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arXiv 1704.08473cs.ITmath.IT
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发射天线选择的渐近性:多个接收天线的影响

Asymptotics of Transmit Antenna Selection: Impact of Multiple Receive Antennas

Saba Asaad, Ali Bereyhi, Ralf R. Müller, Amir M. Rabiei

摘要:

考虑具有$N_\mathrm{t}$发射天线和$N_\mathrm{r}$接收天线的衰落高斯MIMO信道。发射机选择对应于最强信道的$L_\mathrm{t}$天线。对于这种设置,我们研究了当$N_\mathrm{t}$变大时输入输出互信息的分布。我们表明,对于任何$N_\mathrm{r}$和$L_\mathrm{t}$,输入输出互信息的分布是准确地近似的高斯分布,其均值增长大,其方差收敛到零。我们的分析表明,在大的限制,应用Jensen不等式得到的互信息的期望值和相应的上限之间的差距,收敛到一个常数,它只取决于$N_\mathrm{r}$和$L_\mathrm{t}$。该结果将信道硬化的范围扩展到具有多个接收和选择的发射天线的天线选择的一般情况。虽然分析给出了大系统的限制,我们的数值研究表明,即使天线的数量并不大的近似分布的鲁棒性。

英文摘要:

Consider a fading Gaussian MIMO channel with $N_\mathrm{t}$ transmit and $N_\mathrm{r}$ receive antennas. The transmitter selects $L_\mathrm{t}$ antennas corresponding to the strongest channels. For this setup, we study the distribution of the input-output mutual information when $N_\mathrm{t}$ grows large. We show that, for any $N_\mathrm{r}$ and $L_\mathrm{t}$, the distribution of the input-output mutual information is accurately approximated by a Gaussian distribution whose mean grows large and whose variance converges to zero. Our analysis depicts that, in the large limit, the gap between the expectation of the mutual information and its corresponding upper bound, derived by applying Jensen's inequality, converges to a constant which only depends on $N_\mathrm{r}$ and $L_\mathrm{t}$. The result extends the scope of channel hardening to the general case of antenna selection with multiple receive and selected transmit antennas. Although the analyses are given for the large-system limit, our numerical investigations indicate the robustness of the approximated distribution even when the number of antennas is not large.

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