CN108234011A - Extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function - Google Patents
Extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function Download PDFInfo
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- CN108234011A CN108234011A CN201711403619.7A CN201711403619A CN108234011A CN 108234011 A CN108234011 A CN 108234011A CN 201711403619 A CN201711403619 A CN 201711403619A CN 108234011 A CN108234011 A CN 108234011A
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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
- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
- H04B7/0802—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using antenna selection
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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
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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
- H04B7/0602—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 antenna switching
Abstract
The invention discloses a kind of extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function, solve the technical issues of complexity height and not high enough traditional antenna selection method channel capacity that antenna is excessively brought, implementation step is：Define antenna selection parameter；Establish the antenna preference pattern of sub- modular function；Determine the standard of greed selection；With greedy selection algorithm approximate solution model；Complete day line options.Day line options intuitively from the thought of Resource selection, are converted into sub- modular function discrete-variable problem, and to mathematics model solution, complete day line options by the present invention.The present invention devises the greed selection approximate data for solving sub- modular function discrete-variable problem, and approximation ratio is (1 1/e), simplifies calculating, reduces complexity.Implementation complexity of the present invention is low, under equal conditions, and system channel volumetric properties are improved while have performance guarantee in any practical application, available in the extensive multi-input multi-output system of the 5th third-generation mobile communication, cellular cell mobile communication system.
Description
Technical field
The invention belongs to the 5th third-generation mobile communication technical fields, relate generally to a day line options, specifically a kind of extensive more
Antenna selecting method of the input and output scene based on sub- modular function, available in the mobile communication system of cellular cell.
Background technology
With flourishing for information-intensive society, smart mobile phone is popularized in people's daily life, as people
Into daily communication, one of main tool of amusement and shopping online.The universal Internet service that have stimulated of smart mobile phone is with moving
The continuous fusion of communication, in recent years a large amount of mobile Internet business emerge in large numbers in succession.The appearance of these business meets mobile use
The growing application demand in family, while lot of challenges also is brought for future mobile communications, future mobile communications not only will
Realistic existing high data rate, also needs the theory for meeting green communications, can accomplish simultaneously in guarantee high data rate
Efficiently, energy saving, low-power consumption.
Multiple-input and multiple-output (Multiple Input Multiple Output, MIMO) technology can by multiple antennas transmitting-receiving
Space resources is made full use of to improve traffic rate and improves communication quality, is that wireless communication field realizes high speed data transfers
One of key technology.Extensive MIMO (Massive MIMO) is a kind of emerging skill to grow up on the basis of traditional MIMO
Art.Compared with traditional MIMO technology, the aerial array of extensive MIMO technology arrangement is larger, and consideration is hundreds of antennas
The communication scenes of service are provided on same running time-frequency resource for dozens of terminal.Due to introducing large-scale antenna array, system
With many beneficial characteristics.
In extensive multi-input multi-output system, a large amount of antenna is configured in transmitting (or reception) end, it is possible to provide diversity increases
Benefit reduces the bit error rate and improves service quality or provide spatial multiplexing gain raising efficiency of service, brings carrying on communication system performance
It rises, and in practical applications, a large amount of antennas are configured can then be asked by such reality such as hardware cost, signal processing complexities
The limitation of topic.Wherein radio frequency link is directly proportional to number of antennas, and compared to relatively inexpensive antenna, every radio frequency link all includes
The communication devices such as low-noise amplifier, upper (lower) frequency converter and digital-to-analogue (modulus) converter, and these corollary systems and device, valency
Lattice are high；At the same time, the complexity of system processing is also proportional to number of antennas.Factors above results in extensive multi input
Output system cannot use the antenna of arbitrary multi-quantity.It is thus determined that suitable for extensive mimo system antenna selecting plan just
It is particularly important.
In mobile communications, number of antennas can be effectively reduced by day line options, and reduces and send and receive machine
Algorithm complexity, while ensure comparable performance gain.Antenna Selection Algorithem common at present is mostly according to application scenarios, is established
Mathematical model, and solved using convex optimization tool.Due to being select permeability, so common model constraint is mostly (0,1) of permanent mould
Constraint, relaxation, which solves, certain difficulty.The solution acquired using constraint relaxation method need to re-map back (0,1) solution of discrete domain,
And (0,1) solution of this and practical problem can not always ensure to map one by one, cause solving precision limited.At the same time, it uses
The mathematical method of convex optimization constraint relaxation solves the problem, fails to intuitively to excavate the Resource selection that day line options are included and ask
Topic essence so that the method modeled in engineer application it is relative complex, operation and operate it is not concise enough.
In practical communication system applications, traditional antenna selecting method includes advantest method, incremented/decremented method, is based on
The antenna back-and-forth method and random choice method of norm.Its line options advantest method complexity is excessively high, how defeated is not suitable for extensive multi input
Go out communication scenes.Incremented/decremented method complexity is less than advantest method, and simultaneity factor channel capacity performance can approach advantest method, but
Complexity is still higher.Based on the selection method of norm because of its relatively low complexity and the close choosing of successively decreasing of system channel volumetric properties
The characteristics of selecting algorithm is considered more being suitable for extensive multi-input/output antenna selection, but its system channel volumetric properties
It is considered the space for still having promotion；Random choice method complexity is minimum, but system channel volumetric properties can not be protected.
Invention content
The shortcoming that it is an object of the invention to be directed in background technology proposes that a kind of complexity is relatively low and has system
Antenna selecting method of the extensive Multiinputoutput scene of performance guarantee based on sub- mould property.
The present invention is the antenna selecting method based on sub- modular function under a kind of extensive multiple-input and multiple-output scene, feature
It is, including having the following steps：
(1) relevant parameter in day line options is defined：
(1a) definition selection index S：Assuming that base station end main aerial number is M, selection index S is defined as what is be selected
The index of target antenna, number are L, i.e., | S |=L, wherein L are the total number of selected selecting antennas；
(1b) definition selection vector s：The selection vector s of a M dimension { 0,1 } is can obtain by indexing S, at index S location
Vector element value is 1, remaining is 0, and meets condition 1TS=L, 1 represents complete 1 vector of M dimensions；
(1c) defines selection matrix S：Define L × M dimension selection matrixsAccording to index S generations, by indexing S from original
L rows are selected in the M rows of beginning channel matrix G, form new selection channel matrix GS；
(2) the antenna preference pattern under sub- modular function frame is established：Establish about Resource selection problem sub- modular function most
The day line options mathematical model of optimization；
(3) standard of greedy selection algorithm is determined：Specifically so that channel capacity increment maximizes, i.e., by selecting,
In channel matrix G, the row maximum to the contribution of channel capacity increment is found out；By the antenna of the corresponding antenna of maximum row alternatively；
(4) the day line options mathematical model built with greed selection algorithm approximate solution：Design greed selection approximate data,
The sub- modular function antenna preference pattern built with the algorithm approximate solution, obtains selected antenna；
(5) day line options are completed：The performance that selected antenna reaches causes system performance to be ensured.
Capacity increment the present invention is based on sub- modular function property maximizes antenna selecting method, goes out from the angle of set function
Hair completes antenna selection procedure, and can guarantee final extensive multi-input and output communication system performance.
Compared with the prior art, the present invention has the following advantages：
First, since the present invention is from the angle of set function, sub- modular function is mutually tied with antenna selection problem for the first time
Close, antenna selection problem is converted into Resource selection problem, provide compared with the prior art more intuitive analytical mathematics and
Method for solving can be applied in practice；Since the present invention establishes the antenna preference pattern of sub- modular function, and use
Greedy algorithm, solution procedure step is seldom, calculates simple, intuitive, has relatively low complexity.
Second, present system performance and optimal solution can reach the approximation ratio of (1-1/e) so that this method can obtain compared with
Excellent result of calculation.And regardless of the condition of system input data, performance that the channel matrix of selected antenna composition reaches
Approximation ratio with optimal solution is (1-1/e), ensures the stability of this method in practical applications.Emulation proves, by the present invention
It calculates the channel capacity result obtained later and is substantially better than the result based on norm Antenna Selection Algorithem.
Description of the drawings
Fig. 1 is the realization flow chart of the present invention；
Fig. 2 is the present invention and the channel capacity simulation result comparison diagram based on norm day line options.
Specific embodiment
The present invention is described in detail below in conjunction with the accompanying drawings.
Embodiment 1
In extensive multi-input multi-output system, a large amount of antenna is configured in transmitting (or reception) end, it is possible to provide diversity increases
Benefit reduces the bit error rate and improves service quality or provide spatial multiplexing gain raising efficiency of service, brings carrying on communication system performance
It rises.And in practical applications, a large amount of antennas are configured can then be asked by such reality such as hardware cost, signal processing complexities
The limitation of topic.Wherein radio frequency link is directly proportional to number of antennas, although antenna is more cheap in itself, in antenna system
Every radio frequency link all includes the communication devices such as low-noise amplifier, upper (lower) frequency converter and digital-to-analogue (modulus) converter, price
It is high；At the same time, the complexity of system processing is also proportional to number of antennas.Keeping extensive multiple-input and multiple-output
Under the premise of MASSIVE MIMO technology performance advantages, it is that the emphasis that communication system is paid close attention to is asked to reduce the complexity of system and cost
One of topic.Antenna Selection Technology can effectively reduce number of antennas, and reduce the algorithm complexity for the machine that sends and receives, and protect simultaneously
Demonstrate,prove comparable performance gain.In practical communication system applications, based on the selection method of norm because of its relatively low complexity and
The characteristics of system channel volumetric properties are close to decremental selection is considered more being suitable for extensive multi-input/output antenna
Selection.Due to not considering the overall permanence of channel matrix, it is only independent the considerations of channel matrix row two norms it is big
It is small, cause system channel volumetric properties limited.The present invention researchs and proposes a kind of extensive multiple-input and multiple-output scene to this expansion
Under the antenna selecting method based on sub- modular function, for the communication system of extensive multi-input/output antenna, in cellular cell
Multiple single-antenna subscribers are served in interior base station, day line options are carried out in base station end, referring to Fig. 1, including having the following steps：
(1) relevant parameter in day line options is defined：From whole antennas of extensive multi-input multi-output system, selectivity
It can preferably a part of antenna used as system.
(1a) definition selection index S：Each antenna of extensive multi-input multi-output system is numbered, in total M
Root obtains all indexes of antenna.Selection index S is defined as the index for the target antenna being selected, and number is L,
I.e. | S |=L, wherein L are the total number of selected selecting antennas.In the present invention, it needs to select target antenna, quilt from all antennas
The antenna index selected is defined as selection index.
Index S is selected to be widely used in discrete (0,1) selection function problem general, but in traditional antenna selection problem
In, and selection index S is not used.Discrete model of the present invention in day line options practical application introduces selection index S's
Concept so that antenna can be indexed according to the selection and is selected.
L represents the total number of selected selecting antennas, i.e., needs to complete L selection in total, each selection wherein accords with one of standard.
And L needs rationally to determine, if the setting of L values is excessive, system complexity is still excessively high, does not reach the realization of day line options
Purpose；If the setting of L values is too small, the channel capacity performance of system can not be guaranteed, and it is more to lose extensive multi input
The technical advantage of output.
(1b) definition selection vector s：It can obtain the selection vector s of a M dimension { 0,1 } by selection index S, indexed in selection
Vector element value is 1 at S location, remaining is 0, and meets condition 1TS=L, 1 represents complete 1 vector of M dimensions.
Since selection index S and selection vector s are actually one-to-one, i.e., the present invention selects vector s by update
Update selection index S, and then the work antenna being selected just are achieved the purpose that.
Assuming that original a total of 8 of selecting antennas to be selected, 1st, the 3rd, the 5th, the 8th therein totally 4 is selected after calculating
Root antenna alternatively antenna, then it is { 1,3,5,8 } to select index S, at this time the corresponding selection vector s expressions of selection index S
For s=[1；0；1；0；1；0；0；1], L=4.
(1c) defines selection matrix S：Define L × M dimension selection matrixsAccording to selection index S generations, by selecting
Index S selects L rows from the M rows of raw channel matrix G, forms new selection channel matrix GS, i.e. GS=SG, wherein selecting
Matrix S elements are represented by：
Selection matrix S structures meet STS=diag (s), SST=IL, diag () expressions are by vector generation diagonal matrix, IL
Unit matrix is tieed up for L, i, j represent the line number and columns of selection matrix S, i=1 ..., L, j=1 ..., M respectively.
For example, being { 1,3,5,8 } when selecting index S, the corresponding selection vector s of selection index S are expressed as s=[1；0；1；
0；1；0；0；When 1], after corresponding selection matrix S Selecting operations, the new of composition selects channel matrix as GS, GSIt is by original
The the 1st, the 3rd, the 5th of beginning channel matrix and eighth row form.
(2) the antenna preference pattern under sub- modular function frame is established：According to the sub- mould property of sub- modular function, establish about collection
Close the day line options mathematical model that the sub- modular function of select permeability optimizes.
This step is one of core procedure of the present invention, and the present invention is originally by sub- modular function model and antenna selection problem phase
With reference to intuitively from the angle of Resource selection problem, the set that whole antennas form is considered as complete or collected works, will treat the mesh of selection
The set of mark antenna composition is considered as subset.The scheme designed by the present invention is directly selected from antenna complete or collected works and meets selection mark
Accurate antenna subset.The advantage is that the specific implementation of system can be caused to become simple and clear, answering for totality of the invention is also reduced
Miscellaneous degree.
Since the present invention is from the angle of set function, sub- modular function and antenna selection problem are combined for the first time, incited somebody to action
Antenna selection problem is converted into Resource selection problem, provides more concise intuitive method for solving compared with the prior art, makes
It of the invention must have the characteristics that engineering application, extensive use can be able in practice.
(3) standard of greedy selection algorithm is determined：Specifically so that channel capacity increment maximizes, i.e., by selecting,
In channel matrix G, the row maximum to the contribution of channel capacity increment is found out；By the antenna of the corresponding antenna of maximum row alternatively.
The row is added to selection channel matrix GSIn, also this root antenna is added in the subset of selection antenna.
One of core procedure that this step is also embodied for the present invention, this selection criteria can effectively ensure that system is believed
Road capacity is promoted.
Traditional greedy algorithm standard only only accounts for channel capacity maximization, does not ensure that channel capacity always increases
Add.And the channel capacity increment maximization standard that the present invention is selected, not only so that the channel capacity of antenna system is continuously increased, but also energy
So that the aerial band for adding in antenna system every time carrys out maximum channel capacity increment.
Due to the present invention program ergodic channels matrix line by line so that when traversing each time, add in the current antenna of system all
Maximum channel capacity increment can be brought, so being to ensure that overall channel capacity is maximum.
(4) the day line options mathematical model built with greed selection algorithm approximate solution：Design greed selection approximate data,
The sub- modular function antenna preference pattern built with the algorithm approximate solution, obtains selected antenna.
According to present invention determine that channel capacity increment maximize greedy selection method standard, to whole antennas of system by
One is selected, and selects the L root antennas for meeting greedy selection criteria.
(5) day line options are completed：The performance that selected antenna reaches causes system performance to be ensured.
Why the present invention considers day line options being combined with sub- modular function, and one of the main reasons is exactly sub- modular function institute
The sub- mould property having, i.e., after the operation of greedy selection algorithm, the channel capacity performance of system has theoretical guarantee so that this
Invention can be applied effectively in practice, ensure that the high efficiency of system transmission information.
Overall process clear thinking of the present invention, embodiment is simple and practicable, while has theoretical guarantee in performance so that real
There is stability in the application of border.
Embodiment 2
Extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function is the same as embodiment 1, step (2) of the present invention
In the sub- modular function frame of foundation under antenna preference pattern, specifically include：
(2a) states whole channel capacity C of raw channel matrix G with channel capacity formulafull：
Wherein,Expression dimension is NRUnit matrix, NR=128, NT=12 represent reception antenna in up-link respectively
(base station) number and transmission antenna (single-antenna subscriber) number, ρ are signal-to-noise ratio, and det () represents determinant, ()HRepresent square
The conjugate transposition of battle array.
The present invention is applied to reduce the processing complexity of extensive multiple input/output system, if using whole antennas as system
System needs antenna to be used, and high complexity is had under extensive Multiinputoutput scene.In addition to this, if considering channel
The channel that the antenna of the poor part of matrix overall permanence, wherein channel condition is formed, the contribution to system channel volumetric properties
It is extremely limited, from the angle of practical application, which should be abandoned using.
(2b) establishes local channel capacity expression：
In whole channel capacity C of raw channel matrix GfullOn the basis of expression formula, it is assumed that selection matrix S passes through
It is G to select the channel matrix that some antennas forms after completingS, GS=SG, at this point, GSCorresponding local channel capacityIt can be further represented as：
Wherein, (GS)HGS=GHdiag(s)G。
(2c) obtains the day line options mathematical model that sub- modular function optimizes：
Pass through local channel capacityExpression formula increases constraints
1TS≤L, the day line options mathematical model that the sub- modular function established optimizes
s.t.1Ts≤L
In fact, day line options can be considered the sub- modular function in set function, the sub- mould property embodied is：With
The increase of the number of antennas of the system of addition, the capacity increment of system shows the characteristic for first increasing and subtracting afterwards, this property is referred to as
The marginal income decreasing effect of sub- modular function.The present invention is exactly to establish the day line options based on sub- modular function according to this characteristic
Mathematical model.
Originality of the present invention must be by sub- modular function theory applied to this practical problem scene of day line options, and the present invention establishes
The day line options mathematical model that optimizes of sub- modular function, be not related to the convex optimum theory technology of mathematics, the present invention is by conventional method
In continuous optimization problem be converted into a discrete select permeability, can intuitively from discrete Resource selection problem
So that implementing for signal process part in practical application is simple and practicable.Meanwhile the present invention passes through what is be calculated
Solution is exactly discrete (0,1) solution, is not needed to again from continuous domain mapping meeting discrete domain, it will be able to ensure solving precision.
Embodiment 3
Extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function is with embodiment 1-2, in step (3)
The standard for determining greed selection method is to turn to standard with channel capacity increment maximum to carry out day line options, is specifically included：
Traverse raw channel matrixIn every a line ct, and greedy selection is carried out, it finds to channel capacity increment
Contribute maximum row ctar, tar representing matrixesIn tar rows, that is, meet maximum channel capacity increment formula, be specifically shown in
Following formula：
It represents channel capacity increment, defines hereIt is element i in set A
On set function C () functional value increment, wherein A+i represents the union A ∪ { i } of set A and element i, while defines A-i tables
Show set A and element i difference set A { i }.
The present invention turns to standard with channel capacity increment maximum and carries out day line options, total in greedy selection course each time
It is to select so that the maximized antenna of capacity increment, can cause the antenna after selection every time, has to system performance positive
Gain, and gain is maximum.
Traditional greedy selection algorithm foundation is that channel capacity maximizes, but greedy selection can not be completely secured every time
The new channel capacity increase obtained afterwards.And in the present invention, since the standard of selection is so that system channel capacity increment most
Bigization, therefore each currently selected antenna selected has the characteristics that so that system channel capacity gain promotes maximum, all quilts
It is also incremental to select the cumulative channel capacity of antenna.
Embodiment 4
For extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function with embodiment 1-3, step (4) is described
The model built with greedy selection algorithm approximate solution, be to turn to standard with channel capacity increment maximum to carry out day line options,
It has specifically included：
(4a) greedy algorithm parameter initialization inputs：The original antenna sum in system base-station end is M, treats the antenna sum of selection
For L, the number of the antenna of selection is treated in L expressions, and t tables are cycle index, and t=1 represents loop initialization, empty matrixExpression is treated
Newer selection channel matrix, that is, by the channel matrix of day line options, original then channel matrix to be selected after algorithmM ties up full null vector s, and s represents selection vector to be updated, that is, the index of selection antenna is included after algorithm,
Select the element at antenna index position that will be set as 1 in vectorial s, remaining is 0.
(4b) carries out cycle selection with greedy algorithm to whole antennas, to select antenna total number L as loop termination item
Part carries out L cycle and carries out solution selection to all antennas in total.
Standard is maximized according to capacity increment and carries out greedy selection, selects antenna, by the determining maximum capacity of step (3) institute
Standard that is, using antenna all in maximum channel capacity increment formula Ergodic Theory, selects the maximized day of capacity increment
Line alternatively antenna.
(4c) judges channel capacity increment：If channel capacity incrementTarget letter at this time
Number has been unsatisfactory for the sub- mould property of sub- modular function, need to terminate algorithm, willIt is assigned to It is assigned toStop operation, and export selection vector sS, the channel matrix result of calculation G after selectionS。
When channel capacity incrementI.e. maximal increment can not all give system channel volumetric properties band
Carry out gain, system channel capacity can not be caused to continue to increase at this time, illustrate that existing more excellent some antennas has all been chosen more
It is new to add in system, without continuing carry out antenna in remaining antenna relay again, loop computation need to be exited and terminate selection algorithm.
(4d) update selection channel matrixOriginal channel matrix to be selectedWith selection vectorIt willAnd step
Suddenly the c obtained in (4b)tarSet is done mutually to be assigned to the result of operation(i.e.), and by original channel
C in matrixtarRow is rejected (i.e.MatrixThe all elements of tar rows be set to 0),(i.e.
VectorThe tar element be equal to 1).
In the cycle of L times, to the selection vector in selection courseIt is updated, and the antenna having been selected out is added
It is added to selection matrixIn, while treat selection matrix originalIt is middle to remove the row being selected, that is, be selected
Antenna.
(4e) reaches loop termination condition if t ＞=L, has selected the antenna that quantity is L at this time, has enabled Stop operation and export：Select vector sS, the channel matrix result of calculation G after selectionS.According to the selection being calculated
Vectorial sS, with regard to the antenna that can be selected.
(4f) updates t=t+1 if t ＜ L, returns and performs step (4b), reenters selection cyclic process, until complete
Final selection antenna is obtained into whole cyclic processes.
By above-mentioned steps, the greed selection for maximizing standard with capacity increment and carrying out is completed, has been selected to system
The work antenna that channel capacity contribution is larger, performance preferably some antennas is as system.
The present invention uses greedy algorithm originally by sub- modular function theory applied to this practical problem scene of day line options
Search for the approximate solution of model optimal solution of the present invention, overall process clear thinking has sub- mould property theory conduct in system performance
Support so that there is stability in practical application.
Embodiment 5
The antenna selecting method based on sub- modular function is the same as embodiment 1-4, step (5) under extensive multiple-input and multiple-output scene
Described in the performance that reaches of selected antenna system performance is ensured, specifically：No matter the condition of system input data
How, the performance and the approximation ratio of optimal solution that selected antenna reaches are (1-1/e), i.e.,：
Wherein Cselect(sopt) for the attainable system channel volumetric properties of model optimal solution,The present invention obtains
The attainable system channel volumetric properties of approximate solution institute, e are the bottom of natural logrithm.Even if under the conditions of worst input data, (1-
Approximation ratio 1/e) can reach, and this guarantees the system channel volumetric properties of the present invention in practical applications.
Present system performance can reach the approximation ratio of (1-1/e) with optimal solution so that this method can obtain preferably
Result of calculation.And regardless of the condition of system input data, performance that the channel matrix of selected antenna composition reaches with most
The approximation ratio of excellent solution is (1-1/e), ensures the stability of this method in practical applications.Emulation proves, is calculated by the present invention
The channel capacity result obtained later is substantially better than the result based on norm Antenna Selection Algorithem.
A more detailed example is given below, the present invention is further illustrated.
Embodiment 6
Extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function is with embodiment 1-5, with reference to Fig. 1, sheet
The realization step of invention is as follows：
(1) relevant parameter in day line options is defined：
(1a) definition selection index S：Selection index S is defined as the index for the target antenna being selected, wherein including
The index for the target antenna to be selected, number are L, i.e., | S |=L, wherein L are the total number of selected selecting antennas.
In this example, base station end whole antenna may be set to 128, then L can be set as 50, choose close to half number
Performance preferably antenna, it is alternatively that antenna, the work for participating in system use, and can allow extensive multiple-input and multiple-output in this way
Operating mode becomes to simplify, while can approach the attainable performance of whole antenna institutes.
(1b) definition selection vector s：The selection vector s of a M dimension { 0,1 } is can obtain by indexing S, at index S location
Vector element value is 1, remaining is 0, and meets condition 1TS=L, 1 represents complete 1 vector of M dimensions.
If assuming original a total of 12 of selecting antennas to be selected, 1st, the 3rd, the 5th, the 8th therein is selected after calculating
Totally 8 antennas alternatively antenna, then it is { 1,3,5,8,9,10,11,12 } to select index S, and selection index S is corresponding at this time
Selection vector s is expressed as s=[1；0；1；0；1；0；0；1；1；1；1；1].L=8.
(1c) defines selection matrix S：Define L × M dimension selection matrixsAccording to selection index S generations, by indexing S
L rows are selected from the M rows of raw channel matrix G, form new selection channel matrix GS, i.e. GS=SG, wherein selection matrix S
Element is represented by：
Selection matrix S structures meet STS=diag (s), SST=IL, diag () expressions are by vector generation diagonal matrix, IL
Unit matrix is tieed up for L, i, j represent the line number and columns of selection matrix S, i=1 ..., L, j=1 ..., M respectively.
For example, being { 1,3,5,8,9,10,11,12 } when selecting index S, the corresponding selection vector s of selection index S are expressed as
S=[1；0；1；0；1；0；0；1；1；1；1；When 1], after corresponding selection matrix S, the new selection channel matrix of composition
GS, it is made of the row of the 1st, the 3rd, the 5th, the 8th, the 9th, the 10th, the 11st and the 12nd of raw channel matrix.
(2) the antenna preference pattern under sub- modular function frame is established：Establish about Resource selection problem sub- modular function most
The day line options mathematical model of optimization：
(2a) states whole channel capacity C of raw channel matrix G with channel capacity formulafull：
Wherein,Expression dimension is NRUnit matrix, NR=128, NT=12 represent day is received in up-link respectively
Line (base station) number and transmission antenna (single-antenna subscriber) number, ρ are signal-to-noise ratio, and det () represents determinant, ()HIt represents
The conjugate transposition of matrix.
The present invention is applied to reduce the processing complexity of extensive multiple input/output system, if using whole antennas as system
System needs antenna to be used, and high complexity is had under extensive Multiinputoutput scene.In addition to this, if considering channel
The channel that the antenna of the poor part of matrix overall permanence, wherein channel condition is formed, the contribution to system channel volumetric properties
It is extremely limited, from the angle of practical application, which should be abandoned using.
(2b) establishes local channel capacity expression：
In whole channel capacity C of raw channel matrix GfullOn the basis of expression formula, it is assumed that selection matrix S passes through
It is G to select the channel matrix that some antennas forms after completingS, GS=SG, at this point, GSCorresponding local channel capacityIt can be further represented as：
Wherein, (GS)HGS=GHdiag(s)G。
(2c) obtains the day line options mathematical model that sub- modular function optimizes：
Pass through local channel capacityExpression formula increases constraints
1TS≤L, the day line options mathematical model that the sub- modular function established optimizes
s.t.1Ts≤L
Its line options can be considered the sub- modular function in set function, and sub- modular function has exclusive sub- mould property：With
The increase of the number of antennas of addition system, the capacity increment of system show the characteristic for first increasing and subtracting afterwards, this property is referred to as Asia
The marginal income decreasing effect of modular function.The present invention is exactly that the day line options number based on sub- modular function is established according to this characteristic
Learn model.
Sub- modular function theory is applied in day line options this practical applications by the present invention for the first time, and block mold establishes process
Clear thinking is not related to the convex optimum theory technology of mathematics, intuitively from discrete Resource selection problem, completes present invention side
Method designs, and enables to implementing for the signal process part in practical application simple and practicable.
(3) standard of greedy selection algorithm is determined：Specifically so that channel capacity increment maximizes, i.e., by selecting,
In channel matrix G, the row maximum to the contribution of channel capacity increment is found out, by the antenna of the corresponding antenna of maximum row alternatively.
Traverse raw channel matrixIn every a line ct, and greedy selection is carried out, it finds to channel capacity increment
Contribute maximum row ctar(tar representing matrixesIn tar rows), that is, meet maximum channel capacity increment formula, specifically
See below formula：
It represents channel capacity increment, defines hereGathering for element i
Set function C () functional value increment on A, wherein A+i represent the union A ∪ { i } of set A and element i, while define A-i
Represent set A and element i difference set A { i }.
The present invention turns to standard with channel capacity increment maximum and carries out day line options, total in greedy selection course each time
It is to select so that the maximized antenna of capacity increment, can cause the antenna after selection every time, has to system performance positive
Gain, and gain is maximum.And traditional greedy standard is maximized for channel capacity, can not ensure that channel capacity has just every time
To gain.Different from traditional grantings, selection criteria of the invention is thus each so that the maximization of system channel capacity increment
The currently selected antenna selected has the characteristics that so that system channel capacity gain promotes maximum, the accumulation letter of all selected selecting antennas
Road capacity is also incremental, in application system, has important practical significance.
(4) the day line options mathematical model built with greed selection algorithm approximate solution：Design greed selection approximate data,
The sub- modular function antenna preference pattern built with the algorithm approximate solution, obtains selected antenna：
(4a) greedy algorithm parameter initialization inputs：The number of the antenna of selection is treated in positive integer L, L expression, and t=1 is represented
Loop initialization, empty matrixRepresent selection channel matrix to be updated, that is, by the channel of day line options after algorithm
Matrix, original then channel matrix to be selectedM ties up full null vector s, and s represents selection vector to be updated, that is, algorithm knot
The index of selection antenna is included after beam, selects the element at antenna index position that will be set as 1 in vectorial s, remaining is 0.
(4b) maximizes standard according to capacity increment and carries out greedy selection, selects antenna, by the determining capacity of step (3) institute most
Bigization standard that is, using antenna all in maximum channel capacity increment formula Ergodic Theory, selects capacity increment maximization
Antenna alternatively antenna.
(4c) judges channel capacity increment：If channel capacity incrementTarget letter at this time
Number cannot increase channel capacity, need to terminate algorithm, willIt is assigned to It is assigned to sS Stop operation, and export selection vector sS, the channel matrix result of calculation G after selectionS。
When channel capacity incrementI.e. maximal increment can not all give system channel volumetric properties band
Carry out gain, system channel capacity can not be caused to continue to increase at this time, illustrate that existing more excellent some antennas has all been chosen more
It is new to add in system, without continuing carry out antenna in remaining antenna relay again, loop computation need to be exited and terminate selection algorithm.
(4d) update selection channel matrixOriginal channel matrix to be selectedWith selection vectorIt willAnd step
Suddenly the c obtained in (4b)tarSet is done mutually to be assigned to the result of operationI.e.And by original channel
C in matrixtarRow is rejected, i.e.,MatrixThe all elements of tar rows be set to 0,I.e. to
AmountThe tar element be equal to 1.
The cycle each to the present invention is updated, and the antenna having been selected out is added to selection matrixIn, simultaneously
Selection matrix is treated originalIt is middle to remove the row being selected, that is, the antenna being selected.
(4e) reaches loop termination condition if t ＞ L, has selected the antenna of L numbers at this time, enables
Stop operation and export：Vectorial sS, the channel matrix result of calculation G after selectionS。
(4f) updates t=t+1, return to step (4b).
By above-mentioned steps, the greed selection for maximizing standard with capacity increment and carrying out is completed, obtains selecting vectorial sS,
According to vectorial sSResult selected, performance preferably some antennas larger to system channel capacity contribution as system
Work antenna.
The present invention uses greedy algorithm originally by sub- modular function theory applied to this practical problem scene of day line options
Search for the approximate solution of model optimal solution of the present invention, overall process clear thinking has sub- mould property theory conduct in system performance
Support so that there is stability in practical application.
(5) day line options are completed：The performance that selected antenna reaches causes system performance to be ensured.
Condition regardless of system input data, the performance and the approximation ratio of optimal solution that selected antenna reaches are (1-1/
E), i.e.,：Wherein Cselect(sopt) for the attainable system channel of model optimal solution
Volumetric properties,For the attainable system channel volumetric properties of approximate solution that the present invention obtains, e is natural logrithm
Bottom.Even if under the conditions of worst input data, the approximation ratio of (1-1/e) can reach, and this guarantees the present invention actually should
System channel volumetric properties in.
The effect of the present invention can be further illustrated by following emulation：
Embodiment 7
The antenna selecting method based on sub- modular function is the same as embodiment 1-6 under extensive multiple-input and multiple-output scene
1. simulated conditions
Using Matlab R2017a simulation softwares, simulation times are 10000 Monte Carlo simulations, the ginseng of system emulation
Number is consistent with the parameter described in example, and the base station that 128 antennas are configured services 12 single-antenna subscribers, and base station receives user's hair
The signal sent, transmission channel noise are additive white Gaussian noise channel, and signal-to-noise ratio 5dB, cellular cell radius is set as 500
Rice, base station are located at center of housing estate, and user is randomly dispersed in cell.
2. emulation content
To the present invention and the antenna selecting method based on norm carries out channel capacity performance simulation.
3. simulation result
The performance curve of analogue system channel capacity, as shown in Figure 2, wherein there is the curve that " open circles " mark to represent this
The channel capacity performance of invention has the curve that " diamond shape " marks to represent the day line options channel capacity performance based on norm, has " real
The curve of heart circle " label represents the marginal income decreasing effect in antenna selection problem.
Horizontal axis represents the number of selected selecting antennas in Fig. 2, and the longitudinal axis represents channel capacity and original overall channel capacity after selection
Between ratio.
When the number of antennas being selected is smaller, channel capacity performance and the day line selection based on norm that the present invention obtains
Channel capacity performance is selected to be substantially the same.And when increasing the number of antennas being selected, channel capacity performance of the invention is significantly excellent
In the day line options channel capacity performance based on norm, the channel capacity of communication system is increased, it can enough less antennas
Bring larger channel capacity.
In practical engineering application, extensive Multiinputoutput scene is concentrated mainly on entirely by the number of antennas selected
In 1/3rd of portion's number of antennas to the range intervals of half, therefore, the part paid close attention to is concentrated mainly on whole
/ 3rd of number of antennas are to this section of half range, in this section, channel capacity system performance of the invention
It is substantially better than the day line options channel capacity performance based on norm.
Claims (5)
1. a kind of extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function, which is characterized in that including just like
Lower step：
(1) relevant parameter in day line options is defined：
(1a) definition selection index S：Assuming that base station end main aerial number is M, selection index S is defined as the target being selected
The index of antenna, number are L, i.e., | S |=L, wherein L are the total number of selected selecting antennas；
(1b) definition selection vector s：It can obtain the selection vector s of a M dimension { 0,1 } by indexing S, the vector at index S location
Element value is 1, remaining is 0, and meets condition 1TS=L, 1 represents complete 1 vector of M dimensions；
(1c) defines selection matrix S：Define L × M dimension selection matrixsAccording to index S generations, by indexing S from original letter
L rows are selected in the M rows of road matrix G, form new selection channel matrix GS；
(2) the antenna preference pattern under sub- modular function frame is established：It establishes and is optimized about the sub- modular function of Resource selection problem
Day line options mathematical model；
(3) standard of greedy selection algorithm is determined：Specifically so that channel capacity increment maximizes, i.e., by selection, in channel
In matrix G, the row maximum to the contribution of channel capacity increment is found out；By the antenna of the corresponding antenna of maximum row alternatively；
(4) the day line options mathematical model built with greed selection algorithm approximate solution：Design greed selection approximate data, with this
The sub- modular function antenna preference pattern that algorithm approximate solution is built, obtains selected antenna；
(5) day line options are completed：The performance that selected antenna reaches causes system performance to be ensured.
2. extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function according to claim 1, special
Sign is that the antenna preference pattern under the sub- modular function frame of the foundation described in step (2) specifically includes：
(2a) states whole channel capacity C of raw channel matrix G with channel capacity formulafull：
Wherein,Expression dimension is NRUnit matrix, NR=128, NT=12 represent reception antenna (base in up-link respectively
Stand) number and transmission antenna (single-antenna subscriber) number, ρ is signal-to-noise ratio, and det () represents determinant, ()HRepresenting matrix
Conjugate transposition；
(2b) establishes local channel capacity expression：
In whole channel capacity C of raw channel matrix GfullOn the basis of expression formula, it is assumed that selection matrix S, by having selected
The channel matrix formed into some antennas later is GS, GS=SG, at this point, GSCorresponding local channel capacityIt can be further represented as：
Wherein, (GS)HGS=GHdiag(s)G；
(2c) obtains the day line options mathematical model that sub- modular function optimizes：
Pass through local channel capacityExpression formula increases constraints 1Ts≤
L obtains the day line options mathematical model that the sub- modular function of this method foundation optimizes
s.t.1Ts≤L
In fact, the model meets sub- mould property, i.e. increasing with addition system antenna number, the increment of system channel capacity
It shows first to increase the property subtracted afterwards.
3. extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function according to claim 1, special
Sign is that the standard of the determining greedy selection method described in step (3) is to turn to standard with channel capacity increment maximum to carry out day
Line options specifically include：
Traverse raw channel matrixIn every a line ct, and greedy selection is carried out, it finds and channel capacity increment is contributed
Maximum row ctar(tar representing matrixesIn tar rows), that is, meet following formula：
Here it definesSet function C () the functional value increment for being element i on set A, wherein
A+i represent set A and element i union A ∪ { i } (while define A-i expression set A and element i difference set A { i }).
4. extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function according to claim 1, special
Sign is that the model built with greedy selection algorithm approximate solution described in step (4), is turned to channel capacity increment maximum
Standard carries out day line options, has specifically included：
(4a) greedy algorithm parameter initialization inputs：The number of the antenna of selection is treated in positive integer L, expression, and t=1 represents cycle just
Beginningization, empty matrixRepresent selection channel matrix to be updated, that is, by the channel matrix of day line options after algorithm,
Original then channel matrix to be selectedM ties up full null vector s, represents selection vector to be updated, that is, wrapped after algorithm
Containing the index for selecting antenna, the element in vectorial s at selection antenna index position will be set as 1, remaining is 0；
(4b) maximizes standard according to capacity increment and carries out greedy selection, is carried out by step (3).
(4c) ifObject function cannot increase channel capacity at this time, need to terminate algorithm, willIt is assigned to It is assigned toStop operation and export：Select vector sS, selection
Channel matrix result of calculation G afterwardsS；
(4d) update selection channel matrixOriginal channel matrix to be selectedWith selection vectorIt willWith in step
The c obtained in (4b)tarSet is done mutually to be assigned to the result of operation(i.e.), and by original channel square
C in battle arraytarRow is rejected, i.e.,MatrixThe all elements of tar rows be set to 0,It is i.e. vectorialThe tar element be equal to 1；
(4e) reaches loop termination condition if t ＞=L, has selected the antenna of L numbers at this time, enablesStop
Only operation and export：Vectorial sS, the channel matrix result of calculation G after selectionS；
(4f) updates t=t+1 if t ＜ L, returns and performs step (4b), reenters selection cyclic process, until completing complete
Portion's cyclic process obtains final selection antenna.
5. extensive antenna selecting method of the Multiinputoutput scene based on sub- modular function according to claim 1, special
Sign is that the performance that the selected antenna described in step (5) reaches causes system performance to be ensured, specifically：No matter system
How is the condition of input data, and the performance and the approximation ratio of optimal solution that selected antenna reaches are (1-1/e), ensure system performance.
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