On The Capacity of Low-Rank Dyadic Fading Channels in the Low-SNR Regime

TL;DR

This paper reveals that in low-SNR regimes, higher fading severity in low-rank dyadic channels can actually increase capacity, contrary to high-SNR behavior, due to improved tail distributions of channel peaks.

Contribution

It provides a novel analysis showing that increased fading severity can enhance capacity at low SNR in pinhole channels, with a new capacity quantification for double-Nakagami-m fading.

Findings

Higher fading severity improves capacity at low SNR.

Capacity scales inversely with the product of fading severity parameters.

Counter-intuitive capacity behavior at low SNR regimes.

Abstract

We characterize the capacity of a low-rank wireless channel with varying fading severity at low signal-to-noise ratios (SNRs). The channel rank deficiency is achieved by incorporating pinhole condition. The 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 dyadic 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 (tail distribution); for the pinhole channel, the tail distribution improves with fading severity. This allows a transmitter operating at low SNR to exploit channel peaks `more efficiently' and hence improves spectral efficiency. We derive a new key result quantifying the above dependence for the double-Nakagami-$m$ fading pinhole channel - the capacity ${C} \propto (m_T m_R)^{-1}$ at low SNR, where $m_T m_R$ is the severity parameters (product) of the fadings involved.