  Wireless systems that carry delay-sensitive information (such as speech
and/or video signals) typically transmit with fixed data rates, but may
occasionally suffer from transmission outages caused by the random nature of
the fading channels. If the transmitter has instantaneous channel state
information (CSI) available, it can compensate for a significant portion of
these outages by utilizing power allocation. In this paper, we consider optimal
power allocation for a conventional dual-hop bidirectional decode-and-forward
(DF) relaying system with a three-phase transmission protocol. The proposed
strategy minimizes the average power consumed by the end nodes and the relay,
subject to some maximum allowable system outage probability (OP), or
equivalently, minimizes the system OP while meeting average power constraints
at the end nodes and the relay. We show that in the proposed power allocation
scheme, the end nodes and the relay adjust their output powers to the minimum
level required to avoid outages, but will sometimes be silent, in order to
conserve power and prolong their lifetimes. For the proposed scheme, the end
nodes use the instantaneous CSI of their respective source-relay links and the
relay uses the instantaneous CSI of both links.
