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arXiv 0812.3404cs.ITmath.IT
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MIMO静态半双工中继的分集复用折衷

Diversity-Multiplexing Tradeoff for the MIMO Static Half-Duplex Relay

Olivier Leveque, Christophe Vignat, Melda Yuksel

摘要:

在这项工作中,我们研究了多天线(MIMO)静态半双工中继信道的分集复用折衷(DMT)。在一定的假设下,推导出DMT上界的一般表达式,该上界可以通过中继处的压缩转发协议来实现。DMT表达式一般作为最小化问题的解给出,并且当中继信道关于天线数目对称时,即源和目的地每个具有n个天线,并且中继具有m个天线时,找到了显式表达式。观察到,当中继具有单个天线时,静态半双工DMT与全双工DMT匹配,并且当中继具有多个天线时,静态半双工DMT严格低于全双工DMT。此外,上界的推导涉及到球面积分(即关于酉群U(n)上Haar测度的积分)的新的渐近研究,这本身就是一个数学兴趣的话题。

英文摘要:

In this work, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. The DMT expression is given as the solution of a minimization problem in general, and an explicit expression is found when the relay channel is symmetric in terms of number of antennas, i.e. the source and the destination have n antennas each, and the relay has m antennas. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas. Besides, the derivation of the upper bound involves a new asymptotic study of spherical integrals (that is, integrals with respect to the Haar measure on the unitary group U(n)), which is a topic of mathematical interest in itself.

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