On the performance of multi-way relay communications via complex field network coding

In this paper, a novel wireless cooperation scheme with complex-field network coding (CFNC), CFNC-amplify-and-forward (CFNC-AF), is developed for multi-way relay (MWR) communications. In this scheme, orthogonal CFNC vectors and joint signal detection are employed to accomplish information exchange among N(N > 2) user nodes via a helping relay node, and a multi-phase transmission protocol is designed to achieve high throughput and diversity gain. Unlike other MWR communication schemes, our scheme provides the solution for the MWR network where every node has only single antenna. By the analysis of the pairwise error probability (PEP) of the proposed scheme, the design criterion of CFNC, including full diversity criteria and maximal product criteria, are discussed. The developed scheme can achieve throughput as high as approximately 1/2 symbol per user per channel use, and N/2 symbols per channel use in total, which is much higher than that of traditional two-way relay (TWR) communications. Thus for each user node, the channel capacity of the proposed MWR network is much higher than that of the TWR network where each node has single antenna. Moreover, to minimize PEP, the power amplification factor at the relay node is optimized under the total transmission power constraint. Simulation results verify the performance gain of the developed MWR scheme.