Study of Half-Duplex Gaussian Relay Channels with Correlated Noises

In this paper, we consider a half-duplex Gaussian relay channel where the noises at the relay and destination are arbitrarily correlated. For this generalized relay channel, we first evaluate the cut-set bound as well as the achievable rates with three existing relay schemes: Decode-and-Forward (DF), Compress-and-Forward (CF), and Amplify-and-Forward (AF), with performance comparison under various channel settings. We observe that although DF completely disregards the noise correlation while the other two could exploit such extra information, none of the three relay schemes always outperforms the others over different correlation coefficients; however, the exploitation of noise correlation by CF and AF leads to more significant benefit when the source-relay channel is weak. It is further shown that a negative noise correlation is always helpful for AF. We also establish two capacity-achieving results under two special noise correlation coefficients, with one being achieved by DF and the other being achieved by direct link transmission (or a special case of CF), which correspond to the capacity results for the traditional Gaussian degraded relay channel and the Gaussian reversely-degraded one.