In a multiway relay channel (MWRC), pairwise transmission strategy can beused to reduce the computational complexity at the relay and the users withoutsacrificing the data rate, significantly. The performance of such pairwisestrategies, however, is affected by the way that the users are paired totransmit. In this paper, we study the effect of pairing on the common rate andsum rate of an MWRC with functional-decode-forward (FDF) relaying strategywhere users experience asymmetric channel conditions. To this end, we firstdevelop a graphical model for an MWRC with pairwise transmission strategy.Using this model, we then find the maximum achievable common rate and sum rateas well as the user pairings that achieve these rates. This marks the ultimateperformance of FDF relaying in an MWRC setup. Further, we show that the rateenhancement achieved through the optimal user pairing becomes less pronouncedat higher SNRs. Using computer simulations, the performance of the optimalpairing is compared with those of other proposed pairings in the literature.
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