CN103051587B - One class based on lattice and use optimum programming structure higher-dimension planisphere method - Google Patents
One class based on lattice and use optimum programming structure higher-dimension planisphere method Download PDFInfo
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- CN103051587B CN103051587B CN201310017325.6A CN201310017325A CN103051587B CN 103051587 B CN103051587 B CN 103051587B CN 201310017325 A CN201310017325 A CN 201310017325A CN 103051587 B CN103051587 B CN 103051587B
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- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/50—Reducing energy consumption in communication networks in wire-line communication networks, e.g. low power modes or reduced link rate
Abstract
The invention belongs to communication technical field, specially one class is based on lattice the method for using optimum programming constructed higher-dimension planisphere.Such higher-dimension planisphere be by maximize planisphere gain index designed by out.And the gain index of planisphere can resolve into the product of the coding gain of lattice and the shaping gain on planisphere border, therefore the design process of this kind of higher-dimension planisphere is that the maximization procedure of coding gain and shaping gain is configured to two optimization problems, and using the minimum Eustachian distance of planisphere and its symmetry as the constraints of the two optimization problem, obtain required planisphere by solving-optimizing problem.The method can be as designing the universal method of planisphere of any dimension, and design process is simple.Additionally, than existing higher-dimension planisphere, this kind of planisphere power proposed by the invention is more saved, and error sign ratio is lower.
Description
Technical field
The invention belongs to communication technical field, be specifically related to a class based on lattice and use optimum programming structure higher-dimension planisphere method.
Background technology
Nowadays, amplitude and the phase place of electromagnetic wave is modulated being widely used for transmission information.And in order to improve the performance of wireless communication system further, attention is placed in the benefit utilizing polarization of ele parameter to be brought to the information of carrying by increasing research [1]-[6].Andrews et al. points out that in document [1] polarization of electromagnetic wave can bring extra degree of freedom in a wireless communication system, thus improves power system capacity.Discussing the polarity diversity of antenna in document [2]-[4], this kind of technology is a kind of approach utilizing polarization of ele information.Nehorai et al. proposes the amplitude of electromagnetic wave, phase place and its two polarization parameters in document [5] first and can be modulated transmitting information simultaneously.Document [6] mathematic(al) representation based on external electromagnetic field, it is proposed that a kind of novel three-dimensional adjustment method in a wireless communication system electromagnetic wave amplitude, auxiliary polarization angle and polarization phases angle being modulated.To sum up, the design of higher-dimension planisphere there has been practical significance.
Widely known quadrature amplitude modulation (quadratureamplitudemodulation, QAM) is that the amplitude of modulated electromagnetic wave and phase place are to transmit information.In QAM constellation, each constellation point composition has repeatedly grid form, and this grid form is the most common in planisphere designs.Lattice are as a kind of mathematical structure, it is possible to above-mentioned in grid-like point for defining.Therefore, we can design planisphere on the basis of case theory.First the method constructing planisphere generally, based on case theory can choose a kind of lattice, chooses one the most again and comprises appointment number of constellation points purpose border.Character about lattice and planisphere based on lattice elaborates in document [7]-[9].Document [7] proposes gain index (theconstellationfigureofmerit, CFM) this concept of planisphere, and it reflects the efficiency of planisphere based on lattice.When the dimension of planisphere is the biggest (three-dimensional or four-dimensional), the planisphere with larger gain index has the lowest error sign ratio.Proakis et al. demonstrates the gain index of planisphere in document [9] can resolve into coding gain and the planisphere border shaping gain of lattice.Therefore, maximize coding gain respectively and shaping gain can produce the planisphere with maximum CFM value.
Summary of the invention
It is an object of the invention to propose a class based on lattice the method for using optimum programming structure higher-dimension planisphere, such planisphere constructed has the features such as power is saved, error sign ratio is low.
The method of the structure higher-dimension planisphere that the present invention proposes, it is by maximizing the coding gain of lattice and the shaping gain on planisphere border respectively, the gain index making higher-dimension planisphere reaches maximum, so that ultimately constructed higher-dimension planisphere out has the advantage that power is saved, error sign ratio is low.
The structure of this class higher-dimension planisphere proposed by the invention is broadly divided into two parts: one is choosing of n dimension lattice, and another is chosen for n dimension border.
Lattice in one n-dimensional space are RnIn a discrete point set, and this point set has the group structure [9] under vector addition.Generally, the lattice Λ of a n dimension can be by the base vector of n linear independenceRepresent, therefore any point x in lattice can be expressed as:
, (1)
Wherein。
The method of another kind of definition n dimension lattice Λ, is the generator matrix G by n × n dimension, each behavior base vector in G.After having had above-mentioned definition, in lattice Λ, arbitrary lattice point x is represented by
, (2)
WhereinIt is that a n ties up integer vectors.
Assuming that the required planisphere dimension designed is n, the first step of structure higher-dimension planisphere is exactly that the n selecting to have maximum coding gain ties up lattice.The arbitrarily coding gain γ of lattice Λc(Λ) can be stated [9] by following formula:
, (3)
Wherein, dmin(Λ) minimum Eustachian distance [9] of lattice Λ is represented；V (Λ) is the basis volume [9] of lattice Λ；G is the generator matrix of lattice Λ.
Without loss of generality, if the minimum Eustachian distance d of fixed gratingminBeing 1, then we are accomplished by maximizing the coding gain of lattice and obtain the lattice of densification, and remove to construct the planisphere of required higher-dimension power saving further.Reflecting [9] owing to the density degree of lattice can be generated by determinant of a matrix value, therefore, optimization problem just can describe with following formula:
。(4)
By solving this optimization problem (4), just can obtain lattice the closeest in n-dimensional space, can list as Spatial Dimension n=4 below, generator matrix corresponding to the closeest lattice when 5,6.
(5)
The shaping gain of n-dimensional space Zhong-1 block territory R can be stated [9] by following formula:
, (6)
Wherein V (R) is the volume (or area) of region R；Every two dimension mean power Eavg/2DRepresenting that the average energy of a n dimension planisphere quantifies the value after two-dimensional space, it can be calculated by following formula:
, (7)
The number of constellation point during wherein M is n dimension planisphere；xmIt it is the n-dimensional vector of an expression constellation point coordinate.The shaping gain demonstrating ball-type border in document [9] is maximum in all n dimension border.Therefore, we should choose hypersphere in n-dimensional space and go to choose constellation point from a certain given lattice as border.
Assuming that the constellation point number in our n dimension planisphere to be designed is M.In order to choosing border M the lattice point as close possible to n dimension hypersphere in fixing, just the lattice point in lattice first be arranged from small to large by its mould length.Simultaneously as in any lattice the mould length of lattice point be all a non-negative reality discrete series (And), the most just can define n (ri) it is a length of r of lattice middle moldiLattice point number, and define n × n (ri) dimension matrix P (ri) it is mould riPoint set matrix, it is respectively classified as a length of r of mouldiThe coordinate of lattice point.After having had above-mentioned definition, can be described by following optimization problem to the process choosing M constellation point fixing with hypersphere:
, (8)
Wherein；S is that dimension isTwo-dimentional selection matrix；WithRepresent that each row to matrix S and each row are sued for peace respectively, the sequence number of col with row corresponding columns and rows respectively.First constraint of above-mentioned optimization problem ensure that the M obtained some planisphere about origin symmetry, second and the 3rd constraint ensure that and only M lattice point is selected, and constellation point set matrix P (rKEach lattice point in) is at most chosen once.
After solving-optimizing problem (4) obtains lattice the closeest in n-dimensional space, then solve above-mentioned integer programming problem (8), just can obtain higher-dimension planisphere proposed by the invention.
Detailed description of the invention
The performance of the higher-dimension planisphere proposing the present invention is estimated by this part.
In simulation process, the random mark sequence generating a length of L is used as sending signal.Each symbol is taken from a given higher-dimension planisphere, and requires the minimum Eustachian distance d of all planispheresminIt is equal to 1.Receiving terminal can be N by power0The impact of Gauss additive white noise, and receiving terminal uses maximum likelihood detector to carry out symbol detection.
We compare three class four-dimension planispheres, and they are respectively as follows:
First kind four-dimension planisphere: take from four-dimensional integer lattice and border is the three-dimensional constellation map of hypercube.
Equations of The Second Kind four-dimension planisphere: the comprehensive cross planisphere of the four-dimension (4-Dgeneralizedcrossconstellations) that document [7] proposes.
3rd class four-dimension planisphere: four-dimensional planisphere proposed by the invention.
Table I lists the properties of this three classes four-dimension planisphere.Wherein, the severe of planisphere refers in planisphere with arbitrary given constellation point distance is minimum Eustachian distance dminThe number of point；Peak-to-average power ratio refers to the peak power of planisphere and the ratio of mean power.It is that error sign ratio when 512 compares that Fig. 1 gives this three classes four-dimension planisphere in constellation point number.Wherein EavgMean power for planisphere；PeThe bit error rate for planisphere.
By above-mentioned simulation result it can be seen that owing to this class higher-dimension planisphere proposed by the invention has bigger gain index, therefore the planisphere mentioned in they more existing documents has less mean power and lower error sign ratio.
The fundamental characteristics of different four-dimensional planispheres
Table I
List of references
[1]M.R.Andrews,P.P.MitaandR.Carvalho,"Triplingthecapacityofwirelesscommunicationsusingelectromagneticpolarization,"Nature409,pp.316-318,Jan.2001.
[2]R.ComptonJr.,"Thetripoleantenna:Anadaptivearraywithfullpolarizationflexibility,"IEEETrans.AntennasPropag.,vol.29,no.6,pp.944-952,Nov.1981.
[3]A.M.D.Turkmani,A.A.Arowojolu,P.A.JeffordandC.J.Kellett,"Anexperimentalevaluationoftheperformanceoftwo-branchspaceandpolarizationdiversityschemesat1800MHz,"IEEETrans.Veh.Technol.,vol.44,no.2,pp.318-326,May1995.
[4]B.LindmarkandM.Nilsson,"Ontheavailablediversitygainfromdifferentdual-polarizedantennas,"IEEEJ.Sel.AreasCommun.,vol.19,no.2,pp.287-294,Feb.2001.
[5]A.NehoraiandE.Paldi,"Vector-sensorarrayprocessingforelectromagneticsourcelocalization,"IEEETrans.SignalProcess.,vol.42,no.2,pp.376-398,Feb.1994.
[6] Song Hanbin. three-dimensional modem Ph.D. Dissertation. Shanghai: electronic engineering of Fudan University, 2012.
[7]G.D.Forney,JrandL.-F.Wei,"Multidimensionalconstellations.I.Introduction,figuresofmerit,andgeneralizedcrossconstellations,"IEEEJ.Sel.AreasCommun.,vol.7,no.6,pp.877-892,Aug.1989.
[8]G.D.Forney,JrandL.-F.Wei,"Multidimensionalconstellations.II.Voronoiconstellations,"IEEEJ.Sel.AreasCommun.,vol.7,no.6,pp.941-958,Aug.1989.
J.G.ProakisandM.Salehi,"OptimumReceiversforAWGNChannels,"inDigitalCommunications,5thed.,NewYork:McGrawHillInternationalEditions,2008,pp.160-289.。
Claims (1)
1. one kind for communication technology based on lattice the method for using optimum programming constructed higher-dimension planisphere, it is characterised in that concretely comprise the following steps:
(1) setting the lattice in a n-dimensional space is RnIn a discrete point set, and this point set has a group structure under vector addition, and the lattice Λ of a n dimension is by the base vector of n linear independenceRepresenting, any point x in lattice can be expressed as:
, (1)
Wherein, Z represents set of integers；
The method of another kind of definition n dimension lattice Λ, is the generator matrix G by n × n dimension, each behavior base vector in G, in lattice Λ, arbitrary lattice point x is represented by:
, (2)
WhereinIt is that a n ties up integer vectors；
The arbitrarily coding gain γ of lattice Λc(Λ) stated by following formula:
, (3)
Wherein, dmin(Λ) minimum Eustachian distance [9] of lattice Λ is represented；V (Λ) is the basis volume [9] of lattice Λ；G is the generator matrix of lattice Λ；
The minimum Eustachian distance d of fixed gratingminIt is 1, then passes through and solve following optimization problem:
(4)
Obtain lattice the closeest in n-dimensional space；
(2) shaping gain setting n-dimensional space Zhong-1 block territory R is stated by following formula:
, (5)
Wherein V (R) is volume or the area of region R；Every two dimension mean power Eavg/2DRepresent that the mean power of n dimension planisphere is to the value after two-dimensional space；
Eavg/2DCalculated by following formula:
(7),
The number of constellation point during wherein M is n dimension planisphere；xmIt it is the n-dimensional vector of an expression constellation point coordinate；
Choose hypersphere in n-dimensional space to go to choose constellation point from a certain given lattice as border；
If the constellation point number in n dimension planisphere to be designed is M；In order to choosing border M the lattice point as close possible to n dimension hypersphere in fixing, the lattice point in lattice first be arranged from small to large by its mould length；Owing in any lattice, the mould length of lattice point is all a non-negative reality discrete series:And, define n (ri) it is a length of r of lattice middle moldiLattice point number, and define n × n (ri) dimension matrix P (ri) it is mould riPoint set matrix, it is respectively classified as a length of r of mouldiThe coordinate of lattice point；Then can be described by following optimization problem to the process choosing M constellation point fixing with hypersphere:
(6),
Wherein；S is that dimension isTwo-dimentional selection matrix；WithRepresent that each row to matrix S and each row are sued for peace respectively, the sequence number of col with row corresponding columns and rows respectively；
After solving-optimizing problem (4) obtains lattice the closeest in n-dimensional space, then solve above-mentioned integer programming problem (6), just obtain required higher-dimension planisphere.
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| US5706312A (en) * | 1994-10-11 | 1998-01-06 | Lucent Technologies Inc. | Trellis coded modulation employing lower dimensionality convolutional encoder |
| CN1604516A (en) * | 2004-11-11 | 2005-04-06 | 上海交通大学 | Allowable code word lattice point search based vertical layered space-time code spherical decoding method |
| CN101582754A (en) * | 2008-05-05 | 2009-11-18 | 财团法人工业技术研究院 | Method for transmitting data to reduce average power ratio and device |
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