Optimal design and power allocation for multicarrier decode and forward relays

This paper considers a multicarrier communication system assisted by multiple relays, one for each subcarrier. The total power emitted by the source and the total power emitted by the relays are constrained to be less than the respective power budgets. The relays are assumed to operate in the full-duplex decode-and-forward mode, and the objective is to design the codebooks of the source and the relays jointly with the power allocations that maximize the total data rate that can be reliably decoded at the destination. To approach this goal, the design problem is cast as an optimization problem, which is unfortunately nonconvex and difficult to solve. The Karush-Kuhn-Tucker (KKT) system corresponding to this problem is analyzed, and despite the nonconvexity of the problem, we were able to use the KKT system to develop an efficient technique for solving it optimally.