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arXiv 0908.1208cs.ITmath.IT
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实数干涉对齐

Real Interference Alignment with Real Numbers

Abolfazl S. Motahari, Shahab Oveis Gharan, Amir K. Khandani

摘要:

提出了一种适用于单天线网络的编码方案。该方案将单天线系统等效为分数维的多输入多输出(MIMO)系统。干涉可以沿着这些维度对齐,并且可以实现更高的复用增益。数论中的丢番图近似领域的工具被用来表明,所提出的编码方案实际上模仿了MIMO系统中使用的传统方案,其中每个数据流沿着一个方向发送,并且当几个流到达同一方向时发生对齐。编码部分提出了两种类型的星座,即单层星座和多层星座。使用单层星座,该编码方案被应用于两个用户的$X$信道和三个用户的高斯干扰信道(GIC)。在两用户$X$信道的情况下,证明了信道的总自由度(DOF),即4/3,几乎肯定是可实现的。这是第一个例子,它表明,一个时间不变的单天线系统不会达到其总的自由度。使用多层星座,编码方案被应用于对称三用户GIC。推导出所有通道增益的可扩展自由度。作为信道增益的函数,观察到DOF处处不连续。

英文摘要:

A novel coding scheme applicable in networks with single antenna nodes is proposed. This scheme converts a single antenna system to an equivalent Multiple Input Multiple Output (MIMO) system with fractional dimensions. Interference can be aligned along these dimensions and higher Multiplexing gains can be achieved. Tools from the field of Diophantine approximation in number theory are used to show that the proposed coding scheme in fact mimics the traditional schemes used in MIMO systems where each data stream is sent along a direction and alignment happens when several streams arrive at the same direction. Two types of constellation are proposed for the encoding part, namely the single layer constellation and the multi-layer constellation. Using the single layer constellation, the coding scheme is applied to the two-user $X$ channel and the three-user Gaussian Interference Channel (GIC). In case of the two-user $X$ channel, it is proved that the total Degrees-of-Freedom (DOF), i.e. 4/3, of the channel is achievable almost surely. This is the first example in which it is shown that a time invariant single antenna system does not fall short of achieving its total DOF. Using the multi-layer constellation, the coding scheme is applied to the symmetric three-user GIC. Achievable DOFs are derived for all channel gains. As a function of the channel gain, it is observed that the DOF is everywhere discontinuous.

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