A Shannon-Theoretic Perspective on Fading Multihop Networks

We consider a frequency-flat fading multihop network with a single active source-destination pair terminals communicating over multiple hops through a set of intermediate relay terminals. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) for a simple communication protocol based on time-division decode-and-forward relaying in meaningful asymptotic regimes of signal-to-noise ratio (SNR) under a system-wide power constraint on source and relay transmissions. The impact of multi-hopping and channel fading on the key performance measures of the high and low SNR regimes is investigated to shed new light on the possible enhancements in power/bandwidth efficiency and link reliability. In contrast to the common belief that in fading environments communicating over multiple hops suffers significantly in performance due to the worst link limitation, our results indicate that hopping could significantly improve the outage behavior over slow-fading networks and stabilize links against the random channel fluctuations. In particular, we prove that there exists an optimal number of hops that minimizes the end-to-end outage probability and characterize the dependence of this optimal number on the fading statistics and target energy and spectral efficiencies.