[论文解读] The Degrees of Freedom Regions of MIMO Broadcast, Interference, and Cognitive Radio Channels with No CSIT

Chinmay S. Vaze, Mahesh K. Varanasi|arXiv (Cornell University)|Sep 29, 2009

Advanced MIMO Systems Optimization参考文献 30被引用 58

一句话总结

本文在发射端无信道状态信息（CSIT）的条件下，表征了MIMO广播、干扰和认知无线电信道的自由度（DoF）区域，表明基于时分复用的传输在K用户MIMO广播信道中可实现DoF最优。对于两用户MIMO干扰和认知无线电信道，大多数天线配置下内界和外界界一致，确定了CSIT对DoF增益至关重要的条件。

ABSTRACT

The degrees of freedom (DoF) regions are characterized for the multiple-input multiple-output (MIMO) broadcast channel (BC), interference channels (IC) (including X and multi-hop interference channels) and the cognitive radio channel (CRC), when there is perfect and no channel state information at the receivers and the transmitter(s) (CSIR and CSIT), respectively. For the K-user MIMO BC, the exact characterization of the DoF region is obtained, which shows that a simple time-division-based transmission scheme is DoF-region optimal. Using the techniques developed for the MIMO BC, the corresponding problems for the two-user MIMO IC and the CRC are addressed. For both of these channels, inner and outer bounds to the DoF region are obtained and are seen to coincide for a vast majority of the relative numbers of antennas at the four terminals, thereby characterizing DoF regions for all but a few cases. Finally, the DoF regions of the $K$-user MIMO IC, the CRC, and X networks are derived for certain classes of these networks, including the one where all transmitters have an equal number of antennas and so do all receivers. The results of this paper are derived for distributions of fading channel matrices and additive noises that are more general than those considered in other simultaneous related works. The DoF regions with and without CSIT are compared and conditions on the relative numbers of antennas at the terminals under which a lack of CSIT does, or does not, result in the loss of DoF are identified, thereby providing, on the one hand, simple and robust communication schemes that don't require CSIT but have the same DoF performance as their previously found CSIT counterparts, and on the other hand, identifying situations where CSI feedback to transmitters would provide gains that are significant enough that even the DoF performance could be improved.

研究动机与目标

• 在发射端无信道状态信息（CSIT）的条件下，表征K用户MIMO广播、两用户MIMO干扰和认知无线电信道的自由度（DoF）区域。
• 确定在一般衰落和噪声分布下，CSIT的缺失是否导致这些MIMO网络的DoF损失。
• 识别在发射端和接收端天线数满足何种条件时，CSIT反馈可带来显著的DoF增益。
• 证明即使在无CSIT的某些MIMO网络中，简单的时分复用方案也能实现DoF最优性。
• 将结果扩展至具有对称天线配置的K用户干扰、X和认知无线电网络。

提出的方法

• 通过使用已知非意图消息的干扰合并接收机，推导DoF区域的外界界，应用Fano不等式以限制接收信号与预期消息之间的互信息。
• 表明在时分复用传输下，最大加权和DoF与外界界一致，从而证明时分复用在K用户MIMO BC中为DoF最优。
• 利用不同信道实现下变换信号向量（Y~和Z~）的统计等价性，以在一般衰落分布（包括i.i.d.瑞利衰落和莱斯衰落）下保持界的有效性。
• 应用广义信道变换和奇异值分解（SVD），以定义等效的点对点MIMO信道，用于上界DoF之和。
• 通过分析无CSIT条件下的干扰对齐和信号空间约束，为两用户MIMO IC和CRC建立外界界。
• 通过三步框架完成证明：（I）信号变换，（II）变换后信号的统计等价性，（III）应用已知的点对点MIMO信道DoF界。

实验结果

研究问题

• RQ1 当无CSIT时，K用户MIMO广播信道的DoF区域是什么？
• RQ2 对于两用户MIMO干扰和认知无线电信道，在何种天线配置下内界和外界界一致？
• RQ3 在哪些配置下，CSIT的缺失会导致DoF损失？CSIT反馈在何时对DoF增益是必要的？
• RQ4 在无CSIT的MIMO网络中，基于时分复用的传输方案能否实现DoF最优性？
• RQ5 在一般衰落和噪声分布（超越i.i.d.瑞利衰落）下，无CSIT时DoF区域如何变化？

主要发现

• 在无CSIT条件下，K用户MIMO广播信道的DoF区域被完全表征，并证明可通过简单的时分复用方案实现。
• 对于两用户MIMO IC和CRC，除少数天线配置外，DoF区域被精确表征，且在绝大多数情况下内界与外界界一致。
• 两用户MIMO IC的和DoF上界为min(N1, M1 + M2)，且该界在无CSIT时仍为紧界。
• 在两用户MIMO BC中，无CSIT时和DoF被限制为1，即使存在多个发射天线，与完美CSIT情况相比存在显著损失。
• 在所有发射机天线数相等、所有接收机天线数相等的对称天线配置下，推导了K用户MIMO IC、X网络和CRC的DoF区域。
• 本文识别出，仅当接收天线数严格小于所有用户发射天线总数时，CSIT反馈才能带来显著的DoF增益；否则，即使无CSIT，时分复用也是DoF最优的。