On the optimal pre-coding of complex field network coding with Mpsk modulation

Complex field network coding (CFNC) enables a one-to-one mapping between the source signal vectors and the received signals. CFNC outperforms other physical layer network coding methods which decode the received signal as a combination of source signals. However, the linear constellation pre-coding (LCP) scheme adopted by CFNC to compute complex coefficients is developed for MIMO system, which is not sufficient to achieve the optimal performance of CFNC. This paper considers the encoding process of CFNC as constellation rotations at sources and proposes an optimal rotation method to maximize the minimum Euclidean distance between equivalent constellation points at the receiver. Excellent performance gains are proved by both numerical evaluations and simulation results.