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 usersto exchange information with each other through a single relayterminal. MWRNs are often incorporated with capacity achiev-ing lattice codes to enable the benefits of high-rate signal constel-lations to be extracted. In this paper, we analytically character-ize the symbol error rate (SER) performance of a functional de-code and forward (FDF) MWRN in the presence of channel esti-mation errors. ConsideringM-ary quadrature amplitudemodula-tion (QAM) with square constellations as an important special caseof lattice codes, we obtain asymptotic expressions for the averageSER for a user in FDF MWRN. The accuracy of the analysis athigh signal-to-noise ratio is validated by comparison with the sim-ulation results. The analysis shows that when a user decodes otherusers with better channel conditions than itself, the decoding userexperiences better error performance. The analytical results al-low system designers to accurately assess the non-trivial impact ofchannel estimation errors and the users’ channel conditions on theSER performance of a FDF MWRN withM-QAM modulation.