Non-Ergodic Power-Bandwidth Tradeoff in Linear Multi-hop Networks

The prior work on power-bandwidth tradeoff analysis in fading environments has assumed the ergodicity of the channel statistics along with infinite code block-lengths, which allow defining energy and spectral efficiency measures as a function of the Shannon capacity. We generalize the power-bandwidth tradeoff analysis framework to draw insights for a specific form communication under a non-ergodic fading model. In particular, we study the power-bandwidth tradeoff in a one-dimensional slow-fading multi-hop relay network. We characterize the impact of multi-hopping on the statistical properties of the end-to-end conditional mutual information (conditioned on the specific values of the channel fading parameters and therefore treated as a random variable) and on the energy and spectral efficiency measures computed from the conditional mutual information. Our non-ergodic power-bandwidth tradeoff analysis focuses on two asymptotic regimes: (i) Power-limited (low signal-to-noise ratio (SNR)) regime and (ii) bandwidth-limited (high SNR) regime. In both regimes, we investigate the performance of open-loop (fixed-rate) and closed-loop (rate-adaptive) multi-hop relaying mechanisms in terms of their power-band width tradeoffs and end-to-end outage probabilities. Interestingly, our analysis reveals the new notion of "multi-hop diversity" toward enhancing link reliability in diversity-limited fading environments