CIF: Small: Degree of Freedom Region of Interference Networks

对于点对点通信，信道容量是非常好理解的，并且存在接近大多数有用的信道模型的容量的方案。相比之下，多用户通信信道并没有得到很好的理解。渠道模式越来越复杂，种类越来越多，许多重要的问题还没有解决.作为一个众所周知的例子，离散无记忆广播信道的容量问题仍然没有解决。作为另一示例，干扰信道容量区域仅在某些特殊情况（诸如强干扰）下是已知的。最近的研究表明，在多用户无线网络中，干扰往往是影响系统性能的主要因素，特别是在高信噪比的情况下，为了克服这一困难，人们提出了用自由度的概念来描述系统吞吐量的一阶特性。对几种干扰网络的总自由度进行了量化。另一方面，比总自由度更能说明问题的自由度区域，却没有得到很好的理解。对于大多数干扰网络，其自由度区域是未知的，本项目试图量化一类具有多个发射节点和多个接收节点的一般干扰网络的自由度区域，这些干扰网络可能配备有多个天线，并且具有一般的消息需求。特别地，我们将研究X干扰网络，其中包括干扰信道，广播信道，多址信道，作为特殊情况。通过基于向量和理性独立的干扰对齐设计，我们将紧密地约束自由度区域的度，并设计出在自由度意义上最优（或接近最优）的方案。更广泛的影响：该项目将大大推进我们对干扰网络的理解，并对下一代无线网络的设计、架构、信号设计和处理产生积极影响。该项目还将帮助培养下一代信号处理和通信网络领域的研究人员和工程师。

For point-to-point communications, channel capacity is very wellunderstood, and there are schemes that approach the capacity formost useful channel models. In contrast, the multi-user communication channelsare not as well understood. The channel models are more complicated, there aremore varieties, and many important problems remain open. As one well-knownexample, the capacity problem for discrete memoryless broadcast channel isstill unsettled. As another example, the interference channel capacity regionis known only in certain special cases (such as strong interference). What isclear from the recent studies of such channels is that in a multi-userwireless network, the key performance limiting factor is often the interference rather than the noise, especially at high signal-to-noise ratio.To alleviate this difficulty, the notion of degrees of freedom has been used asa first order characterization of the system throughput as normalized by thelogarithm of the signal to noise ratio. The total degrees of freedom ofseveral interference networks have been quantified. On the other hand, thedegrees of freedom region, which is more revealing than the total degrees offreedom, is much less well understood. For most of the interference networks,the regions remain unknown.This project seeks to quantify the degree of freedom regions of aclass of general interference networks with multiple transmit nodes andmultiple receive nodes, possibly equipped with multiple antennas, and withgeneral message demands. In particular, we will study the X interferencenetwork, which include interference channels, broadcast channels, multipleaccess channels, as special cases. Through interference alignment design basedon vector and rational independence, we will bound tightly the degrees offreedom region and devise schemes that are optimal (or near-optimal) in thedegree-of-freedom sense.Broader Impact: The project will advance significantly our understanding ofinterference networks, and positively impact the design, architecture, andsignal design and processing for next generation wireless networks. Theproject will also help train the next generation of researchers and engineersin the field of signal processing and communication networks.