MIMO波束成型系统的干扰对齐技术分析

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一种多用户MIMO系统干扰对齐优化算法

CHEN Yan1,2 ,SONG Yunchao1
(1. College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications,Nanjing 210003,China; 2. College of Electronic and Optical Engineering,
一种多用户 MIMO 系统干扰对齐优化算法*
陈摇艳**1,2 ,宋云超1
(1. 南京邮电大学电子与光学工程学院、微电子学院,南京 210003; 2. 南京理工大学紫金学院电子工程与光电技术学院,南京 210046)
摘摇要:干扰对齐技术可以获得干扰信道自由度的最佳值,从而有效改善系统的性能。在实际系统中干扰对齐技术通常采用迭代的方法进行预编码矩阵与干扰抑制矩阵的设计,而迭代方法都需要对发送预编码矩阵进行初始化处理。然而,目前大多数已有的研究所采用的初始化处理方法都忽略了干扰的影响。因此,在此基础上提出了一种基于新的初始化方法的优化算法,该方法在初始化预编码矩阵中既考虑了干扰信号也考虑了有用信号。首先,选取均方误差和最小化作为优化目标,然后利用正交三角( QR) 分解将信道空间分为有用信号空间与干扰信号空间来进行预编码矩阵的初始化设计,经过反复迭代得到发送预编码矩阵与干扰抑制矩阵的最优解。理论分析和仿真结果表明,所提算法在收敛性、均方误差、和速率等方面都优于其他算法。关键词:MIMO 干扰信道;干扰对齐;迭代算法;预编码初始化
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MIMO干扰信道下的协作干扰对齐优化算法

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MIMO系统干扰对齐相关技术及标准X信道分解方案研究的开题报告

MIMO系统干扰对齐相关技术及标准X信道分解方
案研究的开题报告
本文旨在介绍MIMO系统干扰对齐相关技术及标准X信道分解方案研究的开题报告。

MIMO（Multi-Input Multi-Output）是一种用于无线通讯系统中的技术，它利用多个天线进行数据传输，可以提高系统吞吐量和可靠性。

在MIMO系统中，由于信号传输的复杂性，会产生各种干扰。

为了减小干扰，提高系统性能，研究人员提出了干扰对齐技术。

干扰对齐是指利用多个天线对接收到的信号进行适当的处理，使各个接收天线接收到的干扰相对一致，从而减小干扰。

针对干扰对齐技术，国际电信联盟ITU-T提出了标准X信道分解方案。

该方案基于信道的特性，将信道分为多个子信道，从而实现对MIMO 系统中的干扰进行分离和对齐。

本文的研究目标是探究MIMO系统中干扰对齐相关技术以及标准X 信道分解方案的研究现状和发展趋势，并提出一些改进措施。

通过分析相关文献和实验数据，本文将研究干扰对齐的原理和方法，并对标准X 信道分解方案进行评估和改进以提高系统性能。

最后，本文将总结研究结果，提出未来进一步研究的方向。

MIMO雷达参数估计与抗干扰方法研究

MIMO雷达参数估计与抗干扰方法研究MIMO雷达参数估计与抗干扰方法研究摘要：传统的雷达系统在复杂环境下容易受到干扰的影响，从而影响雷达系统的性能。

近年来，多输入多输出（MIMO）雷达技术已经受到广泛关注，并被证明在提高雷达系统性能方面具有潜力。

本文通过对MIMO雷达参数估计与抗干扰方法的研究，探讨了其在复杂环境下的应用。

一、引言雷达系统是一种广泛应用于武器系统、民航和天气预报等领域的关键技术。

然而，受到天气、地形以及其他人造和自然干扰的影响，传统雷达系统的性能容易受到一定程度的限制。

因此，研究MIMO雷达参数估计与抗干扰方法，对于提高雷达系统的性能具有重要意义。

二、MIMO雷达参数估计1. 频率偏移补偿在传统雷达系统中，频率偏移是一个重要的参数，其导致雷达接收信号的频率与期望频率之间存在差异。

为了准确估计目标的距离和速度等参数，需要对这种频率偏移进行补偿。

MIMO雷达系统通过同时发送多个独立的信号，并利用多个接收天线接收回波信号，可以采用多种估计算法来提高频率偏移的估计精度。

2. 目标角度估计在雷达系统中，准确估计目标的角度是实现目标跟踪和定位的关键。

MIMO雷达系统通过在不同的发射天线和接收天线之间形成不同的天线阵列结构，可以利用多普勒效应以及时延差等特征来实现目标角度的估计。

通过使用MIMO雷达系统，可以提高目标角度估计的精度和可靠性。

三、MIMO雷达抗干扰方法1. 自适应波束形成自适应波束形成是一种通过优化发射波束和接收波束来抑制干扰的方法。

MIMO雷达系统由于具有多个发射和接收天线，可以通过调整各个天线之间的相位和幅度来实现更精确的波束形成。

通过自适应波束形成，MIMO雷达系统可以抑制不同方向上的干扰信号，提高目标的检测和定位精度。

2. 频率偏移校正频率偏移是另一个常见的干扰源，其导致接收到的信号频率与期望频率之间存在差异。

为了准确估计目标的距离和速度等参数，需要对频率偏移进行校正。

MIMO雷达系统可以通过利用多颗星座图或利用频谱的对称特点来进行频率偏移的校正。

基于MIMO系统的干扰对准技术研究

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在富散射环境中，平衰落ＭＩＭＯ信道可由时变的复高斯系数矩阵表示嘲．了表述简明，文的符号中均略为本
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如时分多址（ＤＴＭＡ）频分多址（ＤＭＡ），、Ｆ等则每个用户所能占用的信道资源仅为１／Ｋ．干扰对准技术（ｎＩ—

MIMO干扰网络中基于有限反馈的干扰对齐研究.doc

MIMO干扰网络中基于有限反馈的干扰对齐研究干扰是多用户无线通信系统吞吐量提升的基本障碍。

近年来,无线网络在全局、瞬时发射端信道状态信息(CSIT:channel state information at the transmitter)条件下的干扰对齐(IA:interference alignment)已取得重大研究进展。

然而,CSIT的严格约束使得实际通信系统难以获得理论自由度(DoF:degrees of freedom)增益,尤其是在CSIT受限的分布式网络中,自由度增益只有盲CSIT水平。

一个疑问是,有限CSIT能否提升分布式干扰网络的自由度增益?本文以多天线技术为基础,通过刻画自由度与有限CSIT之间的折中关系,深入研究多输入多输出(MIMO:multiple input and multiple output)广播信道(BC:broadcast channel)、X信道、干扰信道(IC:interference channel)的干扰对齐技术,主要研究内容和创新贡献概括如下:(1)针对对称天线配置下的2?2用户MIMO X信道,探寻CSI反馈时延与系统可达自由度之间的折中域。

首先,研究2?2用户MISO X 信道的可达自由度,提出一种分布式预编码方案。

其次,针对2?2用户MIMO X信道,提出一种基于适当延时CSIT的分布式空时干扰对齐(DSTIA)方案,利用循环填零预编码,给出多天线配置下可达自由度关于CSI反馈时延的折中域,对比分析不同方案下获得的信道可达自由度和可达速率。

结果表明,相比于仅利用过期CSIT的干扰对齐方案,该方案能获得更高的自由度。

进一步,从交替CSIT角度,提出一种基于交替CSIT的DSTIA方案,研究不同天线配置下的系统可达自由度。

结果表明,交替CSIT与适当延时CSIT具有等效性,适用于分布式CSIT体系。

(2)针对M?N用户MIMO X网络,研究多节点、多天线配置下的系统可达自由度和干扰对齐方案。

MIMO系统中的信号干扰抑制方法研究

MIMO系统中的信号干扰抑制方法研究摘要：多输入多输出（MIMO）系统被广泛应用于无线通信领域，以提高系统的容量和可靠性。

然而，在MIMO系统中，信号干扰成为限制系统性能的主要问题之一。

因此，研究MIMO系统中的信号干扰抑制方法具有重要的理论和实际意义。

本文针对MIMO系统中的信号干扰问题，探讨了一些主要的信号干扰抑制方法，包括空间信号处理、预编码技术以及干扰对消方法，并分析了它们的工作原理和应用情况。

1. 引言随着无线通信技术的飞速发展，高速、高容量的通信系统受到了广泛关注。

MIMO技术作为一种有效提高系统容量和可靠性的技术，已经被广泛应用于4G和5G系统中。

然而，由于天线之间的相互干扰，MIMO系统面临着严重的信号干扰问题。

因此，研究MIMO系统中的信号干扰抑制方法变得尤为重要。

2. 空间信号处理方法空间信号处理是一种基于天线阵列的信号处理方法，通过将信号经过天线阵列进行加权、组合，以达到抑制干扰的目的。

最常见的空间信号处理方法包括波束形成、最大比合并（MRC）、相位调控等。

2.1 波束形成波束形成是一种通过调整天线阵列的权值，使得天线阵列在期望信号的方向上形成一个波束，从而增强期望信号的强度，抑制干扰信号的方法。

波束形成方法有线性等，其中线性波束形成最为常见。

例如，利用线性波束形成可以实现空间滤波，在特定方向上对信号进行增强。

2.2 最大比合并（MRC）最大比合并方法通过采集多个接收天线的信号，并分别经过放大和相位调整后，将它们以最大的比例进行合并。

最大比合并方法能够在接收到多个信号的同时，最大程度地提高期望信号的强度并抑制干扰信号。

2.3 相位调控相位调控方法通过调整各个天线上信号的相位差，使得期望信号相位相加增强，而干扰信号相位相消。

相位调控方法能够有效地抑制多径干扰，提高系统的抗干扰性能。

3. 预编码技术预编码技术是一种基于空间域的信号预处理技术，通过提前将数据进行编码再发送，以抑制干扰并提高系统性能。

一种多用户MIMO系统干扰对齐优化算法

一种多用户MIMO系统干扰对齐优化算法陈艳;宋云超【摘要】干扰对齐技术可以获得干扰信道自由度的最佳值,从而有效改善系统的性能.在实际系统中干扰对齐技术通常采用迭代的方法进行预编码矩阵与干扰抑制矩阵的设计,而迭代方法都需要对发送预编码矩阵进行初始化处理.然而,目前大多数已有的研究所采用的初始化处理方法都忽略了干扰的影响.因此,在此基础上提出了一种基于新的初始化方法的优化算法,该方法在初始化预编码矩阵中既考虑了干扰信号也考虑了有用信号.首先,选取均方误差和最小化作为优化目标,然后利用正交三角(QR)分解将信道空间分为有用信号空间与干扰信号空间来进行预编码矩阵的初始化设计,经过反复迭代得到发送预编码矩阵与干扰抑制矩阵的最优解.理论分析和仿真结果表明,所提算法在收敛性、均方误差、和速率等方面都优于其他算法.【期刊名称】《电讯技术》【年(卷),期】2018(058)007【总页数】7页(P785-791)【关键词】MIMO干扰信道;干扰对齐;迭代算法;预编码初始化【作者】陈艳;宋云超【作者单位】南京邮电大学电子与光学工程学院、微电子学院,南京210003;南京理工大学紫金学院电子工程与光电技术学院,南京210046;南京邮电大学电子与光学工程学院、微电子学院,南京210003【正文语种】中文【中图分类】TN929.51 引言作为第四代蜂窝移动通信系统的关键技术之一，多输入多输出(Multiple-Input Multiple-Output，MIMO)技术在不增加系统带宽和天线发射功率的前提下可以显著提高信道的容量及频谱利用率[1]。

单用户MIMO系统若配置的天线数受限会降低系统获得的容量增益，而多用户MIMO系统允许多个用户同时进行通信，可达到更高的容量，但当天线数目及用户数量增加时会引起无线介质的广播与叠加，此时干扰成为制约多用户MIMO系统可靠通信的重要因素之一[2]。

因此，为了改善系统的性能，需要采用有效的措施对用户引起的干扰进行管理。

MIMO系统中波束成形和检测器技术的研究的开题报告

MIMO系统中波束成形和检测器技术的研究的开题报告标题：MIMO系统中波束成形和检测器技术的研究背景介绍：随着无线通信技术的迅速发展，MIMO系统的应用越来越广泛。

MIMO系统通过利用多个天线和信道的多样性，可以提高数据传输的速率和可靠性。

波束成形和检测器技术是MIMO系统中非常重要的技术，能够进一步提高传输速率和可靠性，减少多径干扰，增强信号的捕获能力，提供更好的无线信号覆盖范围。

研究目的：本研究旨在通过对MIMO系统中波束成形和检测器技术的研究，探索如何有效提高MIMO系统的传输速率和可靠性，减少多径干扰，增强信号的捕获能力，提高无线信号的覆盖范围。

具体目标包括：1. 分析MIMO系统的波束成形和检测器技术，探究其原理和特点；2. 研究MIMO系统中不同波束成形和检测器算法的性能比较，探索其优缺点；3. 基于理论分析和仿真实验，优化设计和评估MIMO系统中的波束成形和检测器算法，提高其传输速率和可靠性；4. 实现所提出的波束成形和检测器算法，并在实际应用中评估其效果。

研究内容：本研究主要分为以下部分：1. MIMO系统的基础理论知识，包括MIMO理论，波束成形和检测器技术的原理和基本算法；2. 学习和掌握常用的波束形成算法和检测器，包括最大比合并检测器、SIC检测器、ZF检测器等；3. 设计和实现MIMO系统中的波束成形和检测器算法，并使用Matlab等工具进行仿真实验；4. 对比不同波束成形和检测器算法的性能，评估其优缺点；5. 通过仿真实验和实际应用，验证所提出的波束成形和检测器算法的效果。

研究意义：本研究的主要意义在于：1. 深入研究和探究MIMO系统中波束成形和检测器技术的原理和应用，提高对MIMO系统的理解和掌握；2. 通过对比不同波束成形和检测器算法，分析其性能差异，为实际应用提供参考；3. 通过优化和设计波束成形和检测器算法，提高MIMO系统的传输速率和可靠性，减少多径干扰，增强信号的捕获能力，提供更好的无线信号覆盖范围；4. 为MIMO系统的进一步研究和应用提供可靠且有效的技术支持。

多用户M×NMIMO干扰信道的干扰对齐算法研究

2018年 / 第3期物联网技术290 引言干扰受限的多用户通信系统如认知无线系统、Ad-Hoc 系统及蜂窝无线网络均可以建模为一个干扰信道[1]。

干扰信道研究的一个重点是如何减轻多用户干扰的负面影响。

实际处理干扰的常见方法有：把干扰看成噪声但其容量不可达；信道的正交化处理导致通信资源无效使用、容量不可达；由于其复杂性与安全性，对干扰进行译码再删除的做法在现实中很少采用。

而干扰对齐[2]（Interference Alignment，IA）技术在高SNR 时总自由度可达到最大，与容量的一阶近似，它是用于多用户通信网络如K 用户干扰信道、无线X 网络、多跳干扰网络容量分析的重要工具之一。

干扰对齐的基本思想是通过协作预编码矩阵将用户间的干扰限制到一定的子空间，在接收侧通过解码矩阵恢复无干扰的期望信号。

目前的多输入多输出（Multiple Input Multiple Output，MIMO）系统干扰对齐算法主要分为基于信号空间的干扰对齐算法、基于时间维度的干扰对齐算法及基于频率维度的干扰对齐算法。

其中基于信号空间的干扰对齐算法应用最广，主要通过设计预编码矩阵，将干扰信号重叠映射到接收端特定的信号子空间，接收端通过干扰抑制矩阵解码出期望信号。

信号空间干扰对齐算法的重点是设计发送预编码矩阵，实现 IA 的预编码方法通常分为迭代法和非迭代法两类。

尽管干扰对齐在干扰网络中能获得较好的性能，但很难获得其闭式解，特别当网络用户数较多时是一个开放性问题，因此，当前很多研究工作关注于设计一些低计算复杂度的迭代算法[3,4]。

在干扰网络中有两个著名的迭代算法，即最小干扰泄露算法及最大信噪比算法[3]。

最小干扰泄露算法利用信道的互易性[3]，在原始网络通过最小化接收侧泄露的干扰得到接收侧的干扰抑制矩阵，然后在互易网络中最小化发射侧泄露的干扰，更新发射侧的预编码矩阵。

非迭代法通过直接求解得到干扰对齐预编码矩阵与干扰抑制矩阵的闭式解。

MIMO干扰信道中联合功率分配和干扰对齐算法研究.doc

MIMO干扰信道中联合功率分配和干扰对齐算法研究随着移动通信的普及和广泛应用,用户在生活中更多的通过移动终端来接入网络,再加上频谱是极为有限的资源,这就给系统容量带来巨大挑战。

MIMO系统在发送功率和系统带宽不增加的情况下可以大幅度的提高系统的频谱利用率,但随之而来的就是频谱共享带来的多用户间的干扰问题。

干扰管理技术中的一种叫做干扰对齐的技术,比传统干扰管理技术性能更好,成为移动通信领域研究的热点。

本文首先对MIMO系统和干扰对齐技术中的基本概念进行介绍,给出了时域、频域、空域下干扰对齐的实现方式。

接着介绍了最大化信干噪比、最小化加权干扰泄露、最小均方误差及交替最小化四种分布式干扰对齐算法。

之后对K用户MIMO干扰网络进行深入研究,经典干扰对齐方案中忽略了有用信号所经历的信
道环境,系统容量没有达到最优。

针对这一问题,给出一种基于SVD分解的预编码矩阵优化方法,该方法通过对信道矩阵作SVD分解,根据信道增益特性选出最优的特征子信道,然后在矩阵弦距离准则的基础上,选取与最优特征子信道最为匹配的预编码矩阵,从而使得接收端信号强度和系统容量得到显著改善。

最后,针对传统干扰对齐技术没有考虑功率分配的缺陷而造成系统资源没有得到充分利用的情况,给出一种联合功率分配和干扰对齐算法,该算法在交替最小化算法的基础上引入改进的注水功率分配算法,给发射端的数据流分配功率,此算法既可以利用干扰对齐技术来消除干扰,又可以通过改进的注水功率分配算法来提高系统的总吞吐量,通过仿真比较所提算法与等功率分配时的交替最小化干扰对齐算法的系统性能,显示出所提算法有效地提高了系统吞吐量且降低了总干扰功率。

MIMO无线通信系统中干扰抑制技术研究

MIMO无线通信系统中干扰抑制技术研究随着无线通信技术的不断发展和普及，多输入多输出（MIMO）成为了提高无线通信系统容量和性能的重要技术。

然而，在MIMO系统中，由于多个天线之间的相互干扰，系统性能可能会受到严重影响。

因此，研究MIMO无线通信系统中的干扰抑制技术变得至关重要。

干扰抑制技术在MIMO系统中的意义在于通过降低或消除天线之间的干扰来提高系统容量和可靠性。

在干扰抑制技术的研究中，可以采用空时编码技术、波束成形技术、干扰消除技术等手段来实现。

首先，空时编码技术是一种MIMO系统中常用的干扰抑制技术。

在空时编码技术中，发送端通过在多个天线上发送不同编码的数据流，接收端通过接收和解码并消除多个天线接收到的信号中的干扰。

通过合理设计和选择编码方式，可以最大程度地降低干扰对系统性能的影响。

其次，波束成形技术也是一种有效的干扰抑制技术。

波束成形技术通过调整天线的发射和接收方向性，使得系统能够更好地集中能量，并减少对其他方向的干扰。

这种技术可以通过使用自适应干扰抑制算法来实现，从而自动调整天线的方向和波束形状，以最小化干扰信号的影响。

再次，干扰消除技术是一种通过处理接收信号来抑制干扰的重要方法。

这种技术可以通过均衡器、滤波器等方法对接收信号进行处理，减小多个天线之间的干扰。

同时，干扰消除技术可以结合自适应信号处理算法，根据系统的变化实时调整处理参数，提高系统的性能和容量。

除了以上三种常见的干扰抑制技术，还有其他一些新兴的技术正在被研究和应用于MIMO无线通信系统中。

例如，基于机器学习的干扰预测和抑制技术可以通过学习干扰模型和预测干扰信号的特征来降低干扰对系统的影响。

此外，使用频谱感知技术和分布式功率控制技术也可以在MIMO系统中实现干扰抑制和资源优化。

总结而言，MIMO无线通信系统中的干扰抑制技术研究对于提高系统容量和性能具有重要意义。

通过空时编码技术、波束成形技术、干扰消除技术等手段，可以有效降低或消除天线之间的干扰。

多用户MIMO系统中分布式迭代干扰对齐研究

多用户MIMO系统中分布式迭代干扰对齐研究叶宗刚;赵迎芝;黄祥【摘要】干扰是无线通信网中亟待解决的问题之一,针对多用户MIMO系统,结合最新的分布式算法,总结并比较了几种分布式迭代算法的复杂度以及能够实现的最大系统自由度.不同于两用户的MIMO X信道可以直接得到干扰对齐预编码矩阵,利用了信道互易性的分布式迭代算法能够很好地解决由于用户数和约束条件的增加造成干扰对齐预编码矩阵可能无解的问题.最后仿真验证了分布式迭代算法的有效性.【期刊名称】《北京联合大学学报（自然科学版）》【年(卷),期】2016(030)004【总页数】5页(P48-52)【关键词】无线通信;多输入多输出;干扰对齐;分布式迭代算法【作者】叶宗刚;赵迎芝;黄祥【作者单位】重庆邮电大学移动通信技术重点实验室,重庆400065;重庆邮电大学移动通信技术重点实验室,重庆400065;重庆邮电大学移动通信技术重点实验室,重庆400065【正文语种】中文【中图分类】TN926近年来多媒体业务和宽带因特网业务迅速发展，无线用户数量快速增长，人们对无线数据传输业务的要求越来越高。

由于频谱资源的有限性，如何在有限的频谱资源下获得更髙的频谱利用率，使未来无线通信系统具有更高的容量、更好的可靠性，成为当今无线通信领域的研究热点。

从20世纪末始，输入多输出(Multiple Input Multiple Output,MIMO)的多天线技术已经逐渐从理论研究转化为实际应用，并在各种无线通信系统中得到广泛的应用，有效地提高了无线传输的有效性和可靠性。

研究表明，在高信噪比信道中，信道容量随着发射天线和接收天线的数量最小值呈线性增长。

与单天线通信系统相比，在相同的带宽下MIMO系统利用空间资源不仅可以获得更大的复用增益和自由度，提高无线通信系统的传输速率，也可以获得分集增益，提高无线系统的可靠性[1-2]。

因此，多天线技术已经成为未来无线通信的关键技术。

随着通信技术的发展和用户数的快速增长，通信环境越来越复杂，传统的点对点无线通信系统正逐渐被多用户多天线系统所取代。

相控阵MIMO雷达抗干扰波束形成算法研究

相控阵 MIMO雷达抗干扰波束形成算法研究摘要：现阶段所面临的干扰环境愈加的复杂多变，在对副瓣电平实施控制的时候，相应的雷达系统需要实现更高的增益与自由度。

因此，可针对基于相控阵MIMO雷达的抗干扰波束形成算法进行研究，进而推进该领域的进一步发展。

对此，文章针对相控阵MIMO雷达抗干扰波束形成算法进行了研究。

关键词：相控阵MIMO；雷达抗干扰；波束形成算法；研究引言：在现代的通信、雷达以及导航等领域之中，都非常广泛的对相控阵MIMO进行了使用，主要由于相控阵MIMO通过相应的调整，能够实现对各个阵元的相位波束指向予以控制，可见雷达系统在电子扫描工作之中，可以作为有效的工作方式，实现对信号处理效率的改善。

1.相控阵MIMO抗干扰波束的形成分析通过相应推导算式我们能够获得相控阵MIMO的静态方向图导向矢量，进而实现对MIMO雷达系统发射端形成的零线接收端的低副瓣的有效处理。

基于超视距雷达与极低副瓣雷达之中，当方向图形成零陷对抗干扰之后，仍然需要使其始终保持低副瓣电平。

在对方向图低副瓣抗干扰波束的形成进行计算的时候，可通过一种基于改进线性约束条件下的算法实施计算，在对相控阵MIMO联合导向矢量u（θ）进行计算的时候，可通过改进线性约束条件的方式来对控制方向图副瓣电平体与零线进行兼顾，后者则需要形成相应的零陷抑制干扰。

通过想应计算式的对比，发现要想使兼顾低副瓣与抗干扰性能，就需要保证低副瓣窗函数与约束矩阵之间具有较高的匹配性。

（ win）H cnew=⑴记 = win，并实现 =（H）-1H，进而构造出相应新的协方差矩阵得到满足：=（I-）Rx（I-）Rx = u（θi）u H（θi）⑵其中酉矩阵是其理想协方差矩阵Rx,并且我们能够从中发现（I-）H=（I-），这也证明了阵矩Rx至属于有相似变换关系，所以两者的特征值是相等的，其中所包含的特征矢量信息也是相等的。

又因为H =0，所以当的特征向量成为新约束阵矩时，那么低副瓣权矢量是可以使式(1)得到满足的。

MIMO感知网络中多主用户的干扰对齐算法研究的开题报告

MIMO感知网络中多主用户的干扰对齐算法研究的开题报告一、选题背景在现代通信系统中，为了满足更高的数据传输速率和更低的误码率要求，多天线技术被广泛应用于无线通信系统中。

多输入多输出（MIMO）技术是其中的主要技术之一。

MIMO技术通过利用空间多样性来增加信道容量，并且可以提高系统的性能和可靠性。

然而，在多用户的MIMO系统中，多个用户之间互相干扰，影响了系统的性能。

因此，解决多用户干扰成为MIMO研究的一个重要课题。

在MIMO通信中，由于某些用户同时传输有干扰信号，干扰成为系统中主要的问题之一。

因此，研究如何有效地减小或消除干扰成为了MIMO技术研究的一个重要方向。

针对多用户干扰问题，近年来提出了许多解决方案，其中干扰对齐算法成为了其中比较经典的算法。

二、研究目的本次研究的目的是对干扰对齐算法在MIMO感知网络中的应用进行探究。

通过对干扰对齐算法的研究，能够实现多用户之间干扰的有效减小或消除，从而提高系统性能和可靠性。

同时，研究得出可行的干扰对齐算法方案，能够为MIMO技术的发展提供有力支撑。

三、研究内容本次研究的主要内容包括以下两个方面：1. 针对多用户干扰问题，研究干扰对齐算法的基本原理和应用场景。

通过对干扰对齐算法进行深入研究，了解其在MIMO系统中的应用。

2. 基于干扰对齐算法，设计适用于MIMO感知网络中多主用户的干扰对齐算法方案。

通过实验对比，对算法的实际性能进行评估和优化。

四、研究方法1. 理论分析：通过对多用户的干扰问题进行分析和建模，研究干扰对齐算法的基本原理和应用场景。

2. 设计方案：结合干扰对齐算法的特点，设计适用于MIMO感知网络中多主用户的干扰对齐算法方案。

3. 仿真实验：通过仿真实验验证所设计算法的性能，并对算法进行优化。

五、研究预期成果1. 对干扰对齐算法在MIMO感知网络中的应用进行深入研究。

2. 设计适用于MIMO感知网络中多主用户干扰对齐的算法方案，评估算法的实际性能和优化算法。

多载波MIMO系统的干扰对齐

Interference Alignment Scheme for DownlinkMulti-carrier MIMO Cellular Systems *Jie YANG 1,＊，Rongfang SONG 1,2and Heng DONG 11College of Telecommunications and Information Engineering, Nanjing University of Posts andTelecommuications, Nanjing 210003,China2National Mobile Communications Research Laboratory Southeast University, Nanjing 210096, ChinaAbstractIn this paper ，we propose a practical interference alignment （IA ） scheme for the downlink cellular systems with multi-carrier transmission over multi-input-multi-output （MIMO ） channels, where the interference is decompounded into two parts (inter-cell and intra-cell interference). IA is used to effectively mitigate inter-cell interferences, while the intra-cell interference is suppressed by subcarrier allocation so that some spatial degrees of freedom are released. Assuming L Base stations each with M antennas and K users (having N antennas), we present that a necessary condition for zero inter-cell interference is 1)(-≤-M K N L . In contrast, for a single-carrier MIMO cellular networks, the corresponding condition is known to be 1N M LK +≥+, which does not hold usually. An iterative optimization algorithm for the proposed scheme is given, and numerical results show that the proposed scheme achieves a high spectral efficiency when the number of users is large and the number of transmit and receive antennas is limited.Keywords: Interference alignment, MIMO, multi-carrier, necessary condition, cellular system1 IntroductionRecently, there are intense research interests in the area of interference networks and cellular systems[1]-[18]. In [1] it was shown that the capacity of the interference channel in fading environment is much higher than previously believed. More precisely, regardless of the number of interferers, the d.o.f (degrees of freedom) for the K-user interference channel is /2K assuming independent and identically distributed (i.i.d) parallel channels. The coding scheme in this system that achieves the optimal d.o.f has been based on interference alignment (IA) algorithm. Interference alignment techniques in [2] consisted in separating all interferences from the useful received signal by gathering them into a given subset. IA cooperatively aligns interfering signals over time, space, or frequency dimensions. For multi-input-multi-output interference channels, IA in [3] and [4] has*This work was supported by Graduate Innovation Program()National Natural Science Foundation of China (No. 61271234); Ph.D. Program Foundation of Ministry of Education (No.20123223110002); Open Research Foundation of National Mobile Communications Research Laboratory,Southeast University and Graduate Innovation Program (CXLX12_0472 ).＊Corresponding author.Email address: jyang@ (Jie YANG)aligned all interference signals in the same physical direction, and completely separated those signals from the useful signal.However, the result in [1] is not enough to apply to cellular systems since the channel itself is different. In [5], the d.o.f was found for X-networks which were very similar to cellular networks. The downlink or uplink of a cellular system was seen as multiple mutually interfering broadcast or access channels, respectively, which was interpreted as a special case of the X-network. Recently, a great deal of research has been conducted to find the interference alignment techniques of the cellular systems. The interference alignment schemes for cellular networks were proposed in [6]-[14], termed space interference alignment and frequency interference alignment. MIMO space interference alignment which was first considered in [6] achieved full orthogonalization between the desired user and interference ones. Based on [15] and [16], two distributed interference algorithms for cellular systems were deduced in [10] and [11]. Frequency interference alignment is utilized to enable frequency-domain precoding over parallel subcarriers. A practical approach to “best -effort” interference alignment was investigated in [17] in multi-user orthogonal frequency division multiplexing (OFDM) systems with limited SNR and limited dimensionality. In [18]，the necessary condition for zero interference and the solutions sampling the best out of L aligned solutions were presented for multi-carrier interference alignment networks. Interference alignment based multi-cell cooperative resource allocation was studied in [13] and [14] for the uplink and downlink multi-carrier systems respectively. In [14], the joint optimization of frequency-domain precoding via IA, user subcarrier seletion and power allocation was investigated for three-cell cooperative multi-carrier systems to maximize the downlink throughput.In this paper, we propose a hybrid scheme for the downlink multi-carrier MIMO cellular systems to solve the problem of finite dimensions in space and frequency domain. The hybrid scheme in this paper works for general L cell multi-carrier MIMO interference channels with each base station equipped with M antennas and each user equipped with N antennas. To handle the increased number of interferences from multiple cells efficiently, the space based IA scheme aligns the inter cell interferences on space domain and all users in each cell are separated by different subcarrier sets. Based on this scheme, we derive a feasible condition for zero interference in such a cellular system. The rest of the paper is organized as follows. The system model is first introduced in Section 2 . Then in Section 3 , we determine the feasible condition for a cellular system based on interference alignment algorithms. In Section 4, we derive the IA algorithm in multi-carrier MIMO cellular systems using the up-down duality given in [19]. Section 5 provides numerical evaluations and compares the proposed interference alignment scheme with other methods in terms of spectral efficiency. Finally, Section 6 concludes the paper.The following notations are used in the paper. Bold upper and lower case letters denote matrices and vectors, respectively, and ()H⋅denote the matrix conjugate transpose.2 System ModelWe consider a cellular system with L base stations equipped with M antennas. Each base station exclusively provides wireless services to K users each equipped with N antennas. In this cellular system all users share the same frequency band for simultaneous transmission based on OFDMA with T subcarriers. The users set in cell b is denoted as b B , with b 0l B B =, if b l ≠.The signals from L BSs reach the LK users. Since only one signal from BS l is intended to user k , other remaining signals are the interferers for user k in cell l . The solide line and dashed lined in Fig.1 depicts the desired and interfering channels respectively with three cells.Without loss of generality, we consider the baseband received signal for user k in cell l at subcarrier n , which is given by][][][][][][,1][][,][][,,n n n n n n k l Llb b b b kl l l kl k l n x Ηx H y ++=∑≠= ][][][][][,1][][,',']['][,][][,n n n n n k l Llb b b b kl kk B k l k l kl l kl k l l n x H x Hx H +++=∑∑≠=≠∈ (1)where [],[]b N Ml k n C⨯∈H is the downlink baseband channel response from BS b to user k in cell l at subcarrier n with the elements drawn ...d i i from an arbitrary continuous distribution, the 1⨯M signal vector at subcarrier n , [][][][][][]l l l n n n =⋅x v s , transmitted at BS l is the information –bearing symbol for users in cell l , []1[]l M n C ⨯∈v is the space precoder that maps the subcarrier signal vector ][][n l ssignals, and ][,n k l n is theFrom (1), we can interference. We will At the receiver of user k in cell l , a space interference suppression vector ,l k u is pre-multiplied with receive signal to suppress its out-of-cell interference signals (transmitted by other base stations) , leading to the following equivalent channel model:[][][']['],,,,,,'1'[][][][][][][][]LH l l l l l k l kl k l kl k l k l l ln n n h n n h n n n =≠==++∑y U y s s n (2)where[][][].,,[][][][]l H l l l k l k l k h n n n n =u H v (3)['][']['].,,[][][][]l H l l l k l k l k h n n n n =u H v ,'l l ≠ (4),,,[][]H l k l k l k n n =n u n (5)When the out-of-cell interference has been aligned and nulled out, we can deduce that ['].[]0l l k h n =.From (2), the receive vector across frequency for user k in cell l can be written as[][][][],,,','ˆˆˆl l l l l k l k k l k k l k k k≠=++∑y H s H s n (6) [][][][],,,,,'','ˆˆˆl F l l F l l k l k l k k l k l k k l k k k≠=++∑y H v w H v w n (7)where [][][],,,ˆ([0],,[1])l l l T T l k l kl k diag h h T C ⨯=-∈H is the equivalent multi-subcarriers channel, thesignal vector [][],l F l k l k k =s v w is transmitted to user k in cell l , ,Fl k v is the 1⨯T frequencyprecoding matrix that maps the data stream ][l k w intended for user k in cell l into T transmit dimensions, the transmit signal of user k in cell l is power constrained such that][2][l B k l k P l≤∑∈w , and 1,ˆ⨯∈T k l C n is equivalent Gaussian noise.Let 1,F T l k C⨯∈u be the frequency receive filter used at user k in cell l to recover the signal transmitted by base station l , then the vector of estimated symbols for user k in cell l is()[],,ˆHl F k l k l k =wu y (8) In this system, we assume perfect functioning of the carrier chan nel estimation andsymbol timing synchronization modules.In this section, we utilize the space precoder []l v at base station l and space receive filters ,l k u for user k in cell l to suppress inter-cell interferences. The frequency precoder ,F l k v at bases s t a t i on l f or u s e r k an d f r e qu en c y r e cei ve f i l t e r s ,F l k u f or u s e r k i n c e l ll will be applied to suppress intra-cell interference.As in [10], given the set of precoders and receive filters across users in these systems ,,{,}F F l k l k v u , the signal to interference-plus-noise ratio(SINR) for user k in cell l is given by,,,,2,,,()()()()F H F l k l k l k l k F H F l kl k l kγσ=+u G u u B u (9)where the channel gain covariance matrix and the interference covariance matrix are[][],,,,,ˆˆ()l F l F H l kl k l k l k l k =G H v H v and ''',,',,',,,',,''1'1''ˆˆˆˆ()()l L Kl F l F H l F l F H l k l k l k l k l k l k l k l k l k l k B k l lk k=∈=≠≠=+∑∑∑B H v H v H v H v , respectively. And the corresponding network spectral efficiency is measured as2,11log (1)lLl k l k B C T γ∑=∈=+∑∑ (10)In order to maximize the network spectral efficiency, we would like to optimize over the set [],,,{,,,}l F F l k l k l k v u v u . The design algorithm of the transmit and receive vector will be introduced in Section 4 in detail.3 Feasibility Condition for the Hybrid SchemeIn order to determine whether cellular interference alignment can be achieved, we divide the interference suppression methods into two parts : inter-cell space interference alignment and intra-cell subcarrier-separation approach. First we derive the inter-cell interference alignment condition and thendeduce the intra-cell subcarrier selection.3.1 Inter-cell interference alignment conditionFor inter-cell space interference alignment to be achieved, the selected precoding vector [']1l M C ⨯∈v and receiving filter 1,N l k C ⨯∈u need to satisfy the following conditions:[']['],,0;'H l l l k l k l l =∀≠u H v(11) [][],,0;H l l l k l k H ≠u v(12) Condition (12) is automatically satisfied if the channel matrice do not have any special structure andt h e t r a n s mi t t e r s a n d r e c ei ve r s a r e i s o t r o p i c a l l y d i s t r i b ut e d. T h e n u mb e r of equations in (11) is defined as alignment cell -inter ,e N , which can be expressed asK L L N e )1(alignment cell inter ,-=- (13)Then we count the number of variables of this system. All variables in (11) and (12) come from the precoding and receiving filters.Because each transmit and receive filter can be scaled arbitrarily without affecting the zero forcing (ZF) condition, one variable can be eliminated from each filter []l v and ,l k u (e.g., we can set the top element to one ),such as:[]()l l l l l l l l l M l M l span span span ⎛⎫⎛⎫ ⎪ ⎪ ⎪ ⎪⎛⎫⎛⎫ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪⎪ ⎪ ⎪== ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪⎝⎭ ⎪⎝⎭⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭[]2[][]11[]2[]3[]3[]1[][][]11v v v v v v v v v v v （14) 2,11,,2,3,3,,1,,,1,1()l k l k l k l k l k l k l k l k N l k N l k l k span span span ⎛⎫⎛⎫ ⎪ ⎪ ⎪⎪⎛⎫⎛⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪== ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭ ⎪ ⎪⎪ ⎪ ⎪⎝⎭⎝⎭u u u u u u u u u u u for L l ≤≤1 (15) There are )1(-M variables provided by the each base station precoding filter from (11). And thenwe deduce the variables from the receiving filters. Each user own N antennas, so each receiving f i l t e r s c a n p r o v i d e 1-N v a r i a b l e s. T h u s , t h e t o t a l n u m b e r o f v a r i a b l e s alignment cell -iner ,v N introduced by all percoding and receiving filters is))1(1(alignment cell -iner ,-+-=N K M L N v (16)It is known that a interference network is called feasible if and only if the number of equations does not exceed the number of variables [20]. So the necessary condition for inter-cell interference zeroforcing in this cellular system ise,inter-cell alignment v,inter-cell alignment N N ≤ (17)which leads to1)(-≤-M K N L (18)3.2 Intra-cell subcarriers selectionIn each cell, each subcarrier can serve at most one user due to OFDMA, so the intra-cell interfernce is handled by orthogonal subcarriers. From last discussion, we can obtain equivalent inter-cell links atsubcarrier n from (4) as: ['][']['].,,[][][][]0l H l l l k l k l k h n n n n ==u H v ,'l l ≠. Hence, this intra-cell system can be modeled by a SISO interfering broadcast channel which contains multiple parallel channels corresponding to multi-carrier modulation. Multicarrier trans mission indicates that t he bandwidth is divide d into T e qual -si ze ba ndsindexed by },,2,1{T t =Λ∈, so that the channel matrix [],ˆl T T l k C ⨯∈H for the direct links from base station l to its user k , whose diagonal entries are the channel coefficients across subcarriers, can bewritten as[],[][][],,,[],[0]00ˆ([0],,[1])0000[1]l l k l l l l k l kl k l l k h diag h h T h T ⎡⎤⎢⎥=-=⎢⎥⎢⎥-⎣⎦H (19) where [],[]l l k h n is the equivalent downlink baseband channel response from the base station of cell l to user k in cell l at subcarrier n .In this OFDMA system, every users is orthogonal to other users in the same cell. In order to support all users without interference, the number of users should be no more than the number of subcarriers, i.e.:T K ≤ (20)Therefore for this hybrid space and frequency interference handling scheme, the number of users, c e l l s , b a s e s t a t i o n a n t e n n a s a n d s u b -c a r r e i e r s , d e n o t e d b y K ,L ,N a n d T , respectively, need to satisfy the following inequality:1)(-≤-M K N L and T K ≤ (21)Recall that the feasibility condition of the MIMO cellular system in [29] is given by1N M LK +≥+ and K M ≥ (22)In realistic networks, because the number of users is large and the number of transmit and receive antennas is limited, the condition (22) is usually violated, and zero forcing of the distributed interference alignment becomes impossible. In contrast, from (21), we can obtain that the inequality wi ll al ways hol d tr ue f or t hi s s yst e m wi th a rbitr ar y number of us er s, when the number of the cells is no more than that of the receive antennas.In [12], the partial dimensions of space domain are used to suppress the intra-cell interference, so the remaining dimensions of space are not enough to handle the inter-cell interference alignment. Here we will use orthogonal subcarriers to distinguish users in the same cell, and all the space dimensions can be used to align the inter-cell interference.4 Interference Algorithm Design in Multi-carrier MIMO Cellular SystemsIn this section, we present a hybrid algorithm for jointly optimizing the precoding and receive filters. In general, closed form solutions to interference alignment problem for this system are difficult toobtain even when the dimensionality condition for perfect alignment is satisfied. So we are motivated to consider the iterative algorithm for the optimization, requiring only local channel state information (CSI).We assume each user in each cell transmits one stream of the signal and consider the problem of optimizing the transmit precoders and receive filters. Recently, [9] and [11] respectively proposed interference alignment in a more general setup which applied to the MIMO cellular systems. In this section, we focus on the downlink of cellular system, and we apply space IA algorithms to handle the inter-cell interferences, while intra-cell interferences can be avoided by orthogonal subcarriers. In the following iterative IA algorithm minimizing inter-cell interference is discussed in detail.This algorithm first minimizes the inter-cell interference by optimizing the nth subcarrier receive subspace ,[]l k n u , and the nth subcarrier transmit subspace ,[]l k n v in space domain. Then the frequency-domain precoding vector is chosen via subcarrier scheduling for user selection. (1)Receive Subspace Optimization.The procedure of receive subspace optimization is as follows. The covariance matrices of precoding vectors at the nth subcarrier [][]l n v (L l ,1=∀) with unitary trace at each subcarrier are defined as[][][][][]([])l l l H n n n =Φv v (23)Then the optimal receive subspace of user l k ∈в is given by,min ,[][[]],l k l k n n υ=u A (24)where ]][[,min n k l A υ is the eigenvector corresponding to the smallest eigenvalue of ][,n k l A due to only one stream transmitted by each user. The inter-cell interference covariance matrix is defined as∑∑≠=∈=Lll l B k H l k l l l k l k l l n n n n '1'']'[,]'[]'[,,'])[]([][][H ΦHA (25)In other words, the receive subspace of user k at the subcarriers is selected to minimizethe remaining inter-cell interference in the desired signal subspace. (2)Transmit Subspace Optimization.We can reverse the communication direction to perform the transmit subspace optimization. In the reciprocal network the channel from user k in cell l to base station 'l at the nth subcarrier isgiven by [,][']',[]([])l k l H l l k n n =H H . The transmit precoders have been given by the receiver filters in theforward network, i.e. ,,[][]l k l k n n =v u , and ,,,[][]([])H l k l k l k n n n =Φv v . Now the optimal receive subspace at base station l is given by[][]min [][[]]l l n n υ=u A (26)where the inter-cell interference covariance matrix in the reciprocal network is∑∑≠=∈=L ll l B k H k l l k l k l l l l n n n n '1'],'[,'],'[]['])[]([][][H ΦH A (27)Having found the receive subspace in the reciprocal network, the transmit subspace in the forward network is given by [][][][]l l n n =v u . (3) Intra-cell Orthogonal Subcarrier Allocation.After iteratively optimizing the transmit subspace, each base station l computes the effectivechannels from base station l to user k at the nth subcarrier, [][][].,,[][][][]l H l l l k l k l k h n n n n =u H v , we canobtain the effective channels [][][],,,ˆ([0],,[1])l l l l k l kl k diag h h T =-H in frequency domain.In the cell l , we can assign one orthogonal subcarrier set to a user to avoid intra-cell multiuser interference. So the precoder and the receive filter design is simplified.From (6), the precoding matrix can be designed such that,,'0,'()1,'F HF l k l k k k k k ≠⎧⋅=⎨=⎩v v(28) where 1,F T l k C ⨯∈v , and ,,F F l k l k =u v .Opportunistic Scheduling in [9] will be used here for subcarrier selection. The BS finds *A suchthat∑∈∈+=Ak k l A A )1log(max arg ,*γκ(29)where κ ⊂},,1{T is a collection of subsets of subcarriers that has cardinality ⎪⎪⎭⎫⎝⎛=K T κ.The procedure for finding the transmit and receive subspaces can be summarized as follows: Step 1 Base station l : Start with arbitrary precoding matrices [][]l n v at subcarrier n .Step 2 Receiver k in cell l : Compute the interference suppression matrix ,[]l k n u according to (24).Step 3 Base station l : Update transmit matrix [][][][]l l n n =v u according to (26). Step 4 Iteration: Start from 2) until some termination condition is satisfied.Step 5 Base station l : Compute the frequency transmit precoders ,F l k v according to (28) and (29). The termination conditions are, for example, a maximum number of iterations or minimal residual inter-cell interference power.5 Numerical ResultsBy numerical simulations, the performance of interference alignment is provided for downlink multi-carrier MIMO cellular systems. The algorithm proposed in Section 4 is compared with that used in MIMO cellular system detailed in [10][11]. We use the Jakes model for this MIMO channel, and consider a single stream transmission for each user. The performance of all schemes is evaluated interms of network spectral efficiency normalized by T, that is from (10) as: ∑∑=∈+Ll B k k l lT 1,2)1(log 1γfor all L l ,,1 =.Fig.2 shows the spectral efficiency v.s. SNR for the IA in MIMO and multi-carrier MIMO cellular systems. When the parameters are 6==N M ,3=L and 3=K in each cell, the necessary conditions (21) and (22) are satisfied. Interference alignment scheme in these two systems is not interference limited. We observe that interference alignment scheme in MIMO cellular system where all users occupy the same frequency band (1=T ) outperforms the hybrid scheme in multi-carrier MIMO cellular system. In contrast, when the parameters are 4==N M ,3=L and 3=K , the necessary condition (21) is satisfied, but (22) is not satisfied. In MIMO cellular system, each user receives one desired and eight interfering signals. It is not possible to align all interference in two dimensions. Whereas in multi-carrier MIMO cellular system, intra-cell interference can be avoided by different users selecting different orthogonal subcarriers. So each user has receive space of four dimensions, receiving one desired, and two interfering signals. The inter-cell interference can be suppressed completely. So in this situation, the IA scheme in multi-carrier MIMO cellular system performs significantly better than the scheme in MIMO cellular system.SNR(dB)s p e c t r a l e f f i c i e n c y [b i t s /s e c /H z ]Fig.2: Spectral efficiency versus SNR for the IA in MIMO and multi-carrier MIMOFig. 3 and Fig. 4 compare the spectral efficiency for the different numbers of users per cell in those two systems. We obtain the following observation: if necessary conditions (21) and (22) are satisfied, the spectral efficiency is increased with the number of users increasing in each system, and the interference alignment algorithm in the MIMO cellular systems outperforms the proposed method for multi-carrier MIMO cellular systems due to the larger bandwidth in frequency domain occupied in MIMO cellular systems. But in the same parameters, the conditions in MIMO cellular systems are not met when the number of users in each cell is larger than some value, so serious degradation in spectral efficiency occurs. As seen from Fig.3, the proposed interference alignment method in multi-carrier MIMO cellular systems outperform MIMO cellular systems with larger number of users. The reason is that in multi-carrier MIMO cellular systems the intra-cell interferences are mitigated by multi-subcarriers, there are more subspace dimensions in space to cancel the inter-cell interferences.the number of users per cells p e c t r a l e f f i c e i e n c y [b i t s /s /H z ]Fig.3: Spectral efficiency versus the number of users per cell in the twocellular systems.the number of users per cellt h e s p e c t r a l e f f i c i e n c y (b i t s /s /H z )multi-carrier OFDM cellular system with M=4,N=4Fig.4: Spectral efficiency versus the number of users per cell in multi-carrier MIMO cellular systems.Fig.5 compares the residual interference terms in the denominator of (9) of the minimum leakage inter-cell interference algorithm for MIMO and multi-carrier MIMO cellular systems, where the parameters are M=N=6. We can conclude that the IA scheme in MIMO and multi-carrier MIMO systems consistently converge rapidly to an small value, and the value in the latter is much smaller than that in the former.101010101010-510105iterationsR e s u i d u a l i n t e r f e r e n c e p o w e rFig.5: Resuidual interference power versus iterations for MIMO-OFDMA and MIMO cellular systems.6 ConclusionThis paper studies the downlink interference alignment in cellular multi-carrier MIMO systems and compares its performance with the MIMO ones. We have derived the zero-forcing condition required for perfect alignment, and proposed a hybrid IA-based scheme, which iteratively updates the transmit precoders and receive filters in space dimensions to avoid inter-cell interference, and in each cell allocates orthogonal subcarriers to different users. The spectral efficiency results demonstrate the effectiveness of the proposed hybrid scheme. 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