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

This paper considers a limited feedback system for two-way wireless relaying channels with physical network coding (PNC). For full feedback systems, the optimal structure with the PNC has already been studied where a modulo operation is employed. In this case, phase and power of two end node channels are adjusted to maximize the minimum distance. Based on this result, we design new quantization methods for the phase and the power in the limited feedback system. By investigating the minimum distance of the received constellation, we present a codebook design to maximize the worst minimum distance. Especially, for quantization of the power for 16-QAM, a new power quantization scheme is proposed to maximize the performance. Also, utilizing the characteristics of the minimum distance observed in our code-book design, we present a power allocation method which does not require any feedback information. Simulation results confirm that our proposed scheme outperforms conventional systems with reduced complexity.