We analyze low-power short-range wireless communications through a low-rank fading channel - a bonafide use case in many communication scenarios requiring simple wireless connectivity with much relaxed constraints on throughput and data latency. This is certainly true, for instance, in low-complexity wireless channels in the low-rate wireless personal area networks (LR-WPANs). Low-rate communication on control channels in wireless networks is another relevant example. Specifically, we characterize the capacity of a low-rank wireless channel with varying fading severity at low signal-to-noise ratios (SNRs). The rank deficiency is incorporated by introducing pinhole condition in the channel. The channel capacity degradation with fading severity at high SNRs is well known: the probability of deep fades increases significantly with higher fading severity resulting in poor performance. Our analysis of the double-fading pinhole channel at low-SNR shows a very counter-intuitive result that - \emph{higher fading severity enables higher capacity at sufficiently low SNR}. The underlying reason is that at low SNRs, ergodic capacity depends crucially on the probability distribution of channel peaks (simply tail distribution); for the pinhole channel, the tail distribution improves with increased fading severity. This allows a transmitter operating at low SNR to exploit channel peaks `more efficiently' resulting in net improvement in achievable spectral efficiency. We derive a new key result quantifying the above dependence for the double-Nakagami-$m$ fading pinhole channel - that is, the ergodic capacity ${C} \propto (m_T m_R)^{-1}$ at low SNR, where $m_T m_R$ is the product of fading (severity) parameters of the two independent Nakagami-$m$ fadings involved.

翻译：摘要：本文分析了低功率短距离无线通信中的低秩衰落信道——这是许多需要简单无线连接、对吞吐量和数据延迟要求较为宽松的通信场景中的典型应用实例。例如，低速率无线个域网中的低复杂度无线信道正是如此，无线网络中控制信道上的低速率通信是另一个相关实例。具体而言，我们刻画了低信噪比下具有可变衰落严重程度的低秩无线信道的容量。通过引入信道中的针孔条件来体现秩不足。众所周知，高信噪比下信道容量随衰落严重程度退化：更严重的衰落会显著增加深度衰落的概率，从而导致性能下降。我们对低信噪比下双衰落针孔信道的分析得出一个反直觉的结果：在足够低的信噪比下，更高的衰落严重程度实现了更高的容量。其根本原因在于，低信噪比下遍历容量主要取决于信道峰值的概率分布（即尾部分布）；对于针孔信道，尾部分布随衰落严重程度增加而改善。这使得工作在低信噪比的发射机能够"更高效地"利用信道峰值，从而净提升可达频谱效率。我们推导出一个关键结果，量化上述依赖关系适用于双Nakagami-$m$衰落针孔信道：在低信噪比下，遍历容量${C} \propto (m_T m_R)^{-1}$，其中$m_T m_R$是涉及的两个独立Nakagami-$m$衰落的衰落（严重程度）参数之积。