  In this paper, we consider the problem of sum rate maximization in a
bidirectional relay network with fading. Hereby, user 1 and user 2 communicate
with each other only through a relay, i.e., a direct link between user 1 and
user 2 is not present. In this network, there exist six possible transmission
modes: four point-to-point modes (user 1-to-relay, user 2-to-relay,
relay-to-user 1, relay-to-user 2), a multiple access mode (both users to the
relay), and a broadcast mode (the relay to both users). Most existing protocols
assume a fixed schedule of using a subset of the aforementioned transmission
modes, as a result, the sum rate is limited by the capacity of the weakest link
associated with the relay in each time slot. Motivated by this limitation, we
develop a protocol which is not restricted to adhere to a predefined schedule
for using the transmission modes. Therefore, all transmission modes of the
bidirectional relay network can be used adaptively based on the instantaneous
channel state information (CSI) of the involved links. To this end, the relay
has to be equipped with two buffers for the storage of the information received
from users 1 and 2, respectively. For the considered network, given a total
average power budget for all nodes, we jointly optimize the transmission mode
selection and power allocation based on the instantaneous CSI in each time slot
for sum rate maximization. Simulation results show that the proposed protocol
outperforms existing protocols for all signal-to-noise ratios (SNRs).
Specifically, we obtain a considerable gain at low SNRs due to the adaptive
power allocation and at high SNRs due to the adaptive mode selection.
