SER analysis of multi-way relay networks with M-QAM modulation in the presence of imperfect channel estimation

Multi-way relay networks (MWRNs) allow multiple users to exchange information with each other through a single relay terminal. MWRNs are often incorporated with capacity achieving lattice codes to enable the benefits of high-rate signal constellations to be extracted. In this paper, we analytically characterize the symbol error rate (SER) performance of a functional decode and forward (FDF) MWRN in the presence of channel estimation errors. Considering Μ-ary quadrature amplitude modulation (QAM) with square constellations as an important special case of lattice codes, we obtain asymptotic expressions for the average SER for a user in FDF MWRN. The accuracy of the analysis at high signal-to-noise ratio is validated by comparison with the simulation results. The analysis shows that when a user decodes other users with better channel conditions than itself, the decoding user experiences better error performance. The analytical results allow system designers to accurately assess the non-trivial impact of channel estimation errors and the users’ channel conditions on the SER performance of a FDF MWRN with M-QAM modulation.