  This paper studies the throughput maximization problem for a three-node relay
channel with non-ideal circuit power. In particular, the relay operates in a
half-duplex manner, and the decode-and-forward (DF) relaying scheme is adopted.
Considering the extra power consumption by the circuits, the optimal power
allocation to maximize the throughput of the considered system over an infinite
time horizon is investigated. First, two special scenarios, i.e., the direct
link transmission (only use the direct link to transmit) and the relay assisted
transmission (the source and the relay transmit with equal probability), are
studied, and the corresponding optimal power allocations are obtained. By
transforming two non-convex problems into quasiconcave ones, the closed-form
solutions show that the source and the relay transmit with certain probability,
which is determined by the average power budgets, circuit power consumptions,
and channel gains. Next, based on the above results, the optimal power
allocation for both the cases with and without direct link is derived, which is
shown to be a mixed transmission scheme between the direct link transmission
and the relay assisted transmission.
