QAM Constellation Design for Complex Field Network Coding in Multi-Way Relay Channels

Complex field network coding has been shown to achieve a throughput of 1/2 symbol per user per channel use in a multi-way relay channel. To achieve this throughput, a superimposed combination of user symbols must be distinguishable at the relay. Rectangular QAM constellations are commonly employed in communication systems due to their ease of generation, demodulation, and near optimal performance in AWGN channels. In this paper, an algorithm is presented to provide precoding vectors that guarantee every superposed combination of user symbols at the relay is distinguishable and QAM constellations are received at the relay. The performance in AWGN channels is derived. The algorithm allows users to employ different signal constellations, and also has the flexibility to allow users to join or leave the network at any time.