Limited feedback designs for two-way wireless relaying channels with physical network coding

In this paper, we propose a limited feedback system for two-way wireless relaying channels with physical network coding (PNC). The optimal system with full feedback has already been studied when a modulo operation is employed for the PNC. In this case, phase and power of channels of two end nodes are adjusted to maximize the minimum distance. Based on this full feedback system, we design new quantization methods for the phase and the power. From the observation of the minimum distance, we present a codebook design. Especially, for the quantization of power in the system with 16-QAM, a novel power quantization scheme is proposed to maximize the worst minimum distance. Finally, the simulation results confirm that our proposed scheme outperforms conventional limited systems with reduced complexity.