On the achievable rates of symmetric Gaussian multi-way relay channels

Considering a symmetric Gaussian multi-way relay channel (MWRC) with K users, this work compares two transmission strategies, namely one-way relaying (OWR) and multi-way relaying (MWR), in terms of their achievable rates. While in OWR, only one user acts as data source at each time and transmits in the uplink channel access, users can make simultaneous transmissions in MWR. First, we prove that for MWR, lattice-based relaying ensures a gap less than bit from the capacity upper bound while MWR based on decode-and-forward (DF) or amplify-and-forward (AF) is unable to guarantees this rate gap. For DF and AF, we identify situations where they also have a rate gap less than bit. Later, we show that although MWR has higher relaying complexity, surprisingly, it can be outperformed by OWR depending on K and the system SNR. Summarily speaking, for large K and small users’ transmit power, OWR usually provides higher rates than MWR.