  Multi-hop relaying is an economically efficient architecture for coverage
extension and throughput enhancement in future wireless networks. OFDM, on the
other hand, is a spectrally efficient physical layer modulation technique for
broadband transmission. As a natural consequence of combining OFDM with
multi-hop relaying, the allocation of per-hop subcarrier power and per-hop
transmission time is crucial in optimizing the network performance. This paper
is concerned with the end-to-end information outage in an OFDM based linear
relay network. Our goal is to find an optimal power and time adaptation policy
to minimize the outage probability under a long-term total power constraint. We
solve the problem in two steps. First, for any given channel realization, we
derive the minimum short-term power required to meet a target transmission
rate. We show that it can be obtained through two nested bisection loops. To
reduce computational complexity and signalling overhead, we also propose a
sub-optimal algorithm. In the second step, we determine a power threshold to
control the transmission on-off so that the long-term total power constraint is
satisfied. Numerical examples are provided to illustrate the performance of the
proposed power and time adaptation schemes with respect to other resource
adaptation schemes.
