  This paper studies the optimal power allocation for outage minimization in
point-to-point fading channels with the energy-harvesting constraints and
channel distribution information (CDI) at the transmitter. Both the cases with
non-causal and causal energy state information (ESI) are considered, which
correspond to the energy harvesting rates being known and unknown prior to the
transmissions, respectively. For the non-causal ESI case, the average outage
probability minimization problem over a finite horizon is shown to be
non-convex for a large class of practical fading channels. However, the
globally optimal "offline" power allocation is obtained by a forward search
algorithm with at most $N$ one-dimensional searches, and the optimal power
profile is shown to be non-decreasing over time and have an interesting
"save-then-transmit" structure. In particular, for the special case of N=1, our
result revisits the classic outage capacity for fading channels with uniform
power allocation. Moreover, for the case with causal ESI, we propose both the
optimal and suboptimal "online" power allocation algorithms, by applying the
technique of dynamic programming and exploring the structure of optimal offline
solutions, respectively.
