  We analyze the performance of amplify-and-forward (AF) automatic repeat
request (ARQ) for a two-hop cooperative system with reliability constrains. For
this setup, we first derive the closed-form outage probability expression.
Next, we present a power allocation scheme that allows us to achieve a target
outage probability, while minimizing the outage-weighted average power
expenditure for asymmetric power allocation between the source and relay. This
is cast as an optimization problem, and the optimal power allocation (OPA) is
obtained in closed form by invoking the Karush-Kuhn-Tucker (KKT) conditions. We
evaluate numerically the OPA strategy between different AF-ARQ transmission
rounds and we show that the proposed scheme provides large power gains with
respect to the optimized point-to-point ARQ scheme, as well as with respect to
the equal power allocation (EPA) strategy.
