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We analyze the performance of amplify-and-forward (AF) automatic repeatrequest (ARQ) for a two-hop cooperative system with reliability constrains. Forthis setup, we first derive the closed-form outage probability expression.Next, we present a power allocation scheme that allows us to achieve a targetoutage probability, while minimizing the outage-weighted average powerexpenditure for asymmetric power allocation between the source and relay. Thisis cast as an optimization problem, and the optimal power allocation (OPA) isobtained in closed form by invoking the Karush-Kuhn-Tucker (KKT) conditions. Weevaluate numerically the OPA strategy between different AF-ARQ transmissionrounds and we show that the proposed scheme provides large power gains withrespect to the optimized point-to-point ARQ scheme, as well as with respect tothe equal power allocation (EPA) strategy.

Power Allocation for Type-I ARQ Two-Hop Cooperative Networks for Ultra-Reliable Communication