  The goal of this paper is to establish which practical routing schemes for
wireless networks are most suitable for wideband systems in the power-limited
regime, which is, for example, a practically relevant mode of operation for the
analysis of ultrawideband (UWB) mesh networks. For this purpose, we study the
tradeoff between energy efficiency and spectral efficiency (known as the
power-bandwidth tradeoff) in a wideband linear multihop network in which
transmissions employ orthogonal frequency-division multiplexing (OFDM)
modulation and are affected by quasi-static, frequency-selective fading.
Considering open-loop (fixed-rate) and closed-loop (rate-adaptive) multihop
relaying techniques, we characterize the impact of routing with spatial reuse
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 of the wideband regime. Our analysis particularly deals
with the convergence of these end-to-end performance measures in the case of
large number of hops, i.e., the phenomenon first observed in \cite{Oyman06b}
and named as ``multihop diversity''. Our results demonstrate the realizability
of the multihop diversity advantages in the case of routing with spatial reuse
for wideband OFDM systems under wireless channel effects such as path-loss and
quasi-static frequency-selective multipath fading.
