  In this paper, we consider the amplified-and-forward relaying in an OFDM
system with unitary linear processing at the relay. We proposed a general
analytical framework to find the unitary linear processing matrix that
maximizes the system achievable rate. We show that the optimal processing
matrix is a permutation matrix, which implies that a subcarrier pairing
strategy is optimal. We further derived the optimal subcarrier pairing schemes
for scenarios with and without the direct source-destination path for
diversity. Simulation results are presented to demonstrate the achievable gain
of optimal subcarrier pairing compared with non-optimal linear processing and
non-pairing.
