﻿ 基于射线跟踪的大规模MIMO信道建模
 计算机系统应用  2019, Vol. 28 Issue (3): 59-65 PDF

1. 西安理工大学 自动化与信息工程学院, 西安 710048;
2. 西安电子科技大学 通信工程学院, 西安 710071

Massive MIMO Channel Modeling Based on Ray Tracing
YAO Jun-Liang1, LIU Qing1, ZHANG Yan2, YAO Wen-Lei2
1. Faculty of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China;
2. School of Telecommunications Engineering, Xidian University, Xi’an 710071, China
Foundation item: National Natural Science Foundation of China (61401354, 61502385); Fundamental Research Program of Natural Science Fund of Shaanxi Province (2016JQ6015); Key Laboratory Fund of Education Bureau of Shaanxi Province (17JS086)
Abstract: Massive Multiple-Input Multiple-Output (MIMO), with giant array size and multi-dimensional array structure, has been widely considered as a key physical layer technique in future wireless communications. With regarding the large number of antenna elements, some new challenges and issues are arising. To solve these problems, a statistical channel model based on the spherical wave-front theory is proposed. Furthermore, the map-based ray-tracing algorithm with low complexity is used to compute the parameters of the proposed channel modeling. Finally, several statistical characteristics, such as delay spread and spatial distance, are given. The analysis results show that the proposed channel model is able to describe the main characteristics of massive MIMO channel.
Key words: channel modeling     massive MIMO     ray tracing     diffraction theory     delay spread

1 大规模MIMO信道模型 1.1 信道模型基本框架

 $R \geqslant 2{L^2}/\lambda$ (1)

 图 1 平面阵大规模MIMO链路示意图

 $\begin{array}{l} {H_{u,s,n}}(t) = \sqrt {\dfrac{{{P_n}}}{M}} \displaystyle\sum\limits_{m = 1}^M {\left[ {\begin{array}{*{20}{c}} {{F_{rx,u,\gamma }}({\gamma _{n,m}},{\phi _{n,m}})}\\ {{F_{rx,u,\phi }}({\gamma _{n,m}},{\phi _{n,m}})} \end{array}} \right]Q({\gamma _{n,m}},{\phi _{n,m}}){M_{n,m,u,s}}P({\theta _{n,m}},{\varphi _{n,m}})\left[ {\begin{array}{*{20}{c}}{{F_{tx,s,\theta }}({\theta _{n,m}},{\varphi _{n,m}})}\\ {{F_{tx,s,\varphi }}({\theta _{n,m}},{\varphi _{n,m}})} \end{array}} \right]} \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \times \exp \left( {j2\pi \lambda _0^{{\rm{ - }}1}\left( {D_{n,m,s}^{tx} + D_{n,m,u}^{rx}} \right) + {\alpha _0}} \right) \cdot \exp \left( {j2\pi {\nu _{n,m}}t} \right) \end{array}$ (2)

1.2 天线姿态对信道模型的影响

 $\left\{ {\begin{array}{*{20}{c}} {{F_\theta }(\theta ,\phi ) = {F_{\theta '}}(\theta ',\phi ')\cos \psi - {F_{\phi '}}(\theta ',\phi ')\sin \psi } \\ {{F_\phi }(\theta ,\phi ) = {F_{\theta '}}(\theta ',\phi ')\sin \psi + {F_{\phi '}}(\theta ',\phi ')\cos \psi } \end{array}} \right.$ (3)

 $\psi = \arg \left( {\sin \theta \cos \beta - \cos \phi \cos \theta \sin \beta + j\sin \phi \sin \beta } \right)$
1.3 转换矩阵 $P$ $Q$

 $\left\{ {\begin{array}{*{20}{c}} {P({\theta _{n,m}},{\varphi _{n,m}}) = \left[ {\begin{array}{*{20}{c}} {\cos {\varphi _{n,m}}}&0 \\ {\sin {\varphi _{n,m}}\sin {\theta _{n,m}}}&{\cos {\theta _{n,m}}} \end{array}} \right]} \\ {Q({\gamma _{n,m}},{\phi _{n,m}}) = \left[ {\begin{array}{*{20}{c}} {\cos {\phi _{n,m}}}&{\sin {\phi _{n,m}}\sin {\gamma _{n,m}}} \\ 0&{\cos {\gamma _{n,m}}} \end{array}} \right]} \end{array}} \right.$ (4)

 $\left\{ {\begin{array}{*{20}{c}} {P({\theta _{n,m}},{\varphi _{n,m}}) = \left[ {\begin{array}{*{20}{c}} {\cos {\varphi _{n,m}}}&0 \\ 0&1 \end{array}} \right]} \\ {Q({\gamma _{n,m}},{\phi _{n,m}}) = \left[ {\begin{array}{*{20}{c}} {\cos {\phi _{n,m}}}&0 \\ 0&1 \end{array}} \right]} \end{array}} \right.$ (5)
2 基于地图的射线跟踪算法

2.1 场景地图的建立

 图 2 基于地图的射线跟踪算法

2.2 确定传播路径上的交点类型和坐标

 ${\Psi _k} = \left\{ {{x_{ki}},{y_{ki}},{z_{ki}},{T_{ki}}} \right\},k = 1,2, \cdots ,K; i = 1,2, \cdots ,{I_k}$ (6)

(1) 反射. 利用射线光学原理, 以所有能被TX“看见”的面为镜面, 得到TX镜像点. 从镜像点出发, 与镜面有交点的“直射”路径即为反射径, 与镜面的交点为反射点.

(2) 绕射. 分为建筑物垂直边绕射和建筑物顶边绕射两种. 垂直边绕射是与TX有LoS径直达或通过一次镜面反射可达TX的角边(Corner), 绕射点的 $x,y$ 坐标为角边坐标, $z$ 坐标需要在TX-RX路径确定后才能获得. 建筑物顶边绕射: 如果收(发)端高于楼顶, 则会存在顶边绕射(如图5). 绕射点的确定采用VPL (Vertical-Plane-Launch)方法: 过TX和RX做一垂直平面, 该平面与顶边的交点即为绕射点. 若经过一次反射到达RX, 则过TX(RX)和RX(TX)镜像点做垂直平面, 平面与对应镜面和顶边的交点分别为反射点和绕射点. 若经过两次反射到达RX, 则过TX镜像点和RX镜像点做垂直平面, 平面与对应镜面和顶边的交点分别为反射点和绕射点.

 图 5 建筑物顶边绕射

 图 6 绕射角示例

(3) 散射. 考虑两类散射体: 第一类是 TX或RX节点附近并且有LoS径可达的散射体, 第二类是在两个节点之间、并与两个节点都LoS可达的散射体(这里的节点可以是TX、RX、反射点、绕射点). 为了降低复杂度同时又不影响模型准确性, 需要舍弃满足下述条件的弱散射体.

 $20 {\rm log} 10 \left( {\dfrac{R\cdot d_{\rm direct}}{2d_1d_2}} \right) < - 30 \;{\rm {dB}}$ (7)

 图 7 TX-RX的射线示例

 图 8 功率时延谱

3 基于射线跟踪的信道模型分析

3.1 时延扩展

 ${\sigma _\tau } = \sqrt {E\left( {{\tau ^2}} \right) - {{\left( {\overline \tau } \right)}^2}}$ (8)

 $\left\{ {\begin{array}{*{20}{c}} {E\left( {{\tau ^2}} \right) = \dfrac{{\displaystyle\sum\limits_k {h_k^2\tau _k^2} }}{{\displaystyle\sum\limits_k {h_k^2} }} = \dfrac{{\displaystyle\sum\limits_k {P\left( {{\tau _k}} \right)\tau _k^2} }}{{\displaystyle\sum\limits_k {P\left( {{\tau _k}} \right)} }}} \\ {\overline \tau = \dfrac{{\displaystyle\sum\limits_k {h_k^2{\tau _k}} }}{{\displaystyle\sum\limits_k {h_k^2} }} = \dfrac{{\displaystyle\sum\limits_k {P\left( {{\tau _k}} \right){\tau _k}} }}{{\displaystyle\sum\limits_k {P\left( {{\tau _k}} \right)} }}} \end{array}} \right.$ (9)

3.2 散射簇到天线距离分布

3.3 算法复杂度分析

 图 9 散射簇到天线距离概率分布

 图 10 Berg递归模型和UTD的性能对比

4 结语

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