In this paper, we consider a functional decode and forward (FDF) multi-way relay network (MWRN) where a common user facilitates each user in the network to obtain messages from all other users. We propose a novel user pairing scheme, which is based on the principle of selecting a common user with the best average channel gain.This allows the user with the best channel conditions to contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. Considering M -ary quadrature amplitude modulation with square constellation as a special case of lattice code transmission, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. The proposed pairing scheme also has lower average SER compared to existing schemes. We show that overall, the MWRN performance with the proposed pairing scheme is more robust, compared to existing pairing schemes, especially under worst case channel conditions when majority of users have poor average channel gains.
Index TermsMulti-way relay network, functional decode and forward, pairing scheme, wireless network coding.The authors are with the Research this paper are as follows:• Considering an L-user FDF MWRN employing sufficiently large dimension lattice codes, we derive upper bounds for the common rate and sum rate with the proposed pairing scheme (cf. Theorems 1 − 2).• Considering an L-user FDF MWRN with M-ary quadrature amplitude modulation (QAM) based transmission, which is a special case of lattice code based transmission, we derive the asymptotic average SER with the proposed pairing scheme (cf. Theorem 3). • We present important insights, obtained from a careful analysis of the results in Theorems 1-3, in the form of Propositions 1-9. Analyzing the results in Theorems 1-3, we compare the performance of the proposed pairing scheme with the existing pairing schemes and show that: -For the equal average channel gain scenario, the average common rate and the average sum rate are the same for the proposed and existing pairing schemes, but the average SER improves with the proposed pairing scheme (cf. Propositions 1, 4 and 7).-For the unequal average channel gain scenario, the average common rate, the average sum rate and the average SER all improve for the proposed pairing scheme (cf. Propositions 2, 5 and 8).-For the variable average channel gain scenario, the average common rate for the proposed pairing scheme is practically the same as the existing schemes, whereas, the average sum rate and the average SER improve for the proposed pairing scheme (cf. Propositions 3, 6 and 9).The rest of the paper is organized as follows. The system model is presented in Section II. The proposed pairing scheme is discussed in Section III and the general lattice code based transmissions with the proposed pairi...