Abstract-In this paper, we study the effect of users' transmission ordering on the common rate and sum rate of pairwise multiway relay channels (MWRCs) with functional-decodeforward strategy. To this end, we first develop a graphical model for the data transmission in a pairwise MWRC. Using this model, we then find the optimal orderings that achieve the maximum common rate and sum rate of the system. The achieved maximum common/sum rate is also found. Moreover, we show that the performance gap between optimal orderings and a random ordering vanishes when SNR increases. Computer simulations are presented for better illustration of the results.

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In a multiway relay channel (MWRC), pairwise transmission strategy can be used to reduce the computational complexity at the relay and the users without sacrificing the data rate, significantly. The performance of such pairwise strategies, however, is affected by the way that the users are paired to transmit. In this paper, we study the effect of pairing on the common rate and sum rate of an MWRC with functional-decode-forward (FDF) relaying strategy where users experience asymmetric channel conditions. To this end, we first develop a graphical model for an MWRC with pairwise transmission strategy. Using this model, we then find the maximum achievable common rate and sum rate as well as the user pairings that achieve these rates. This marks the ultimate performance of FDF relaying in an MWRC setup. Further, we show that the rate enhancement achieved through the optimal user pairing becomes less pronounced at higher SNRs. Using computer simulations, the performance of the optimal pairing is compared with those of other proposed pairings in the literature. Index TermsMultiway relay channels, functional-decode-forward, pairwise relaying, common rate, sum rate.The authors are with the

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