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首页> 外文期刊>IEEE Transactions on Information Theory >Central Limit Theorem for Mutual Information of Large MIMO Systems With Elliptically Correlated Channels
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Central Limit Theorem for Mutual Information of Large MIMO Systems With Elliptically Correlated Channels

机译：具有椭圆相关通道的大型MIMO系统互信息的中心极限定理

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摘要

By considering elliptical correlations in the channel matrix of a large MIMO system, this paper investigates how the non-linear dependency affects the asymptotic behaviors of Shannon's mutual information, as the numbers of antennas at transmitter and receiver both tend to infinity at the same rate. Beyond the almost sure convergence of the information per transmit antenna, we also propose several central limit theorems for the information statistics under various scenarios. The results show that the non-linear correlation has a little impact on the almost sure convergence but has a tremendous effect on the fluctuation of the information statistics. In particular, the centralized information statistics could experience a phase transition in convergence rate when the strength of the non-linear correlation increases. As extensions, several central limit theorems are established as well for general linear spectral statistics of large sample covariance matrices in elliptical distributions.
机译：通过考虑大型MIMO系统的信道矩阵中的椭圆相关性，本文研究了非线性相关性如何影响Shannon互信息的渐近行为，因为发送器和接收器上的天线数量趋于以相同的速率无穷大。除了每个发射天线的信息几乎可以肯定地收敛之外，我们还针对各种情况下的信息统计提出了几个中心极限定理。结果表明，非线性相关性对几乎确定的收敛性影响不大，但对信息统计的波动性影响很大。特别是，当非线性相关性的强度增加时，集中式信息统计可能会遇到收敛速率的相变。作为扩展，还建立了几个中心极限定理，用于椭圆分布中大样本协方差矩阵的一般线性光谱统计。

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