A Non-Orthogonal DF Scheme for the Single Relay Channel and the Effect of Labelling

We consider the uncoded transmission over the half-duplex single relay channel, with a single antenna at the source, relay and destination nodes, in a Rayleigh fading environment. The phase during which the relay is in reception mode is referred to as Phase 1 and the phase during which the relay is in transmission mode is referred to as Phase 2. The following two cases are considered: the Non-Orthogonal Decode and Forward (NODF) scheme, in which both the source and the relay transmit during Phase 2 and the Orthogonal Decode and Forward (ODF) scheme, in which the relay alone transmits during Phase 2. A near ML decoder which gives full diversity (diversity order 2) for the NODF scheme is proposed. Due to the proximity of the relay to the destination, the Source-Destination link, in general, is expected to be much weaker than the Relay-Destination link. Hence it is not clear whether the transmission made by the source during Phase 2 in the NODF scheme, provides any performance improvement over the ODF scheme or not. In this regard, it is shown that the NODF scheme provides significant performance improvement over the ODF scheme. In fact, at high SNR, the performance of the NODF scheme with the non-ideal Source-Relay link, is same as that of the NODF scheme with an ideal Source-Relay link. In other words, to study the high SNR performance of the NODF scheme, one can assume that the Source-Relay link is ideal, whereas the same is not true for the ODF scheme. Further, it is shown that proper choice of the mapping of the bits on to the signal points at the source and the relay, provides a significant improvement in performance, for both the NODF and the ODF schemes.