3GPP TR 36.873 V12.0.0: 3D通道模型研究 for LTE (Release 12)

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"3GPP TR 36.873 V12.0.0 (2014-09)" 是一份2014年9月由3GPP（第三代合作伙伴计划）技术规范组无线接入网络研究的文档，专注于3D信道模型在LTE（长期演进）中的应用研究。这份报告属于3GPP Release 12，旨在探讨3D信道模型在移动通信系统中的扩展与改进，特别是针对3GPP SCM（统计信道模型）的3D扩展以及3D MIMO（多输入多输出）技术。 3GPP是全球性的标准组织，致力于制定移动通信系统的统一技术规格。TR（Technical Report）是3GPP的一种文档类型，它通常包含了技术研究、探索性工作或未来可能纳入标准的技术分析。3GPP TR 36.873 V12.0.0就是这样一个研究型文档，它对3D信道建模进行了深入研究，以支持和优化LTE网络的性能，尤其是对于3D空间分集和空间多工技术的运用。 SCM模型是3GPP定义的一种用于模拟无线通信信道行为的统计模型，它是评估和设计通信系统性能的关键工具。在3D环境下，SCM模型的扩展使得信道建模更符合实际环境，考虑了天线阵列的高度差异、建筑物的三维结构以及空间中的多重反射和散射，从而更准确地反映信号传播的复杂性。 3D MIMO是现代无线通信系统中一个重要的技术进步，它利用空间维度来增加系统容量和传输效率。通过在基站和用户设备上部署多天线，3D MIMO能够同时服务于多个用户，提供更高的数据速率和更好的覆盖性能。3GPP TR 36.873 V12.0.0的研究可能包括了新的3D MIMO算法、信道估计方法、多用户调度策略以及与之相关的系统性能评估。这份报告虽然未经3GPP组织伙伴的正式批准，但它为3GPP未来的工作提供了理论基础和技术参考。任何想要实施3GPP标准的组织应通过3GPP官方出版部门获取正式的技术规格和报告。关键词：LTE，无线模型，3GPP 报告的发布表明，3GPP在持续努力推动移动通信技术的发展，尤其是在提升网络容量和性能方面，而3D信道模型和3D MIMO技术是实现这一目标的关键组成部分。对于系统开发者、研究人员以及通信行业的从业者来说，理解和掌握这些技术细节至关重要。

3GPP TR 36.873 V12.0.0 (2014-09)

Release 12

the equations in clause 5.13.

Note that any arbitrary mechanical orientation of the array can be achieved by rotating the LCS with respect to the GCS.

5.1.3 Transformation from a LCS to a GCS

A GCS with coordinates (x, y, z,

) and unit vectors (

) and an LCS with "primed" coordinates (x’, y’, z’,

) and "primed" unit vectors (

) are defined with a common origins in Figures 5.1.3-1 and 5.1.3-2. Figure 5.1.3-1

illustrates the sequence of rotations that relate the GCS (gray) and the LCS (blue).

Figure 5.1.3-2 shows the coordinate direction and unit vectors of the GCS (gray) and the LCS (blue).

Note that the vector fields of the antenna array elements are defined in the LCS. In Figure 5.1.3-1 we consider an

arbitrary 3D-rotation of the LCS with respect to the GCS given by the angles

. The set of angles

can also

be termed as the orientation of the antenna array with respect to the GCS.

Note that the transformation from a LCS to a GCS depends only on the angles

. The angle

is called the bearing

angle,

is called the downtilt angle and

is called the slant angle.

Figure 5.1.3-1: Orienting the LCS (blue) with

respect to the GCS (gray) by a sequence of 3

rotations:

Figure 5.1.3-2: Definition of spherical

coordinates and unit vectors in both the GCS

and LCS.

Let

)

','(

φθ

denote an antenna element pattern in the LCS and

),(

φθ

denote the same antenna element pattern in the

GCS. Then the two are related simply by

)','

('),(

φθφθ

AA =

with

and

given by (5.6) and (5.7).

Let us denote the polarized field components in the LCS by

,'(

φθ

)','(

φθ

and in the GCS by

),(

φθ

),(

φθ

. Then they are related by equation (5.10).

Any arbitrary 3-D rotation can be specified by at most 3 elemental rotations, and following the framework of

Figure 5.1.3-1, a series of rotations about the z,



and



axes are assumed here, in that order.

The dotted and double-dotted marks indicate that the rotations are intrinsic, which means that they are the result of one

(⋅) or two (⋅⋅) intermediate rotations. In other words, the



axis is the original y axis after the first rotation about z, and

the



axis is the original x axis after the first rotation about z and the second rotation about



A first rotation of

about z sets the antenna bearing angle (i.e. the sector pointing direction for a BS antenna element).

3GPP TR 36.873 V12.0.0 (2014-09)

Release 12

The second rotation of

about



sets the antenna downtilt angle.

Finally, the third rotation of

about



sets the antenna slant angle.

The orientation of the x, y and z axes after all three rotations can be denoted as







and



These triple-dotted axes represents the final orientation of the LCS, and for notational purposes denoted as the x’, y’ and

z’ axes (local or "primed" coordinate system.

In order to establish the equations for transformation of the coordinate system and the polarized antenna field patterns

between the GCS and the LCS, it is necessary to determine the composite rotation matrix that describes the

transformation of point (x, y, z) in the GCS into point (x’, y’, z’) in the LCS.

This rotation matrix is computed as the product of three elemental rotation matrices.

The matrix to describe rotations about the z,



and



axes by the angles

and

respectively and in that order is

defined in equation (5.1).

( ) ( ) ( )













−+













+−













−+

γγ

ββ

αα

γβα

cossin0

sincos0

001

cos0sin

010

sin0cos

100

0cossin

0sincos

XYZ

RRRR

(5.1)

The reverse transformation is given by the inverse of R, which is also equal to the transpose of R since it is orthogonal.

( ) ( ) ( )

ZYX

RRRRR =−−−=

−

αβγ

(5.2)

The simplified forward and reverse composite rotation matrices are given in equations (5.3) and (5.4).













−

−+

+−

βγββ

γαγβαγα

γβαβα

γαγβαγ

αγβαβα

coscossincossin

sincoscossinsincoscossinsinsincossin

sinsincossincoscossinsinsincoscos

cos

(5.3)













−+

+−

−

γβγ

αγβαγα

γβα

γβ

γαγβα

βαβα

coscos

sincoscossinsinsin

sincossincos

sincos

coscossinsinsincos

sinsinsincos

sincossin

coscos

(5.4)

These transformations can be used to derive the angular and polarization relationships between the two coordinate

systems.

In order to establish the angular relationships, consider a point (x, y, z) on the unit sphere defined by the spherical

coordinates (

=1,

), where

is the unit radius,

is the zenith angle measured from the +z-axis, and

is the azimuth

angle measured from the +x-axis in the x-y plane. The Cartesian representation of that point is given by equation (5.5).

























φθ

cos

sinsin

cossin

(5.5)

The zenith angle is computed as

( )

arccos ⋅

and the azimuth angle as

)

arg(

ρρ

⋅+⋅ yjx

, where

and

are the Cartesian unit vectors. If this point represents a location in the GCS defined by

and

, the corresponding

position in the LCS is given by

1−

, from which local angles

’ and

’ can be computed. The results are given in

equations (5.6) and (5.7).

( ) ( ) ( )( )( )

θαφγαφγβθγβρφθγβαθ

sinsinsincoscossincoscoscosacos

arccos,;,,'

−−−+=

























−

(5.6)

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