Phase offset equalization based on half-blind pre-distortion for asynchronous physical-layer network coding

Phase offset is inevitable in asynchronous physical-layer network coding (PNC) systems, which restricts the accuracy of PNC decoding. To address this issue, this paper proposes a half-blind equalization based on pre-distortion. In the scheme, the intentional phase distortion is pre-brought into the symbols of one user, and then, it is utilized by the relay to equalize the received signals and modify the updating equations in the decoding process. By formulating a phase gain-loss factor model, the upper bound of proposed equalization is proved. On the basis of that, a threshold is proposed to avoid unnecessary distortion. Simulation results verify the effectiveness of the theoretical analysis, and show that the bit error rate performance can be improved by the proposed algorithm.