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首页> 外文期刊>IEEE Transactions on Information Theory >Large $n$ Analysis of Amplify-and-Forward MIMO Relay Channels With Correlated Rayleigh Fading
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Large $n$ Analysis of Amplify-and-Forward MIMO Relay Channels With Correlated Rayleigh Fading

机译：具有相关瑞利衰落的放大转发MIMO中继信道的大型分析

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摘要

In this correspondence, the cumulants of the mutual information of the flat Rayleigh fading two-hop amplify-and-forward multiple-input multiple-output (MIMO) relay channel under independent and identically distributed (i.i.d.) Gaussian input vectors are derived in the large array limit. The analysis is based on the replica trick and covers both spatially independent and Kronecker correlated fading. Beamforming at all terminals is restricted to weight matrices that are independent of the channel realization and constant over time. Expressions for mean and variance of the mutual information are obtained. Their parameters are determined by a nonlinear equation system. All higher cumulants are shown to vanish as the number of antennas per terminal, $n$, grows to infinity. In conclusion, the distribution of the mutual information $I$ becomes Gaussian in the large $n$ limit. In this asymptotic regime, it is completely characterized by the expressions obtained for mean and variance of $I$, which are in $Theta(n)$ and ${cal O}(1)$, respectively. Comparisons with simulation results show that the asymptotic results serve as excellent approximations for systems with only few antennas at each terminal.
机译：在这种对应关系中，在独立且均匀分布的（iid）高斯输入矢量下，推导了平坦瑞利衰落两跳放大和转发多输入多输出（MIMO）中继信道下互信息的累积量数组限制。该分析基于副本技巧，涵盖了空间独立和Kronecker相关衰落。所有终端的波束成形仅限于权重矩阵，该权重矩阵与通道实现无关，并且随时间变化是恒定的。获得了互信息的均值和方差的表达式。它们的参数由非线性方程组确定。随着每个终端的天线数量（n $）增长到无穷大，所有更高的累积量都消失了。总而言之，互信息$ I $的分布在$ n $的较大限制下变为高斯分布。在这种渐近状态下，它的特征完全在于为$ I $的均值和方差获得的表达式，分别为$ Theta（n）$和$ {cal O}（1）$。与仿真结果的比较表明，对于每个终端只有很少天线的系统，渐近结果可以作为极好的近似值。

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