Power allocation optimization in selective DF relaying with different modulation levels in the presence of imperfect channel estimations

In this paper, we focus on the systematic optimization of power allocation in a selective relaying scheme with imperfect channel estimation in a multi-relay decode-and-forward cooperative network in which the relays have the flexibility to employ a modulation level different than that of the source, whenever there is a merit. First, we obtain an asymptotic expression for the error probability in the presence of Gaussian imperfect channel estimations. Then, by using this expression, we derive the power allocation scheme that minimizes the asymptotic error probability. We show that the power allocation problem can suitably be presented as a geometric programming problem that is solved by an efficient convex programming technique. Finally, the derivations are confirmed through Monte Carlo simulations