基于分布式空時(shí)干擾對(duì)齊的MIMO干擾信道自由度研究

應(yīng)騰達(dá)，馮文江，蔣衛(wèi)恒，劉國(guó)嶺，姚楚楠，包濤濤

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基于分布式空時(shí)干擾對(duì)齊的MIMO干擾信道自由度研究

應(yīng)騰達(dá)，馮文江，蔣衛(wèi)恒，劉國(guó)嶺，姚楚楠，包濤濤

（重慶大學(xué)通信工程學(xué)院，重慶 400044）

針對(duì)個(gè)用戶MIMO干擾信道（IC），研究基于分布式空時(shí)干擾對(duì)齊（DSTIA）的信道可達(dá)自由度。利用分布式當(dāng)前和過(guò)期發(fā)射端信道狀態(tài)信息（CSIT）設(shè)計(jì)預(yù)編碼，分別給出MISO系統(tǒng)可達(dá)自由度關(guān)于CSI反饋時(shí)延和反饋頻率的折中域；分析發(fā)射端天線數(shù)對(duì)MISO系統(tǒng)可達(dá)自由度的影響，導(dǎo)出逼近系統(tǒng)自由度外界的條件。進(jìn)一步研究MIMO系統(tǒng)接收端天線數(shù)對(duì)系統(tǒng)自由度的影響，給出保持系統(tǒng)可達(dá)自由度的CSI反饋時(shí)延范圍。理論和數(shù)值分析表明，所提DSTIA方案能充分消除用戶間干擾，獲得更高的自由度增益，縮小可達(dá)界與外界的差距，提高系統(tǒng)的可達(dá)速率。

自由度；分布式空時(shí)干擾對(duì)齊；MIMO干擾信道；CSI有限反饋

1 引言

2 系統(tǒng)模型

2.1 K個(gè)用戶MIMO IC模型

個(gè)用戶MIMO IC可看成是多小區(qū)蜂窩鏈路間干擾的抽象。例如，個(gè)用戶MISO IC是個(gè)鄰近小區(qū)下行鏈路用戶間干擾的抽象。如圖1所示，個(gè)用戶MIMO IC由對(duì)發(fā)射—接收節(jié)點(diǎn)組成。發(fā)射端配置根天線，接收端配置根天線，。每個(gè)發(fā)射端僅向相應(yīng)的接收端發(fā)送單一信息。其信號(hào)模型為

圖1 K個(gè)用戶MIMO IC模型

2.2 CSI反饋模型

假設(shè)接收端（用戶）執(zhí)行預(yù)定的周期性反饋協(xié)議將CSI反饋給發(fā)射端。周期性反饋協(xié)議可以通過(guò)控制信號(hào)實(shí)現(xiàn)，適用于當(dāng)前主流的蜂窩移動(dòng)通信標(biāo)準(zhǔn)，如3GPP LTE[22]。分別考慮2個(gè)導(dǎo)致CSIT時(shí)延的因素——反饋時(shí)延和反饋頻率[1]。

其中，為瞬時(shí)（instantaneous）CSIT；為適當(dāng)延時(shí)（temperately-delayed）CSIT；為完全延時(shí)（completely-delayed）CSIT。發(fā)射端在時(shí)隙可用的本地CSI記為，這里，。因此，發(fā)射端的發(fā)送信號(hào)向量可看作是發(fā)送信息與本地延時(shí)CSIT的函數(shù)，即，為發(fā)射端的預(yù)編碼函數(shù)。

2.3 自由度

相應(yīng)地，個(gè)用戶MIMO IC在本地CSIT下的總自由度定義為

3 K個(gè)用戶MISOIC的自由度折中域

3.1 分布式空時(shí)干擾對(duì)齊

此時(shí)，各接收端觀測(cè)到一個(gè)期望信號(hào)與干擾信號(hào)疊加的線性方程。

其中，表示從中選取對(duì)應(yīng)中剩余個(gè)未知數(shù)的列組成的方陣，表示去除零元素后剩余未知元素按相對(duì)位置排序的矢量。由于信道系數(shù)的獨(dú)立同分布特性，此時(shí)，每列求解出的未知元素以概率1不為0。

3.2 自由度折中域

3.2.1 反饋時(shí)延受限自由度折中域

圖5 K個(gè)用戶MISO（）IC關(guān)于反饋時(shí)延的自由度折中域

3.2.2 反饋頻率受限自由度折中域

圖6 個(gè)用戶MISO（）IC關(guān)于反饋頻率的自由度折中域

4 K個(gè)用戶MIMO IC的可達(dá)自由度

4.1 可達(dá)自由度

證明類似定理1，采用DSTIA方案獲取定理2的可達(dá)自由度。此時(shí)，式(12)可表示為

4.2 CSI有限反饋條件

圖7 最大(小)歸一化CSI反饋時(shí)延(頻率)隨接收端天線數(shù)N的變化

5 數(shù)值分析

表1 K個(gè)用戶M×1(M≥1) MISO IC不同方案下的總自由度

圖8 用戶平均可達(dá)自由度隨總體用戶數(shù)K的變化情況

2) 信道和速率

圖9 3個(gè)用戶MIMO IC天線數(shù)與平均吞吐率的關(guān)系

3) CSI有限反饋條件

圖10 3個(gè)用戶MIMO IC可達(dá)自由度折中域

6 結(jié)束語(yǔ)

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Degrees of freedom of MIMO interference channel with distributed space-time interference alignment

YING Tengda, FENG Wenjiang, JIANG Weiheng, LIU Guoling, YAO Chunan, BAO Taotao

College of Communication Engineering, Chongqing University, Chongqing 400044, China

In the context of-user MIMO interference channel (IC), achievable degrees of freedom (DoF) were investigated with distributed space-time interference alignment (DSTIA). By precoding with distributed current and outdated channel state information at the transmitters (CSIT), new tradeoff regions between achievable DoF and CSI feedback delay/frequency were achieved for MISO system. The impact of the number of transmit antennas on achievable DoF in the MISO system was analyzed, revealing that DoF results approach to the outer bound as the number of transmit antennas increases. Further, the impact of the number of receive antennas on achievable DoF was characterized, deriving the range of CSI feedback delay that preserves achievable DoF in the MIMO system. Theoretical and numerical analyses show that, the proposed DSTIA scheme can achieve better sum-DoFs by eliminating inter-user interference perfectly, tighten the gap between achievable DoF and outer bound, as well as improve the achievable rate of the system.

degree of freedom, distributed space-time interference alignment, MIMO interference channel, limited CSI feedback

TN919.1

A

2017-05-24；

2017-10-30

應(yīng)騰達(dá)，tengdaying@cqu.edu.cn

中央高?；究蒲袠I(yè)務(wù)費(fèi)基金資助項(xiàng)目（No.106112016CDJXY500002）；重慶市基礎(chǔ)科學(xué)與前沿技術(shù)研究重點(diǎn)基金資助項(xiàng)目（No.cstc2017jcyjBX0047, No.cstc2015jcyjA40021）

10.11959/j.issn.1000-436x.2018017

應(yīng)騰達(dá)（1991-），男，浙江永康人，重慶大學(xué)博士生，主要研究方向?yàn)镸IMO無(wú)線通信、信息論等。

馮文江（1963-），男，四川西充人，重慶大學(xué)教授、博士生導(dǎo)師，主要研究方向?yàn)閷拵o(wú)線接入技術(shù)、認(rèn)知無(wú)線電、通信信號(hào)處理等。

蔣衛(wèi)恒（1985-），男，湖北枝江人，重慶大學(xué)講師，主要研究方向?yàn)闊o(wú)線通信與網(wǎng)絡(luò)、移動(dòng)云計(jì)算等。

劉國(guó)嶺（1989-），男，遼寧北票人，重慶大學(xué)碩士生，主要研究方向?yàn)镸IMO無(wú)線通信、全雙工等。

姚楚楠（1994-），男，湖南婁底人，重慶大學(xué)碩士生，主要研究方向?yàn)镸IMO無(wú)線通信、移動(dòng)邊緣計(jì)算等。

包濤濤（1993-），男，湖北孝感人，重慶大學(xué)碩士生，主要研究方向?yàn)镸IMO無(wú)線通信、圖像處理等。

: The Fundamental Research Funds for the Central Universities (No.106112016CDJXY500002), The Key Project of Chongqing Basic Science and Advanced Technology Research (No.cstc2017jcyjBX0047, No.cstc2015jcyjA40021)