Channel Coherence in the Low-SNR Regime

Channel capacity in the limit of vanishing signal-to-noise ratio (SNR) per degree of freedom is known to be linear in SNR for fading and nonfading channels, regardless of channel state information at the receiver (CSIR). It has recently been shown that the significant engineering difference between the coherent and the noncoherent fading channels, including the requirement of peaky signaling and the resulting spectral efficiency, is determined by how the capacity limit is approached as SNR tends to zero, or in other words, the sublinear term in the capacity expression. In this paper, we show that this sublinear term is determined by the channel coherence level, which we define to quantify the relation between the SNR and the channel coherence time. This allows us to trace a continuum between the case with perfect CSIR and the case with no CSIR at all. Using this approach, we also evaluate the performance of suboptimal training schemes