Degrees of freedom region of the MIMO X channel
Degrees of freedom region of the MIMO X channel
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DOI：
10.1109/tit.2007.911262
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发表时间：
2008-01-01
影响因子：
2.5
通讯作者：
Shamai, Shlomo (Shitz)
中科院分区：
文献类型：
--
作者：
Jafar, Syed A.;Shamai, Shlomo (Shitz)
我们为多输入多输出（MIMO）X信道的自由度区域提供了可扩展性以及匡威结果，即，具有两个发射机的两个接收机的系统，每个接收机配备有多个天线，其中独立的消息需要通过固定信道从每个发射机传送到每个接收机。当整数自由度对于每个消息是最优的时，自由度区域的内边界和外边界是紧的。对于每个节点处的M = 1个天线，我们发现总（速率总和）自由度上下有界，因为1 < eta*x 1，并且信道矩阵是非退化的，然后精确的自由度eta*x = 4/3。因此，当M不是3的倍数时，MIMO X信道具有非整数自由度。无需脏纸编码或连续解码的简单迫零足以实现4/3 M自由度。如果信道随时间/频率变化，则在所有节点处具有单个天线（M = 1）的X个信道具有精确的自由度。自由度可互换性的关键思想是干涉补偿，即，信号空间在它们构成干扰的接收机处对齐，而在它们需要的接收机处是可分离的。我们还探讨了增加的自由度时，一些消息提供给发射机或接收机的认知无线电的方式。
We provide achievability as well as converse results for the degrees of freedom region of a multiple-input multiple-output (MIMO) X channel, i.e., a system with two transmitters' two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. The inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message. With M = 1 antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as 1 < eta*x 1 and channel matrices are nondegenerate then the precise degrees of freedom eta*x = 4/3. Thus, the MIMO X channel has noninteger degrees of freedom when M is not a multiple of 3. Simple zero forcing without dirty paper encoding or successive decoding, suffices to achieve the 4/3M degrees of freedom. If the channels vary with time/frequency then the X channel with single antennas (M = 1) at all nodes has exactly degrees of freedom. The key idea for the achievability of the degrees of freedom is interference alignment-i.e., signal spaces are aligned at receivers where they constitute interference while they are separable at receivers where they are desired. We also explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio.