In this paper, we derive asymptotic expressions for the ergodic capacity of the multiple-input multiple-output (MIMO) keyhole channel at low SNR in independent and identically distributed (i.i.d.) Nakagami-$m$ fading conditions with perfect channel state information available at both the transmitter (CSI-T) and the receiver (CSI-R). We show that the low-SNR capacity of this keyhole channel scales proportionally as $\frac{\textrm{SNR}}{4} \log^2 \left(1/{\textrm{SNR}}\right)$. Further, we develop a practically appealing On-Off transmission scheme that is aymptotically capacity achieving at low SNR; it requires only one-bit CSI-T feedback and is robust against both mild and severe Nakagami-$m$ fadings for a very wide range of low-SNR values. These results also extend to the Rayleigh keyhole MIMO channel as a special case.
翻译:在本文中,我们以独立和同样分布的(i.d.) Nakagami-$m$ 淡化条件和发报机(CSI-T)和接收机(CSI-R)都可获得的完美频道状态信息。 我们从中得出以独立和同样分布的(i.d.) Nakagami-$form-trom-prog-progy) 以低SNR为主的多投入多输出(MIMO)密钥孔通道的性能的无症状表达。 我们显示,这个关键孔通道的低核反应能力与$\fraft(1/ textrm{SNR}4}\log%2\left(1/ textrm{SNR_rärrrright)成比例成正比。 此外,我们开发了一种实际上呼吁的即发自发式传输计划,即发自发即发式传输能力在低SRRire;它只需要一位CSI-T的反馈,对轻重的和重的Nakami-munt-met两种低核价值都有相当范围的低范围的微值都有强。这些结果也延伸到Rayleile。这些结果也延伸至Ryle。