRmin(dB) | -0.97 | 1.80 | 4.77 | 7.00 | 12.05 | 15.56 |
According to the parameter request of LTE system, simulation parameter sets as follows：ENB transmitting antenna sum is set to 4, user
The total number of users K=4 of work in end configuration single antenna, system；System bandwidth is 1.4MHz；System uses extended cyclic prefix,
That is CP=32；Channel is the accidental channel that flat multiple Gauss is distributed.
Fig. 2 gives the system and capacity comparison of power distribution method of the present invention and existing power distribution algorithm
Figure, it can be seen that water-filling algorithm and volumetric properties it is optimal, it is to be reached using sacrificing fairness and user's request between user as cost
To higher and capacity, the optimal iterative power allocation algorithm in the present invention comes second, when SNR is more than 10dB, the two
It is close with capacity, in addition, compared to suboptimization algorithm proposed by the present invention and channel self-adapting power distribution algorithm, difference
There is 10% and 15% performance boost.
Fig. 3, which gives power distribution method of the present invention and the removal demand of existing power distribution algorithm, not to be expired
Foot user and capacity comparison figure, it can be seen that when SNR be more than 7dB when, the present invention in optimal iterative power allocation algorithm
Best performance.Comparison diagram 2, water-filling algorithm and channel self-adapting power distribution algorithm are big due to have ignored user's request, performance
Width is reduced, for example, work as SNR=15dB, and water-filling algorithm with capacity is reduced to 21Mbps by 26Mbps.There is provided two of the present invention
It is close in the performance and Fig. 2 of algorithm, because the present invention considers user's request and then improves fairness between user.
Fig. 4 gives the average interrupt probability pair of power distribution method of the present invention and existing power distribution algorithm
Than figure, when the SINR received is less than minimum SINR requirements, interrupts and occur.As can be seen that two calculations that the present invention is provided
The outage probability of method is below 0.1, and channel self-adapting power distribution algorithm and water-filling algorithm are respectively higher than 0.4 and 0.3.
Fig. 5 gives to be possessed under different minimum SINR demands in user, power distribution method of the present invention and existing
The comparison diagram for the SINR that the user of some power distribution algorithms receives, it can be seen that two algorithms that the present invention is provided can
The minimum SINR limitations of each user are met, and SINR is much smaller than for UE4, the SINR of water-filling algorithmmin, channel self-adapting work(
Rate allocation algorithm can not meet UE1 and UE3 demand.
The power point of the consideration user's request based on SLNR wave beam formings of the present invention it can be seen from embodiments above
Method of completing the square can reach preferable laser propagation effect.Wherein, optimal iterative power allocation algorithm can effectively lifting system and capacity,
Ensure the demand and matched beam figuration matrix and power distribution matrix of customer service, suboptimization algorithm is relative to optimum allocation
Algorithm, substantially reduces complexity, and capacity only has 10% decline, can preferably meet user's request.
The present invention can also have other various embodiments, in the case of without departing substantially from spirit of the invention and its essence, this area
Technical staff works as can make various corresponding changes and deformation according to the present invention, but these corresponding changes and deformation should all belong to
The protection domain of appended claims of the invention.
Claims (3)
1. a kind of power distribution method of the consideration user's request based on SLNR wave beam formings, it is characterised in that methods described
Implementation process is：
Step one：Under conditions of constant power distribution, obtained accordingly using the SLNR beam form-endowing methods for combining user power
Wave beam formed matrix；
The SLNR beam form-endowing methods for combining user power are used to obtain the mistake of corresponding wave beam formed matrix in the step one
Cheng Wei：
When the transmission power of user terminal configurations match filtering receiver and user has been normalized, user k SLNR is represented
For：
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</msup>
<msub>
<mi>I</mi>
<msub>
<mi>N</mi>
<mi>t</mi>
</msub>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>w</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, wkIt is user k wave beam formed matrix, NrIt is the reception antenna number of user terminal, NtIt is the transmitting antenna of base station end
Number,Wherein K is the number of users that base station is serviced, HiIt is user i channel square
Battle array,WhereinFor NtThe unit matrix of dimension, pkThe performance number that user k distribution is obtained is represented, whereinRepresent
The Frobenius norms of matrix A, trace (A) is the mark of matrix A, σ2For user k noise power；
When SLNR is maximized, the user k of optimization wave beam formed matrix is：
<mrow>
<msubsup>
<mi>w</mi>
<mi>k</mi>
<mrow>
<mi>o</mi>
<mi>p</mi>
<mi>t</mi>
</mrow>
</msubsup>
<mo>=</mo>
<munder>
<mrow>
<mi>arg</mi>
<mi>max</mi>
</mrow>
<msub>
<mi>w</mi>
<mi>k</mi>
</msub>
</munder>
<mrow>
<mo>(</mo>
<msub>
<mi>SLNR</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Step 2：Under the wave beam formed matrix that step one is obtained, feasible power initial value is obtained by initial point selection algorithm；
The process of initial point selection algorithm is in step 2：
Step 2 one：By constant power apportioning cost initial value P the mostm, m=0, i-th of constraints of optimization problem is set to ci(P)；
Step 2 two：Calculate non-effective collection J, setting J={ j:cj(Pk)>0 }, if Empty set is represented, algorithm terminates,
Obtain rational power initial vector；Otherwise, step 2 three is continued executing with；
Step 2 three：J ∈ J are taken, with PmFor initial value, following problem is solved using interior point method：
min cj(P)j∈J
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>s</mi>
<mo>.</mo>
<mi>t</mi>
<mo>.</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>c</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mo>&le;</mo>
<mn>0</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>i</mi>
<mo>&NotElement;</mo>
<mi>J</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Step 2 four：If the optimal solution P of this subproblemm+1Meet cj(Pm+1)≤0, then m=m+1, performs step 2 two；
Step 3：Under the power initial value that step 2 is obtained, the approximate convex optimization problem for the power optimization targets set up is solved, is obtained
Obtain the power assignment value of user；
The power optimization targets in step 3 are modeled as：
<mrow>
<mi>max</mi>
<mi>C</mi>
<mrow>
<mo>(</mo>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mi>l</mi>
<mi>o</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>SINR</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
s.t.SINRi≥SINRimin
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>&le;</mo>
<msub>
<mi>P</mi>
<mi>T</mi>
</msub>
</mrow>
1
In formula,C (P) is when power distribution matrix is P
And capacity, optimization aim is system and capacity is reached maximization, and top n constraints represents the SINR that user i is received
Value is greater than user i minimum SINR limit values SINRimin, the limitation of last constraints distributes to the power and not of each user
The maximum transmission power level of base station, wherein P must be exceededTFor the general power of Base Transmitter antenna；One shared N+1 limitation bar
Part；
For object function, maximizeIt is equal to maximizationDue to SINRi
More than zero, therefore maximizeEquivalent to minimumObject function is converted into：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msub>
<mi>SINR</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>&NotEqual;</mo>
<mi>i</mi>
</mrow>
</munder>
<msubsup>
<mi>w</mi>
<mi>j</mi>
<mi>H</mi>
</msubsup>
<msubsup>
<mi>H</mi>
<mi>i</mi>
<mi>H</mi>
</msubsup>
<msub>
<mi>H</mi>
<mi>i</mi>
</msub>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<msub>
<mi>p</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>&Element;</mo>
<mi>U</mi>
</mrow>
</munder>
<msubsup>
<mi>w</mi>
<mi>j</mi>
<mi>H</mi>
</msubsup>
<msubsup>
<mi>H</mi>
<mi>i</mi>
<mi>H</mi>
</msubsup>
<msub>
<mi>H</mi>
<mi>i</mi>
</msub>
<msub>
<mi>w</mi>
<mi>j</mi>
</msub>
<msub>
<mi>p</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Pi;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>&NotEqual;</mo>
<mi>i</mi>
</mrow>
</munder>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>p</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>&Element;</mo>
<mi>U</mi>
</mrow>
</munder>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>p</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula,U=1,2 ..., N }；It is approximately by F (P)：
<mrow>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>P</mi>
<mo>)</mo>
</mrow>
<mo>&ap;</mo>
<msup>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</msup>
<msubsup>
<mi>p</mi>
<mn>1</mn>
<msubsup>
<mi>&beta;</mi>
<mn>1</mn>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</msubsup>
</msubsup>
<mn>...</mn>
<msubsup>
<mi>p</mi>
<mi>N</mi>
<msubsup>
<mi>&beta;</mi>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</msubsup>
</msubsup>
</mrow>
In formula,L represents iterations, approximate function
Original object function can be approached in certain iterations, the new object function that can be solved is obtained；
The conversion of form is carried out for constraints, logarithm is removed to object function and constraints, the work(described in step 2 is obtained
The approximate convex optimization problem of rate optimization problem：
<mrow>
<mi>m</mi>
<mi>i</mi>
<mi>n</mi>
<mi> </mi>
<mi>l</mi>
<mi>o</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</msup>
<msubsup>
<mi>p</mi>
<mn>1</mn>
<msubsup>
<mi>&beta;</mi>
<mn>1</mn>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</msubsup>
</msubsup>
<mn>...</mn>
<msubsup>
<mi>p</mi>
<mi>N</mi>
<msubsup>
<mi>&beta;</mi>
<mi>N</mi>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</msubsup>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>s</mi>
<mo>.</mo>
<mi>t</mi>
<mo>.</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>log</mi>
<mfrac>
<mrow>
<msub>
<mi>SINR</mi>
<mrow>
<mi>i</mi>
<mi>min</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>SINR</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mi>log</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<msub>
<mi>SINR</mi>
<mrow>
<mi>i</mi>
<mi>min</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>i</mi>
</mrow>
</msub>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>(</mo>
<mrow>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>&NotEqual;</mo>
<mi>i</mi>
</mrow>
</munder>
<msub>
<mi>G</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>p</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<msup>
<mi>&sigma;</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>&le;</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mi>l</mi>
<mi>o</mi>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>P</mi>
<mi>T</mi>
</msub>
</mfrac>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>p</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&le;</mo>
<mn>0</mn>
</mrow>
Above formula is the convex formula of geometric programming, and geometric programming can be solved using interior point method, obtain power assignment value；
Step 4：The power distribution result that step 3 is obtained is repeated before step 3, and judgement as the initial value of step 3
Whether the difference of the power assignment value obtained twice afterwards is sufficiently small, and satisfaction then performs step 5, now, obtains temporary transient optimal power
Apportioning cost；
Step 5：Under the optimal power allocation value that step 4 is obtained, corresponding wave beam is obtained using SLNR beam form-endowing methods
Figuration matrix, performs step 2 to step 4, if the front and rear optimization aim system obtained twice and the difference of capability value are sufficiently small,
Terminate algorithm, obtain final optimal power allocation result.
2. the power distribution method of the consideration user's request according to claim 1 based on SLNR wave beam formings, its feature
It is, the condition for judging whether to perform step 5 described in step 4 is：
<mrow>
<mo>|</mo>
<msubsup>
<mi>p</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>p</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>L</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>|</mo>
<mo>&le;</mo>
<mi>&epsiv;</mi>
<mo>,</mo>
<mo>&ForAll;</mo>
<mi>j</mi>
<mo>;</mo>
</mrow>
2
In formula,Represent the power for the user i that the L times approximate iteration is obtained.
3. the power distribution method of the consideration user's request according to claim 2 based on SLNR wave beam formings, its feature
It is, condition that the evaluation algorithm described in step 5 terminates is：
|C(Pn)-C(Pn-1)|≤ε2；
In formula, PnRepresent that n-th repeats the step two in claim 2 to four obtained power distribution results, C (Pn) table
Show that in power distribution matrix be PnWhen and capacity.
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