  The goal of this paper is to understand the key merits of multihop relaying
techniques jointly in terms of their energy efficiency and spectral efficiency
advantages in the presence of multiuser diversity gains from opportunistic
(i.e., channel-aware) scheduling and identify the regimes and conditions in
which relay-assisted multiuser communication provides a clear advantage over
direct multiuser communication. For this purpose, we use Shannon-theoretic
tools to analyze the tradeoff between energy efficiency and spectral efficiency
(known as the power-bandwidth tradeoff) over a fading multiuser relay channel
with $K$ users in the asymptotic regime of large (but finite) number of users
(i.e., dense network). Benefiting from the extreme-value theoretic results of
\cite{Oyman_isit07}, we characterize the power-bandwidth tradeoff and the
associated energy and spectral efficiency measures of the bandwidth-limited
high signal-to-noise ratio (SNR) and power-limited low SNR regimes, and utilize
them in investigating the large system behavior of the multiuser relay channel
as a function of the number of users and physical channel SNRs. Our analysis
results in very accurate closed-form formulas in the large (but finite) $K$
regime that quantify energy and spectral efficiency performance, and provides
insights on the impact of multihop relaying and multiuser diversity techniques
on the power-bandwidth tradeoff.
