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The analysis of modulation schemes for the physical layer network-coded twoway relaying scenario is presented which employs two phases: Multiple access(MA) phase and Broadcast (BC) phase. It was shown by Koike-Akino et. al. thatadaptively changing the network coding map used at the relay according to thechannel conditions greatly reduces the impact of multiple access interferencewhich occurs at the relay during the MA phase. Depending on the signal set usedat the end nodes, deep fades occur for a finite number of channel fade statesreferred as the singular fade states. The singular fade states fall into thefollowing two classes: The ones which are caused due to channel outage andwhose harmful effect cannot be mitigated by adaptive network coding arereferred as the \textit{non-removable singular fade states}. The ones whichoccur due to the choice of the signal set and whose harmful effects can beremoved by a proper choice of the adaptive network coding map are referred asthe \textit{removable} singular fade states. In this paper, we derive an upperbound on the average end-to-end Symbol Error Rate (SER), with and withoutadaptive network coding at the relay, for a Rician fading scenario. It is shownthat without adaptive network coding, at high Signal to Noise Ratio (SNR), thecontribution to the end-to-end SER comes from the following error events whichfall as $\text{SNR}^{-1}$: the error events associated with the removablesingular fade states, the error events associated with the non-removablesingular fade states and the error event during the BC phase. In contrast, forthe adaptive network coding scheme, the error events associated with theremovable singular fade states contributing to the average end-to-end SER fallas $\text{SNR}^{-2}$ and as a result the adaptive network coding schemeprovides a coding gain over the case when adaptive network coding is not used.

Performance Analysis of Adaptive Physical Layer Network Coding for Wireless Two-way Relaying