Symbol Error Probability of a Physical Layer Network Coded System in Nakagami Fading Channels

Abstract

In this paper, we consider a two-way relay (TWR) system, where two user nodes exchange their information within two transmission phases, by the help of a relay node adopting physical layer network coding. In the system, two users transmit their binary phase shift keying symbols simultaneously in the first phase, and the relay node decodes the XORed version of two user data and broadcasts it back to two users in the second phase. The performance of the system is analyzed in terms of the average end-to-end symbol error probability in Nakagami-m fading channels, for which a tight upper bound is derived in a closed form to provide an accurate and handy estimate on the performance. The results show that our upper bounds are almost indistinguishable from simulation results for various channel and system configurations. In addition, the optimal relay location and power allocation for various conditions can be obtained quickly with our analysis.