Analysis of compute-and-forward with QPSK in two-way relay fading channels

In this paper, the error performance of compute-and-forward with QPSK over Rayleigh fading two-way relay channels is analyzed. We investigate the optimal way to select the computation coefficients to minimize the error probability at the relay. This is equivalent to maximizing the minimum Euclidean distance between the network coded messages on a superimposed two-user constellation at the relay. We derive the performance upper bound for the decoding of the network coded messages at the relay in a closed form. Both analytical results and simulation results demonstrate that when QPSK is employed, the diversity order of decoding the network coded messages at the relay can reach 1, rather than being halved as reported in previous literature where 4-PAM was considered.