Noncoherent two- and three-phase two-way relaying (TWR) techniques are bandwidth efficient and entail no pilot symbol-related rate loss. However, noncoherent two-phase TWR (2P-TWR) has not been compared with three-phase TWR (3P-TWR), and several unanswered questions remain. In this paper, we focus on the noncoherent detection of the relay with the decode-and-forward technique. For the noncoherent maximum-likelihood detector at the relay, we propose a distance measure for the transmitted signals of the two terminal nodes. For 2P-TWR, we propose that the signal constellation of one terminal node is the signal constellation of the other terminal node rotated by an angle. Using the proposed distance measure, we obtain the optimal angles and thus resolve those unanswered questions pertaining to 2P-TWR. Finally, noncoherent 3P-TWR was found to significantly outperform noncoherent 2P-TWR in simulations and distance analyses.
- Differential encoding
- noncoherent detection
- physical-layer network coding
- two-way relaying