CN107425895A - A kind of 3D MIMO statistical channel modeling methods based on actual measurement - Google Patents

A kind of 3D MIMO statistical channel modeling methods based on actual measurement Download PDF

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CN107425895A
CN107425895A CN201710476525.6A CN201710476525A CN107425895A CN 107425895 A CN107425895 A CN 107425895A CN 201710476525 A CN201710476525 A CN 201710476525A CN 107425895 A CN107425895 A CN 107425895A
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msub
angle
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cluster
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CN107425895B (en
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张阳
李晨
庞立华
栾英姿
李�杰
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Guangzhou Its Communication Equipment Co ltd
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Xidian University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • 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
    • 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
    • H04B7/0891—Space-time diversity
    • H04B7/0897—Space-time diversity using beamforming per multi-path, e.g. to cope with different directions of arrival [DOA] at different multi-paths
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/0204—Channel estimation of multiple channels
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods

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Abstract

The invention belongs to wireless communication technology field, discloses a kind of 3D MIMO statistical channel modeling methods based on actual measurement, effectively reflects true three-dimension channel circumstance exactly, improves the precision of channel model；The statistical nature of large scale parameter is extracted by outer field measurement, the cross-correlation matrix for generating large scale parameter solves the problems, such as the non-positive definite of the matrix in existing model, extended using the angle of pitch of linear model statistical modeling 3D mimo channels, increase the dependence of perpendicular domains angle spread and distance, sub- footpath azimuth and the sub- footpath angle of pitch with mutual dependence are generated at random by mixing Von Mises Fisher distributions；Each characterization parameter of channel model is determined according to the statistical analysis of outer field measurement, generates 3D mimo channel coefficients.The present invention has expanded the application of 3D mimo channel models, and strong instrument is provided accurately and efficiently to assess 3D mimo system related algorithms.

Description

A kind of 3D MIMO statistical channel modeling methods based on actual measurement
Technical field
The invention belongs to wireless communication technology field, more particularly to a kind of 3D MIMO statistical channels modeling based on actual measurement Method.
Background technology
Wireless channel is the basis of the research such as new generation of wireless Communication System Design and new communication technologies algorithm, therefore accurately Ground carries out Channel Modeling and seems most important.Current most of statistical channel models based on geometry framework are all two-dimentional, are expired The traditional city macrocell Wireless Channel Modeling requirement of foot.And with the continuous refinement of Channel Modeling scene, two dimensional channel mould Type can not accurately describe the wireless channel of various actual scenes.Therefore, the characteristic of channel is accurately described in order to more objective, carried Three-dimensional multiple-input and multiple-output (3D MIMO) channel model is gone out.Existing standard channel model such as SCM, WINNER, QuaDRiGa Model is proposed the modeling method and thinking of mimo channel 3Dization.Compared with traditional 2DMIMO, change maximum 3D MIMO It is exactly the utilization to spatial domain pitching dimensional information.Pitching angle of arrival (EoA) and pitching are left in channel model angle (EoD) this two Individual important angle parameter is modeled, and reflects extension wireless propagation environment well, therefore has been obtained extensive Concern and research.3D MIMO obtain more spatial degrees of freedom using channel perpendicular domains, improve the handling capacity of system, together When significantly improve the average and edge spectrum efficiency of cell, reduce multi-user interference.Due to the advantage of itself, 3D MIMO Penetrate into various main flow wireless communication systems (for example, LTE, LTE-advanced and following 5G standards).
3D mimo channels modeling at present has preliminary progress, while there is also some problems：In WINNER+ models Corresponding 3D mimo channel argument sections are obtained by literature survey, not by complete outer field measurement so that thus establish Channel model some mistakes occur；The perpendicular domains angle character of channel is extremely important for 3D mimo channels, Germicidal efficacy Extended to the angle of pitch and depend on the distance between base station (BS) and user terminal (UE), but most of existing channel models pair Angle extension ESD is left in pitching and pitching angle of arrival extension ESA distance dependencies feature does not illustrate；Most 3D MIMO Channel model isolates the generating process at azimuth and the angle of pitch consideration of coming without studying between azimuth and the angle of pitch Cross correlation so that the channel model thus established is not accurate enough, and the feature with actual propagation environment is not inconsistent yet.Therefore, 3D Mimo channel is complete and accurate model just is particularly important.In addition, wireless channel can be modeled by statistical, It can be divided mainly into following a few classes：Statistical model (GBSMs) based on geometry framework, based on correlation statistical model (CBSMs) and Parameter random model (PSMs).By the predefined distribution of scattering object in communication environments, the reflection based on electromagnetic wave, reflect, spread out The philosophy penetrated and scattered can build GBSM.CBSM counts earth's surface by introducing cross correlation between channel matrix element Levy mimo channel feature.PSM the arrival of power and multipath or leaves the characteristic parameter of angle to characterize by using such as postponing Multipath component (MPC).Based on PSM frameworks, the present invention puies forward the 3D MIMO statistical channel models based on actual measurement and has redefined mould In type the statistics characterizing method of partial parameters and rely on outfield it is actual measurement provide its recommendation.
In summary, the problem of prior art is present be：The non-positive definite of the cross-correlation matrix of large scale parameter in existing model The problem of, angle extension ESD is not left to pitching for most of channel models and pitching angle of arrival extension ESA distance dependencies are special Sign illustrate and existing 3D mimo channels model the generating process at azimuth and the angle of pitch is isolated come consideration without Study the cross correlation between azimuth and the angle of pitch.
The content of the invention
The problem of existing for prior art, the invention provides a kind of 3D MIMO statistical channels modeling based on actual measurement Method.
The present invention is achieved in that a kind of 3D MIMO statistical channel modeling methods based on actual measurement, passes through outfield channel The statistic of measurement extraction large scale parameter, generate the cross-correlation matrix of large scale parameter；Utilize linear model statistical modeling 3D The angle of pitch extension of mimo channel, shows the dependence of perpendicular domains angle spread and distance in large scale parameter；Introduce mixing VMF distributions portray the mutual dependence at more cluster azimuths and the angle of pitch and generate the angle of arrival of 3d space and leave angle；
Further, the 3D MIMO statistical channel modeling methods based on actual measurement comprise the following steps：
Step 1, channel measurement activity is carried out, channel impulse response is obtained by channel measurement, according to channel impulse response Extract channel multi-path component；
Step 2, modeling generation large scale parameter LSPs simultaneously generates its cross-correlation matrix using filter method is circulated, seven big Scale parameter is respectively：Angle extension (ASD), the extension of orientation angle of arrival are left in delay extension (DS), shadow fading (SF), orientation (ASA), angle extension (ESD), pitching angle of arrival extension (ESA) and Lay this K factor (K) are left in pitching；
Seven large scale parameters can be modeled as logarithm normal distribution, and the LSPs of generation is：
Wherein, s is large scale parameter vector, μ and average and standard difference vector that σ is logarithm normal distribution, and it can pass through External field measurement data carry out statistical analysis and obtained,Be describe large scale parameter between correlation parameter vector,A For the cross-correlation matrix of seven large scale parameters, ξ is generated by using correlation distance using circulation filter method, do not obtain it is related away from From in the case of then by average be 0, variance be 1 Gauss independent same distribution variable generate at random.
For the different large scale parameters on same link, the following institute of coefficient correlation of two different large scale parameters Show：
Wherein, ρxyFor large scale parameter x, y coefficient correlation, CxyFor large scale parameter x, y covariance, Cxx, CyyRespectively It is large scale parameter x, y variance；
Step 3, extended using the angle of pitch of linear model statistical modeling 3D mimo channels, show to hang down in large scale parameter The dependence of straight domain angle spread and distance；
Step 4, introduce the angle of arrival of mixing Von Mises Fisher distribution modeling generation 3d spaces and leave angle； In 3D MIMO statistical channel models, angle parameter shares four, the i.e. azimuth of transmitting-receiving two-end and the angle of pitch；
Step 5, the statistical analysis according to channel measurement determine each characterization parameter of model；Cross-correlation including LSPs Matrix；The slope and intercept of linear model；Mix number of clusters, cluster extension, azimuth and the angle of pitch in VMF distributions；
Step 6, the generation of channel coefficients；
(1) initial random phase is set, for m strips footpath in nth bar cluster at four kinds of polarization modes (vv, vh, hv, hh) Lower setting random initial phaseInitial phase is equally distributed in (- π, π)；
(2) steering vector and Doppler frequency of aerial array are determined；S-th of transmitting antenna is to u-th reception antenna The channel response matrix of n-th of cluster can obtain according to following formula：
Wherein, Hu,s,n(t) it is the channel coefficient matrix of the n-th cluster, M bar rays, P is shared in every clusternFor the work(of n-th of cluster Rate, F are the field pattern of transmitting antenna or reception antenna when horizontally or vertically polarizing,It is orientation angle of arrival φn,m,AoA With vertical angle of arrival θn,m,EoANormalization angle vector, from following formula
It is that angle φ is left in orientationn,m,AoDWith vertically leave angle θn,m,EoDNormalization angle vector, from following formula
It is reception antenna u and transmitting antenna s position vector respectively；κn,mIt is the cross-pole in the range of linearity Change power ratio；λ0It is the wavelength of carrier frequency；Doppler-frequency component vn,mBy angle of arrival (AoA, EoA) and UE velocity v Obtain.
Wherein
When LOS path be present, the channel coefficients of LOS path are calculated：
Further, LSPs statistical parameters are generated in the step 2 and its detailed process of cross-correlation matrix is：
(1) preliminary transform domain large scale parameter (TLSPs) is generated in the transform domain as illustrated.Gaussian distributed, inciting somebody to actionReflect Penetrate to obtain siBefore,Will be withIt is associated,Correspond to other LSP or the transform domain large scale parameter of other links. For different network topology, TLSPs generation method is different, considers the following two kinds communication network：
A) between link is a BS to multiple UE
UE coordinates are (x1,y1),···(xk,yk), a grid is generated, seven Gausses are generated to each node Stochastic variable, 7 TLSP are corresponded to respectively, and find out position loc1lock of the k user in lattice point；Generation corresponds to This seven TLSP autocorrelation filter response：
Wherein, λmFor each LSP auto-correlation distance；D is the coordinate extended value in grid；With wave filter to each knot Seven Gaussian random variables filtering in point, 7 groups of data that position after filtering is loc1lock are designated as this k bar link TLSPs；
B) link is BS a to UE
Directly generate seven Gaussian random variables, the TLSPs as the link；
(2) cross-correlation between each TLSPs is added
7 transform domain large scale parameter ξ of each link are obtained, cross-correlation matrix is A (7 × 7), then final TLSPs is：
(3) LSPs is converted into by TLSPs
Further, extended, shown big using the angle of pitch of linear model statistical modeling 3D mimo channels in the step 3 The dependence of perpendicular domains angle spread and distance in scale parameter：
The angle character of perpendicular domains depends on the distance between BS and UE, and corresponding angle spread is modeled as lognormal Random distribution：
It is illustrated in figure 2 the relation of 3D mimo channel perpendicular domains angle spreads and distance under the conditions of LOS.
The dependence of ESD and ESA to correlation distance is represented by linear model：
μ=λ d+ η；
Wherein λ and η is linear function coefficients, and d is the distance between BS and UE, in units of rice.
Further, the angle of arrival of mixing Von Mises Fisher distribution modeling generation 3d spaces is introduced in the step 4 With leave angle；In 3D MIMO statistical channel models, angle parameter shares four, the i.e. azimuth of transmitting-receiving two-end and the angle of pitch. By taking the AoD and EoD of BS sides as an example, generation method is as follows, and the AoA and EoA of UE sides can be generated using similar method.Specific steps For：
(1) be based on outer field measurement, using block laplacian distribution fitting the angle of pitch, block Gauss Distribution Fitting orientation Angle；Calculate inverse gaussian sum against Laplace function as input by the use of cluster power and the extension of their own angle, obtain AoD with EoD；
Azimuth angle power spectrum PAS is obeyed and is blocked Gaussian Profile, by cluster power PnWith root mean square angle spread σASDNext life Into random angles AoD：
Wherein σASDIt is that angle extension is left in the orientation obtained by step 2, constant C is the scale factor related to number of clusters, Depending on this K factor of Lay in the case of LOS, C is usedLOSInstead of：
CLOS=C (1.1035-0.028K-0.002K2+0.0001K3)；
Angle of pitch power azimuth spectrum PAS is obeyed and is blocked laplacian distribution, by cluster power PnWith root mean square angle spread σESD To generate random angles EoD：
Wherein σESDIt is that angle extension is left in the pitching obtained by step 2, C is the scale factor related to number of clusters, in LOS feelings Depending on this K factor of Lay under condition, C is usedLOSInstead of：
CLOS=C (1.3086+0.0339K-0.0077K2+0.0002K3)；
(2) AoD and EoD of the n cluster to being generated based on outer field measurement carry out random pair, form n groups AoD and EoD Angle set, the average angle of pitch and azimuth as ray in cluster, generate the average wave hair/weighting vector vector for specifying cluster； Average wave hair/weighting vector vector of cluster represents by unit vector Δ, Δ=[sin θocosφo sinθosinφo cosθo]T, Wherein θoAnd φoThe average angle of pitch and azimuth respectively as ray in cluster；
(3) using the 3D angle Joint Distributions of Von Mises Fisher distribution modeling single clusters, azimuth and pitching are described Angle φ is left in the cluster angle spread at angle, the orientation for obtaining n-th of cluster, m-th of sub- footpathn,mAngle θ is left with pitchingn,m；According to VMF points Cloth can characterize the correlation between azimuth and the angle of pitch；
The probability density function of VMF distributions is expressed as：fp(Ω；Δ, κ)=Cp(κ)exp(κΔTΩ)sinθ；
Wherein, Ω=[sin θ cos φ sin θ sin φ cos θ]TRepresent any one ripple hair/Bo Dafang on unit ball To θ is the angle of pitch, and φ is azimuth.Δ is vectorial for average wave hair/weighting vector of cluster, i.e. the sensing of the cluster heart；Convergence parameter κ The diffusion of cluster ripple hair/weighting vector is described, κ is bigger, and cluster angle is more concentrated, and becomes anisotropy, cluster angle during and κ=0 There is isotropic scatterning；As shown in figure 4, when z-axis is as symmetry axis, it was observed that the influence that convergence parameter κ is distributed to VMF. Id(κ) is first kind modified Bessel function, and its exponent number is d, andThe p=3 in 3d space scene；
Cluster average wave hair/weighting vector vector Δ, Δ=[sin θ can be obtained by (2)ocosφo sinθosinφo cosθo ]T, κ is modeled as logarithm normal distribution, then the probability density function (PDF) of VMF distributions is re-written as：
fp(θ,φ|θo,φo, κ) and=Cp(κ)exp{κ[sinθosinθcos(φ-φo)+cosθocosθ]}sinθ；
Wherein ΔTScalar form, Δ are reduced to Ω inner productTΩ=sin θosinθcos(φ-φo)+cosθocos θ。
The PDF being distributed by VMF, φ and θ marginal probability density function can be calculated.Therefore generating in cluster has Angle φ is left in the azimuth of angle spread and the angle of pitch, the orientation for having obtained each sub- footpathn,mAngle θ is left with pitchingn,m。
The cross correlation between explanation azimuth and the angle of pitch is distributed by VMF again, it can be seen that VMF PDF is depended on Rotation axes of symmetry Δ and convergence parameter κ.With θo,φoIts PDF is discussed again exemplified by=0,0, now rotation axes of symmetry is z Axle, Δ=[0 0 1]T, VMF distribution PDF be
θ edge PDF is represented as
φ edge PDF is obeyed and is uniformly distributed, and is expressed as
In this case, the angle of pitch is independently distributed with azimuth.But most cluster in actual propagation environment Mean direction vector θo,φo≠ 0,0, the rotation axes of symmetry of Δ is pointed to beyond z-axis.So the angle of pitch is with related to azimuth Property.
What deserves to be explained is there is a large amount of scattering objects in wireless channel, channel is more clusters, it is therefore desirable to mixes VMF The propagation characteristic on distribution table levies in kind border.Structure mixing VMF distributions are related to：Angle should belong to the optimum number of which cluster and cluster The two problems of mesh.Need to be determined the number of angle and cluster with clustering algorithm.It can be gathered using soft expectation-maximization algorithm Class angle cluster and determination number of clusters.
Another object of the present invention is to provide a kind of to be built by the 3D MIMO statistical channel modeling methods based on actual measurement Vertical three dimensional channel model.
Advantages of the present invention and good effect are：The statistic of large scale parameter (LSPs) is extracted by outer field measurement, it is raw Solve the problems, such as the non-positive definite of the matrix in existing model, the related pitching of increase distance into the cross-correlation matrix of large scale parameter Angle extends, and introduces mixing Von Mises Fisher distributions to describe the pass that interdepends between azimuth and the angle of pitch System, improve the precision of current standardized 3D channel models.Based on PSM frameworks, the present invention puies forward the 3D MIMO statistics based on actual measurement Channel model has redefined the statistics characterizing method of partial parameters in model and has relied on the actual measurement in outfield to provide its recommendation.
Compared with existing 3D mimo channels statistical modeling method, present invention energy is more efficient and reflects exactly true Three dimensional channel environment, it is extracted LSPs by actual channel measurement statistics and obtains the cross-correlation matrix of its positive definite；Utilize line Property model illustrates the relation of channel perpendicular domains characteristic parameter and BS-UE distances；Mixing VMF distribution feature more cluster azimuths and The mutual dependence of the angle of pitch.Model can generate the channel impulse response with good statistical nature.The present invention has expanded 3D The research and application of mimo channel model, strong work is provided accurately and efficiently to assess 3D mimo system related algorithms Tool.
Brief description of the drawings
Fig. 1 is the 3D MIMO statistical channel modeling method flow charts based on actual measurement.
Fig. 2 is the relation schematic diagram of 3D channels perpendicular domains angle spread and distance under LOS path.
Fig. 3 is that EAS and dependence of 2DBS-UE distances under LOS and NLOS propagation conditions of the embodiment of the present invention are illustrated Figure.
Fig. 4 is the influence schematic diagram that convergence parameter κ is distributed to VMF when z-axis is as symmetry axis.
Fig. 5 is the map of website of measurement activity provided in an embodiment of the present invention and related street view.
Fig. 6 is the power azimuth spectrum by mixing VMF distribution generations in measuring route 5 (LOS) provided in an embodiment of the present invention Schematic diagram.
Fig. 7 is the validation verification schematic diagram of 3D MIMO statistical channel modeling methods provided in an embodiment of the present invention.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.
The application principle of the present invention is further described below in conjunction with the accompanying drawings.
As shown in figure 1, statistical channel modeling method provided by the invention is, it is necessary to establish the 3D MIMO statistics based on actual measurement Channel model, specifically comprise the following steps：
Step 1, channel measurement activity is carried out, channel impulse response is obtained by channel measurement, according to channel impulse response Extract channel multi-path component.
Xi'an national high and new technology industrial development zone carry out outfield channel measurement activity, measurement route around there is Strong static scatterer, surrounding environment are that typical city macrocell (UMa) propagates scene.Propagated with and without LOS Several diverse locations record experimental data, as much as possible comprehensively capture wireless channel.XDU channels are used in channel measurement activity Detector, by sending periodicity spread-spectrum signal come acquisition time, frequency and spatial information (si), realize that wireless channel detects.It is right In aerial array, emitter is equipped with a planar antenna array；Coronal aerial array is used at receiver, it is therefore an objective to identify From omnidirectional space it is all come wave path.It is horizontal and vertical at intervals of 0.5 between the adjacent array element of two aerial arrays Wavelength.Emitter is placed on the edge of building roof, about 40m, highly considerably beyond surrounding environment, and receiver then along The measurement route movement preplaned.Therefore, descending measurement is only carried out during measurement activity.BS positions in channel measurement activity Put, UE movement routes and corresponding street view are as shown in Figure 5.
Step 2, modeling generation large scale parameter LSPs simultaneously generate its cross-correlation matrix using filter method is circulated.It is seven big Scale parameter is respectively：Angle extension (ASD), the extension of orientation angle of arrival are left in delay extension (DS), shadow fading (SF), orientation (ASA), angle extension (ESD), pitching angle of arrival extension (ESA) and Lay this K factor (K) are left in pitching.
Seven large scale parameters can be modeled as logarithm normal distribution, and the LSPs of generation is：
Wherein, s is large scale parameter vector, μ and average and standard difference vector that σ is logarithm normal distribution, and it can pass through External field measurement data carry out statistical analysis and obtained,Be describe large scale parameter between correlation parameter vector,A For the cross-correlation matrix of seven large scale parameters, ξ is generated using correlation distance using circulation filter method, does not obtain correlation distance In the case of then by average be 0, variance be 1 Gauss independent same distribution variable generate at random.
In whole channel, correlation be present between large scale parameter, for the different large scales on same link Parameter, it can be described with cross correlation matrix number, the coefficient correlation of two different large scale parameters is as follows：
Wherein, ρxyFor large scale parameter x, y coefficient correlation；CxyFor large scale parameter x, y covariance；Cxx, CyyRespectively It is large scale parameter x, y variance.
WINNER+ models generate the mapping of cross-correlation large scale parameter, QuaDRiGa models using filtering method is circulated Employ same method, but it considers diagonally opposed simultaneously, extends the algorithm of mapping generation, further supports UE pairs The autocorrelation performance of large scale parameter during angular movement.ByUnderstand, in order to calculateThen cross-correlation matrix A must be protected Demonstrate,prove positive definite.The cross-correlation matrix A of 3D channels orthotropicity can not ensure in WINNER+ models, therefore be surveyed by actual channel LSPs cross-correlation matrix is measured, all characteristic values of the matrix are all positive, ensure that A orthotropicity.As shown in table 1 It is comparison of the cross correlation with WINNER+ models of vertical field parameter.
The cross correlation of 1 vertical field parameter of table and the comparison of WINNER+ models
The cross-correlation matrix of seven large scale parameters is obtained based on outer field measurement, occurrence is as shown in table 2.Wherein perpendicular domains Cross-correlation information generated according to the data statistics extraction of actual outer field measurement, other parameters continue to use the number of WINNER+ models According to finally giving the 3D large scale parameter cross-correlation matrix A (LOS/NLOS) under the macrocell scene of city.
The 3D large scale parameter cross-correlation matrix A (LOS/NLOS) of table 2
DS ASD ESD ASA ESA SF K
DS 1 0.4/0.4 -0.3/-0.3 0.8/0.6 0.13/-0.05 -0.4/-0.4 -0.4/NaN
ASD 0.4/0.4 1 0.27/0.43 0.3/0.4 0.44/-0.2 -0.5/-0.6 0.1/NaN
ESD -0.3/-0.3 0.27/0.43 1 -0.28/0 0.08/-0.01 0/0 0.22/NaN
ASA 0.8/0.6 0.3/0.4 -0.28/0 1 0.3/0 -0.5/-0.3 -0.2/NaN
ESA 0.13/-0.05 0.44/-0.2 0.08/-0.01 0.3/0 1 -0.8/-0.5 0/NaN
SF -0.4/-0.4 -0.5/-0.6 0/0 -0.5/-0.3 -0.8/-0.5 1 0.3/NaN
K -0.4/NaN 0.1/NaN 0.22/NaN -0.2/NaN 0/NaN 0.3/NaN 1
Step 3, extended using the angle of pitch of linear model statistical modeling 3D mimo channels, show perpendicular domains angle spread With the dependence of distance：The angle character of perpendicular domains depends on the distance between BS and UE, corresponding angle spread (EAS) It is modeled as lognormal random distribution.
It is the relation of channel perpendicular domains angle spread and BS-UE correlation distances as shown in Figure 2.Have due to ground return One LOS path another be NLOS paths dual path downlink propagation scene.ESD and ESA are represented by linear model To the dependence of correlation distance：
μ=λ d+ η；
Wherein λ and η is linear function coefficients, and on LOS or NLOS paths, ESD and ESA λ and η recommendation are total Knot is in table 6；D is the distance between BS and UE.
Characteristic related on distance to ESA ESD is as shown in Figure 3.It can be seen that in the case of LOS, ESA has than ESD More obvious distance dependencies.Specifically, BS-UE distances are between 50m to 350m, and ESA linear fit approximation is with 0.04 The speed of degree/rice reduces.When BS-UE distances are less than 50m in outer field measurement, ESD and ESA are relatively small.This is attributed to two realities Border limits：(1) bottom of receiving device, which may block some, has the reflection path of big incidence angle, causes less ESA； (2) path of leaving with wide-angle is located at outside the main lobe of antenna field pattern, causes ESD smaller.
Step 4, introduce the angle of arrival of mixing Von Mises Fisher distribution modeling generation 3d spaces and leave angle； In 3D MIMO statistical channel models, angle parameter shares four, the i.e. azimuth of transmitting-receiving two-end and the angle of pitch.With the AoD of BS sides Exemplified by EoD, generation method is as follows, and the AoA and EoA of UE sides can be generated using similar method.Concretely comprise the following steps：
(1) be based on outer field measurement, using block laplacian distribution fitting the angle of pitch, block Gauss Distribution Fitting orientation Angle.Inverse gaussian sum is calculated with cluster power and the extension of their own angle against Laplace function, obtains AoD and EoD.
Azimuth angle power spectrum PAS is obeyed and is blocked Gaussian Profile, by cluster power PnWith root mean square angle spread σASDNext life Into random angles AoD：
Wherein σASDIt is that angle extension is left in the orientation obtained by step 2, constant C is the scale factor related to number of clusters, such as Shown in table 3.
The C of table 3 and number of clusters relation
Number of clusters 4 5 8 10 11 12 14 15 16 20
C 0.779 0.860 1.018 1.090 1.123 1.146 1.190 1.211 1.226 1.289
Depending on this K factor of Lay in the case of LOS, C is usedLOSInstead of：
CLOS=C (1.1035-0.028K-0.002K2+0.0001K3)；
Angle of pitch power azimuth spectrum PAS is obeyed and is blocked laplacian distribution, by cluster power PnWith root mean square angle spread σESD To generate random angles EoD：
Wherein σESDIt is that angle extension is left in the pitching obtained by step 2, C is the scale factor related to number of clusters, such as the institute of table 4 Show.
Table 4C and number of clusters relation
Number of clusters 12 19 20
C 1.104 1.184 1.178
Depending on this K factor of Lay in the case of LOS, C is usedLOSInstead of：
CLOS=C (1.3086+0.0339K-0.0077K2+0.0002K3)；
(2) to AoD the and EoD random pairs of the n cluster generated based on outer field measurement, formation n groups AoD and EoD angle Set, the average angle of pitch and azimuth as ray in cluster, generate the average wave hair/weighting vector vector for specifying cluster.Cluster Average wave hair/weighting vector vector represents by unit vector Δ, Δ=[sin θocosφo sinθosinφo cosθo]T, wherein θoAnd φoThe average angle of pitch and azimuth respectively as ray in cluster.
(3) the 3D angle Joint Distributions of single cluster are modeled using Von Mises Fisher distributions (VMF), describes azimuth With the cluster angle spread of the angle of pitch, angle φ is left in the orientation for obtaining n-th of cluster, m-th of sub- footpathn,mAngle θ is left with pitchingn,m。VMF Distribution can characterize the correlation between azimuth and the angle of pitch.
The probability density function of VMF distributions is expressed as：
fp(Ω；Δ, κ)=Cp(κ)exp(κΔTΩ)sinθ；
Wherein, Ω=[sin θ cos φ sin θ sin φ cos θ]TRepresent any one ripple hair/Bo Dafang on unit ball To (bay is located at the centre of sphere), θ is the angle of pitch, and φ is azimuth.Δ is average wave hair/weighting vector vector of cluster in (2), That is the sensing of the cluster heart.Convergence parameter κ describes the diffusion of cluster ripple hair/weighting vector, and κ is bigger, and cluster angle is more concentrated, and becomes each Anisotropy, there is isotropic scatterning in cluster angle during and κ=0.As shown in figure 4, when z-axis is as symmetry axis, it was observed that convergence The influence that parameter κ is distributed to VMF.Id(κ) is first kind modified Bessel function, and its exponent number is d, andIn 3d space P=3 in scene.
Cluster average wave hair/weighting vector vector Δ, Δ=[sin θ can be obtained by (2)ocosφo sinθosinφo cosθo ]T, κ is modeled as logarithm normal distribution, then the probability density function (PDF) of VMF distributions can be re-written as：
fp(θ,φ|θo,φo, κ) and=Cp(κ)exp{κ[sinθosinθcos(φ-φo)+cosθocosθ]}sinθ；
Wherein ΔTScalar form, Δ are reduced to Ω inner productTΩ=sin θosinθcos(φ-φo)+cosθocos θ。
The PDF being distributed by VMF, φ and θ marginal probability density function can be calculated.Therefore generating in cluster has Angle φ is left in the azimuth of angle spread and the angle of pitch, the orientation for having obtained each sub- footpathn,mAngle θ is left with pitchingn,m。
The cross correlation between explanation azimuth and the angle of pitch is distributed by VMF again, it can be seen that VMF PDF is depended on Rotation axes of symmetry Δ and convergence parameter κ.With θo,φoIts PDF is discussed again exemplified by=0,0, now rotation axes of symmetry is z Axle, Δ=[0 0 1]T, VMF distribution PDF be：
θ edge PDF is represented as
φ edge PDF is obeyed and is uniformly distributed, and is expressed as
In this case, the angle of pitch is independently distributed with azimuth.But the most of cluster in actual propagation environment Mean direction vector θo,φo≠ 0,0, the rotation axes of symmetry of Δ is pointed to beyond z-axis.So the angle of pitch is with related to azimuth Property.
What deserves to be explained is there is a large amount of scattering objects in wireless channel, channel is more clusters, it is therefore desirable to mixes VMF The propagation characteristic on distribution table levies in kind border.Structure mixing VMF distributions are related to：Angle should belong to the optimum number of which cluster and cluster The two problems of mesh.Need to be determined the number of angle and cluster with clustering algorithm.It can be gathered using soft expectation-maximization algorithm Class angle cluster and determination number of clusters.BS sides based on outer field measurement activity in measurement route 5 (LOS) utilize soft expectation maximization Algorithm determines angle cluster, and the parameter generated is listed in table 5, and value that last in table arranges defines each by F points of the particular VM The prior probability of the direction vector of cloth generation.And represent corresponding angular power spectrum by mixing VMF distributions in figure 6 (PAS)。
The parameter that table 5 is extracted from (LOS) the BS sides of measuring route 5 using soft expectation-maximization algorithm
ID θo([°]) φo([°]) κ Prior probability
1 118 73 543 0.217
2 90 117 612 0.331
3 79 143 183 0.09
4 84 131 129 0.024
5 92 89 347 0.121
6 82 54 331 0.078
7 88 126 277 0.027
8 110 82 94 0.112
As seen from Figure 6, due to convergence parameter κ and the joint effect of prior probability, the PAS of cluster 1,2 and 5 is than other clusters All become apparent, therefore special scenes can be described well with 6 even 3 clusters.The dominant path of cluster 2 can be deduced Come from LOS path, the mean direction angle calculated by the mean direction angle and the geometry that are obtained based on map of website information is carried out Compare to verify.In addition, observe that the convergence parameter κ values of cluster 2 are maximum from table 5, because the azimuth of LOS path and the angle of pitch Extend smaller.In general, cluster angle spread is more scattered generally under UE sides and NLOS paths.Further it can be seen that institute The mean direction vector for having cluster is pointed to beyond z-axis, therefore azimuth and the angle of pitch are generally related in actual propagation environment.
Step 5, the statistical analysis according to channel measurement determine each characterization parameter of model；Cross-correlation including LSPs The ginsengs such as matrix, the slope λ and intercept η of linear model, number of clusters, cluster extension, azimuth and the angle of pitch in mixing VMF distributions Number.Other model parameters can continue to use the characterization parameter in the main models such as WINNER series or QuaDRiGa.It is specific as follows：
After obtaining measurement data, utilization space alternating generalized expectation-maximization (SAGE) algorithm removes day from measurement result Line directional diagram, obtain pure nature of radio propagation；Deconvolution is carried out to detectable signal waveform using improved CLEAN algorithms again, carried Take pure CIR；12 channel characteristics parameters, including power finally are extracted, is postponed, Doppler frequency, the ripple hair/direction of arrival in sub- footpath The parameter such as degree and channel latency and angle spread.Channel measurement activity is carried out in 2.6GHz or so, but the spy of these extractions Sign parameter is equally applicable to the 3D MIMO CIR that carrier frequency is 2-6GHz, and these parameters are in special frequency channel without significant frequency Rate dependence.
Table 6 summarizes the statistical result of the channel parameter extracted in the macrocell scene of city from the measurement data of outfield, It is mainly reflected in perpendicular domains and delay domain.Path loss and cross polarization power ratio (XPR) are in WINNER series channels models Good research has been obtained, has continued to use these information in model, so as to obtain complete model parameter.
The channel model parameters that table 6 extracts from UMa scenes
Step 6, the generation of channel coefficients.
(1) initial random phase is set.For m strips footpath in nth bar cluster at four kinds of polarization modes (vv, vh, hv, hh) Lower setting random initial phaseInitial phase is equally distributed in (- π, π).In LOS bars Under part, initial phase when vv and hh polarizes need to be only calculated
(2) steering vector and Doppler frequency of aerial array are determined.
The channel response matrix of s-th of transmitting antenna to n-th of cluster of u-th of reception antenna can obtain according to following formula：
Wherein, Hu,s,n(t) it is the channel coefficient matrix of the n-th cluster, M bar rays, P is shared in every clusternFor the work(of n-th of cluster Rate, F are the field pattern of transmitting antenna or reception antenna when horizontally or vertically polarizing,It is orientation angle of arrival φn,m,AoA With vertical angle of arrival θn,m,EoANormalization angle vector, from following formula
Wherein n represents cluster, and m represents the ray in nth bar cluster.It is that angle φ is left in orientationn,m,AoDWith vertically leave angle θn,m,EoDNormalization angle vector, from following formula
In addition,It is reception antenna u and transmitting antenna s position vector respectively.κn,mIt is in the range of linearity Cross polarization power ratio.λ0It is the wavelength of carrier frequency.Doppler-frequency component vn,mCan be by angle of arrival (AoA, EoA) and UE VelocityObtain：
Wherein
When LOS path be present, the channel coefficients of LOS path are calculated：
Channel model validation verification.In order to verify proposed parameterized model, using normalizing space cross-correlation letter (CCF) is counted to represent the validity of channel model：
Wherein, subscript k, k ' and l, l ' represent BS and UE kth, the individual bays of k ' and the individual antenna array of l, l ' respectively Member, n represent n-th of cluster in communication environments, and γ and ε are the respective bay intervals in BS and UE sides.ρkl,k′l′,n(γ,ε； T) represent to connect transmitting antenna k at moment tWith reception antenna lTransmitting of the link with being connected n-th of cluster Antenna k 'With reception antenna l 'Link between normalization space cross-correlation function CCF.
The application effect of the present invention is explained in detail with reference to emulation.
Link level simulation checking is considered, as UE moves along linear track away from BS in measurement activity.First, set The distance of BS to cell boarder is 350m, and UE initial positions are placed at distance BS50m.Between 50m to 350m, 7 are utilized Individual random and independent measurement route obtains simulation result.In the figure 7, respectively according to BS sides under the conditions of LOS and NLOS Different normalization antenna spacing γ reflects the curve of channel space cross correlation to draw | ρk1,k′1,1(γ,0；T) |, it is actual During test, the minimum interval of antenna array elements used in BS sides is 0.5 wavelength, is up to 1.5 wavelength.
In Fig. 7, it can be seen that actual measurement and simulation result almost overlap under LOS and NLOS scenes, carried 3D is illustrated Mimo channel model can characterize the statistical property of true propagation environment well.What deserves to be explained is space CCF under LOS path Absolute value apparently higher than the space CCF under NLOS paths absolute value.Because under NLOS scenes, the angle of multipath expands Exhibition and cluster extension are all bigger, cause the transmission of more disperse.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention All any modification, equivalent and improvement made within refreshing and principle etc., should be included in the scope of the protection.

Claims (6)

  1. A kind of 1. 3D MIMO statistical channel modeling methods based on actual measurement, it is characterised in that the 3D MIMO based on actual measurement Statistical channel modeling method extracts the statistic of large scale parameter by outer field measurement, generates the cross-correlation square of large scale parameter Battle array；The dependence of perpendicular domains angle spread and distance is represented using linear model；Introduce mixing VMF distributions and portray more cluster orientation The mutual dependence of angle and the angle of pitch simultaneously generates the angle of arrival of 3d space and leaves angle；Statistical analysis further according to outer field measurement determines Each characterization parameter of channel model, ultimately generate 3D mimo channel coefficients.
  2. 2. the 3D MIMO statistical channel modeling methods based on actual measurement as claimed in claim 1, it is characterised in that described to be based on The 3D MIMO statistical channel modeling methods of actual measurement comprise the following steps：
    Step 1, channel measurement activity is carried out, channel impulse response is obtained by channel measurement, extracted according to channel impulse response Channel multi-path component；
    Step 2, modeling generation large scale parameter LSPs simultaneously generate its cross-correlation matrix, seven large scales using filter method is circulated Parameter is respectively：Angle extension, the extension of orientation angle of arrival are left in delay extension, shadow fading, orientation, and pitching is left angle extension, bowed Face upward angle of arrival extension and this K factor of Lay；
    Seven large scale parameter models are logarithm normal distribution, and the large scale parameter (LSPs) of generation is：
    <mrow> <mi>s</mi> <mo>=</mo> <mn>10</mn> <mo>^</mo> <mrow> <mo>(</mo> <mi>&amp;mu;</mi> <mo>+</mo> <mover> <mi>s</mi> <mo>~</mo> </mover> <mo>&amp;CenterDot;</mo> <mi>&amp;sigma;</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
    Wherein, s is large scale parameter vector, μ and average and standard difference vector that σ is logarithm normal distribution, and it can be by external Field measurement data carry out statistical analysis and obtained,Be describe large scale parameter between correlation parameter vector,A is seven The cross-correlation matrix of individual large scale parameter, ξ are generated by using correlation distance using circulation filter method, do not obtain correlation distance In the case of then by average be 0, variance be 1 Gauss independent same distribution variable generate at random；
    It is as follows for the different large scale parameters on same link, the coefficient correlation of two different large scale parameters：
    <mrow> <msub> <mi>&amp;rho;</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </msub> <msqrt> <mrow> <msub> <mi>C</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> <msub> <mi>C</mi> <mrow> <mi>y</mi> <mi>y</mi> </mrow> </msub> </mrow> </msqrt> </mfrac> <mo>;</mo> </mrow>
    Wherein, ρxyFor large scale parameter x, y coefficient correlation, CxyFor large scale parameter x, y covariance, Cxx, CyyIt is big respectively Scale parameter x, y variance；
    Step 3, extended using the angle of pitch of linear model statistical modeling 3D mimo channels, show perpendicular domains in large scale parameter The dependence of angle spread and distance；
    Step 4, introduce the angle of arrival of mixing Von Mises Fisher distribution modeling generation 3d spaces and leave angle；In 3D In MIMO statistical channel models, angle parameter shares four, the i.e. azimuth of transmitting-receiving two-end and the angle of pitch；
    Step 5, the statistical analysis according to channel measurement determine each characterization parameter of model, include LSPs cross-correlation matrix, The slope and intercept of linear model, number of clusters, cluster extension, azimuth and the angle of pitch in mixing VMF distributions, other model ginsengs Number can continue to use the characterization parameter in the main models such as WINNER series or QuaDRiGa；
    Step 6, the generation of channel coefficients；
    (1) initial random phase is set, divided into for m strips footpath in nth bar cluster in four kinds of polarization modes (vv, vh, hv, hh) Put random initial phaseInitial phase is equally distributed in (- π, π)；
    (2) steering vector and Doppler frequency of aerial array are determined；N-th to u-th of reception antenna of s-th of transmitting antenna The channel response matrix of cluster can obtain according to following formula：
    <mrow> <mtable> <mtr> <mtd> <mrow> <mi>H</mi> <msub> <mrow> <mi>u</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <msub> <mi>P</mi> <mi>n</mi> </msub> </msqrt> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>M</mi> </munderover> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>j&amp;Phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> <mrow> <mi>v</mi> <mi>v</mi> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msqrt> <msub> <mi>&amp;kappa;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </msqrt> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>j&amp;Phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> <mrow> <mi>v</mi> <mi>h</mi> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msqrt> <msub> <mi>&amp;kappa;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> </msqrt> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>j&amp;Phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> <mrow> <mi>h</mi> <mi>v</mi> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>j&amp;Phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> <mrow> <mi>h</mi> <mi>h</mi> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>c</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mn>2</mn> <msubsup> <mi>&amp;pi;&amp;lambda;</mi> <mn>0</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> <mi>T</mi> </msubsup> <mo>.</mo> <msub> <mover> <mi>d</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>u</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mn>2</mn> <msubsup> <mi>&amp;pi;&amp;lambda;</mi> <mn>0</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> <mi>T</mi> </msubsup> <mo>.</mo> <msub> <mover> <mi>d</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;v</mi> <mrow> <mi>n</mi> <mo>,</mo> <mi>m</mi> </mrow> </msub> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
    Wherein, Hu,s,n(t) it is the channel coefficient matrix of the n-th cluster, M bar rays, P is shared in every clusternFor the power of n-th of cluster, F It is transmitting antenna or reception antenna in the field pattern horizontally or vertically to polarize,It is orientation angle of arrival φn,m,AoAWith it is vertical Angle of arrival θn,m,EoANormalization angle vector,It is that angle φ is left in orientationn,m,AoDWith vertically leave angle θn,m,EoDNormalization Angle vector；WithIt is reception antenna u and transmitting antenna s position vector respectively；κn,mIt is the cross-pole in the range of linearity Change power ratio；λ0It is the wavelength of carrier frequency；Doppler-frequency component vn,mBy angle of arrival (AoA, EoA) and UE velocity v Obtain；
    When LOS path be present, the channel coefficients of LOS path are calculated：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>H</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mfrac> <mn>1</mn> <mrow> <mi>K</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </msqrt> <msub> <mi>H</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mi>&amp;delta;</mi> <mrow> <mo>(</mo> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> <msqrt> <mfrac> <mi>K</mi> <mrow> <mi>K</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </msqrt> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>s</mi> <mo>,</mo> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>j&amp;Phi;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>j&amp;Phi;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> <mo>.</mo> </mrow>
    <mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>F</mi> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>u</mi> <mo>,</mo> <mi>h</mi> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>&amp;theta;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>E</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;phi;</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> <mo>,</mo> <mi>A</mi> <mi>o</mi> <mi>A</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mn>2</mn> <msubsup> <mi>&amp;pi;&amp;lambda;</mi> <mn>0</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> <mi>T</mi> </msubsup> <mo>.</mo> <msub> <mover> <mi>d</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>r</mi> <mi>x</mi> <mo>,</mo> <mi>u</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> <mo>.</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mn>2</mn> <msubsup> <mi>&amp;pi;&amp;lambda;</mi> <mn>0</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msubsup> <mover> <mi>r</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> <mi>T</mi> </msubsup> <mo>.</mo> <msub> <mover> <mi>d</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mi>t</mi> <mi>x</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>.</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;v</mi> <mrow> <mi>L</mi> <mi>O</mi> <mi>S</mi> </mrow> </msub> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
  3. 3. the 3D MIMO statistical channel modeling methods based on actual measurement as claimed in claim 2, it is characterised in that the step Modeling generation large scale parameter LSPs and using circulating filter method and generating the detailed process of its cross-correlation matrix it is in two：
    (1) preliminary transform domain large scale parameter (TLSPs) is generated in the transform domain as illustrated；Gaussian distributed, inciting somebody to actionMap To siBefore,Will be withIt is associated,Correspond to other LSP or the transform domain large scale parameter of other links；For Different network topology, TLSPs generation method is different, considers the following two kinds communication network：
    A) between link is a BS to multiple UE
    UE coordinates are (x1,y1),···(xk,yk), a grid is generated, generating seven gaussian randoms to each node becomes Amount, 7 TLSP are corresponded to respectively, and find out position loc1lock of the k user in lattice point；Generation corresponds to this seven TLSP autocorrelation filter response：
    <mrow> <msub> <mi>h</mi> <mi>m</mi> </msub> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mfrac> <mi>d</mi> <msub> <mi>&amp;lambda;</mi> <mi>m</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mo>,</mo> <mi>m</mi> <mo>=</mo> <mi>D</mi> <mi>S</mi> <mo>,</mo> <mi>A</mi> <mi>S</mi> <mi>D</mi> <mo>,</mo> <mi>A</mi> <mi>S</mi> <mi>A</mi> <mo>,</mo> <mi>E</mi> <mi>S</mi> <mi>D</mi> <mo>,</mo> <mi>E</mi> <mi>S</mi> <mi>A</mi> <mo>,</mo> <mi>S</mi> <mi>F</mi> <mo>,</mo> <mi>K</mi> <mo>;</mo> </mrow>
    Wherein, λmFor each LSP auto-correlation distance；D is the coordinate extended value in grid；With wave filter in each node Seven Gaussian random variables filtering, by position after filtering be loc1lock 7 groups of data be designated as this k bar link TLSPs；
    B) link is BS a to UE
    Directly generate seven Gaussian random variables, the TLSPs as the link；
    (2) cross-correlation between each TLSPs is added
    7 transform domain large scale parameter ξ of each link are obtained, cross-correlation matrix is A (7 × 7), then final TLSPs is：
    <mrow> <mover> <mi>s</mi> <mo>~</mo> </mover> <mo>=</mo> <msqrt> <mi>A</mi> </msqrt> <mo>&amp;CenterDot;</mo> <mi>&amp;xi;</mi> <mo>;</mo> </mrow>
    (3) LSPs is converted into by TLSPs
    <mrow> <mi>s</mi> <mo>=</mo> <mn>10</mn> <mo>^</mo> <mrow> <mo>(</mo> <mi>&amp;mu;</mi> <mo>+</mo> <mover> <mi>s</mi> <mo>~</mo> </mover> <mo>&amp;CenterDot;</mo> <mi>&amp;sigma;</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  4. 4. the 3D MIMO statistical channel modeling methods based on actual measurement as claimed in claim 2, it is characterised in that the step Extended in three using the angle of pitch of linear model statistical modeling 3D mimo channels, show that perpendicular domains angle expands in large scale parameter Exhibition and the dependence of distance：
    The angle character of perpendicular domains depends on the distance between BS and UE, and it is random that corresponding angle spread is modeled as lognormal Distribution：
    <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> </mrow> </msqrt> <mi>&amp;sigma;</mi> <mi>x</mi> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mn>10</mn> <mi>x</mi> <mo>-</mo> <mi>&amp;mu;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> <mo>;</mo> </mrow>
    Dependence μ=λ d+ the η of ESD and ESA to correlation distance are represented by linear model；
    Wherein λ and η is linear function coefficients, and d is the distance between BS and UE, in units of rice.
  5. 5. the 3D MIMO statistical channel modeling methods based on actual measurement as claimed in claim 2, it is characterised in that the step The angle of arrival of mixing Von Mises Fisher distribution modeling generation 3d spaces is introduced in four and leaves angle, is counted in 3D MIMO In channel model, angle parameter shares four, the i.e. azimuth of transmitting-receiving two-end and the angle of pitch；By taking the AoD and EoD of BS sides as an example, Generation method is as follows, and the AoA and EoA of UE sides can be generated using similar method；Concretely comprise the following steps：
    (1) be based on outer field measurement, using block laplacian distribution fitting the angle of pitch, block Gauss Distribution Fitting azimuth；With Cluster power and the extension of their own angle calculate inverse gaussian sum as input against Laplace function, obtain AoD and EoD；
    Azimuth angle power spectrum PAS is obeyed and is blocked Gaussian Profile, by cluster power PnWith root mean square angle spread σASDCome generate with Machine angle A oD：
    <mrow> <msub> <mi>&amp;phi;</mi> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>A</mi> <mi>S</mi> <mi>D</mi> </mrow> </msub> <mo>/</mo> <mn>1.4</mn> <mo>)</mo> </mrow> <msqrt> <mrow> <mo>-</mo> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>n</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>(</mo> <msub> <mi>P</mi> <mi>n</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msqrt> </mrow> <mi>C</mi> </mfrac> <mo>;</mo> </mrow>
    Wherein σASDIt is that angle extension is left in the orientation obtained by step 2, constant C is the scale factor related to number of clusters, in LOS feelings Depending on this K factor of Lay under condition, C is usedLOSInstead of：
    CLOS=C (1.1035-0.028K-0.002K2+0.0001K3)；
    Angle of pitch power azimuth spectrum PAS is obeyed and is blocked laplacian distribution, by cluster power PnWith root mean square angle spread σESDNext life Into random angles EoD：
    <mrow> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mo>-</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>E</mi> <mi>S</mi> <mi>D</mi> </mrow> </msub> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>n</mi> </msub> <mo>/</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>(</mo> <msub> <mi>P</mi> <mi>n</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <mi>C</mi> </mfrac> <mo>;</mo> </mrow>
    Wherein σESDIt is that angle extension is left in the pitching obtained by step 2, C is the scale factor related to number of clusters, in the case of LOS Depending on this K factor of Lay, C is usedLOSInstead of：
    CLOS=C (1.3086+0.0339K-0.0077K2+0.0002K3)；
    (2) AoD and EoD of the n cluster to being generated based on outer field measurement carry out random pair, form n groups AoD and EoD angle Set, the average angle of pitch and azimuth as ray in cluster, generate the average wave hair/weighting vector vector for specifying cluster；Cluster Average wave hair/weighting vector vector represents by unit vector Δ, Δ=[sin θocosφo sinθosinφo cosθo]T, wherein θoAnd φoThe average angle of pitch and azimuth respectively as ray in cluster；
    (3) using the 3D angle Joint Distributions of Von Mises Fisher distribution modeling single clusters, azimuth and the angle of pitch are described Angle φ is left in cluster angle spread, the orientation for obtaining n-th of cluster, m-th of sub- footpathn,mAngle θ is left with pitchingn,m；Can according to VMF distributions Characterize the correlation between azimuth and the angle of pitch；
    The probability density function of VMF distributions is expressed as：fp(Ω；Δ, κ)=Cp(κ)exp(κΔTΩ)sinθ；
    <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;kappa;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msup> <mi>&amp;kappa;</mi> <mi>d</mi> </msup> <mrow> <msup> <mrow> <mo>(</mo> <mn>2</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>I</mi> <mi>d</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;kappa;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow>
    Wherein, Ω=[sin θ cos φ sin θ sin φ cos θ]TRepresent any one ripple hair/direction of arrival on unit ball, θ For the angle of pitch, φ is azimuth；Δ is vectorial for average wave hair/weighting vector of cluster, i.e. the sensing of the cluster heart；Convergence parameter κ is described The diffusion of cluster ripple hair/weighting vector, κ is bigger, and cluster angle is more concentrated, and becomes anisotropy, and cluster angle occurs during and κ=0 Isotropic scatterning；Id(κ) is first kind modified Bessel function, and its exponent number is d, andThe p in 3d space scene =3；
    Cluster average wave hair/weighting vector vector Δ, Δ=[sin θ can be obtained by (2)ocosφo sinθosinφo cosθo]T, κ builds Mould is logarithm normal distribution, then the probability density function (PDF) of VMF distributions is re-written as：
    fp(θ,φ|θo,φo, κ) and=Cp(κ)exp{κ[sinθosinθcos(φ-φo)+cosθocosθ]}sinθ；
    Wherein ΔTScalar form, Δ are reduced to Ω inner productTΩ=sin θosinθcos(φ-φo)+cosθocosθ；
    The PDF being distributed by VMF, φ and θ marginal probability density function can be calculated；Therefore generating in cluster has angle Angle φ is left in the azimuth of extension and the angle of pitch, the orientation for having obtained each sub- footpathn,mAngle θ is left with pitchingn,m；
    The correlation between explanation azimuth and the angle of pitch is distributed by VMF again, it can be seen that VMF PDF depends on rotation pair Claim axle Δ and convergence parameter κ；With θo,φoIts PDF is discussed again exemplified by=0,0, now rotation axes of symmetry is z-axis, Δ= [0 0 1]T,
    <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mi>&amp;theta;</mi> <mo>,</mo> <mi>&amp;phi;</mi> <mo>|</mo> <mi>&amp;kappa;</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&amp;kappa;</mi> <mi>exp</mi> <mrow> <mo>(</mo> <mrow> <mi>&amp;kappa;</mi> <mi>cos</mi> <mi>&amp;theta;</mi> </mrow> <mo>)</mo> </mrow> <mi>sin</mi> <mi>&amp;theta;</mi> </mrow> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> <mi>sinh</mi> <mi>&amp;kappa;</mi> </mrow> </mfrac> <mo>;</mo> </mrow>
    θ edge PDF is represented as
    <mrow> <msub> <mi>f</mi> <mi>e</mi> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&amp;kappa;</mi> <mi>exp</mi> <mrow> <mo>(</mo> <mi>&amp;kappa;</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>&amp;theta;</mi> </mrow> <mrow> <mn>2</mn> <mi>sinh</mi> <mi>&amp;kappa;</mi> </mrow> </mfrac> <mo>;</mo> </mrow>
    φ edge PDF is obeyed and is uniformly distributed, and is expressed as
    In this case, the angle of pitch is independently distributed with azimuth；But most clusters is averaged in actual propagation environment Direction vector θo,φo≠ 0,0, the rotation axes of symmetry of Δ is pointed to beyond z-axis；So the angle of pitch and azimuth are with correlation 's；
    What deserves to be explained is there is a large amount of scattering objects in wireless channel, channel is more clusters, it is therefore desirable to mixes VMF distributions Characterize actual propagation characteristic；Structure mixing VMF distributions be related to angle should belong to which cluster and cluster optimal number this Two problems；Need to be determined the number of angle and cluster with clustering algorithm, angle can be clustered using soft expectation-maximization algorithm Spend cluster and determine number of clusters.
  6. 6. the three of a kind of 3D MIMO statistical channels modeling method foundation as described in Claims 1 to 5 any one based on actual measurement Tie up channel model.
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