  In this paper, a point-to-point Orthogonal Frequency Division Multiplexing
(OFDM) system with a decode-and-forward (DF) relay is considered. The
transmission consists of two hops. The source transmits in the first hop, and
the relay transmits in the second hop. Each hop occupies one time slot. The
relay is half-duplex, and capable of decoding the message on a particular
subcarrier in one time slot, and re-encoding and forwarding it on a different
subcarrier in the next time slot. Thus each message is transmitted on a pair of
subcarriers in two hops. It is assumed that the destination is capable of
combining the signals from the source and the relay pertaining to the same
message. The goal is to maximize the weighted sum rate of the system by jointly
optimizing subcarrier pairing and power allocation on each subcarrier in each
hop. The weighting of the rates is to take into account the fact that different
subcarriers may carry signals for different services. Both total and individual
power constraints for the source and the relay are investigated. For the
situations where the relay does not transmit on some subcarriers because doing
so does not improve the weighted sum rate, we further allow the source to
transmit new messages on these idle subcarriers. To the best of our knowledge,
such a joint optimization inclusive of the destination combining has not been
discussed in the literature. The problem is first formulated as a mixed integer
programming problem. It is then transformed to a convex optimization problem by
continuous relaxation, and solved in the dual domain. Based on the optimization
results, algorithms to achieve feasible solutions are also proposed. Simulation
results show that the proposed algorithms almost achieve the optimal weighted
sum rate, and outperform the existing methods in various channel conditions.
