On Power Allocation for Dual-Hop Amplify-and-Forward OFDM Relay Systems

The solutions to an optimal power allocation problem in dual-hop amplify-and-forward (non-regenerative) OFDM relay systems over given channel gains are provided with a joint transmit power constraint. We analytically derive the allocated power to each hop/subcarrier that satisfies the Karush-Kuhn-Tucker (KKT) conditions by solving simultaneous equations. The solutions imply that at most 3^N - 1 possible power allocation candidates could exist on both source and relay nodes satisfying KKT conditions when N is the number of subcarriers. Based on the solution, a sub-optimal power allocation method that selects only significant allocated power in strong subcarriers is proposed and achieves higher capacity (achievable rate) than conventional sub-optimal methods. As for the feasibility, the number of candidates to be evaluated is N in the proposed method.