Full Diversity Physical-Layer Network Coding in Two-Way Relay Channels With Multiple Antennas

Abstract

This paper studies a two-way relay channel where two single-antenna users exchange messages via a relay with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> antennas. A new physical-layer network coding (PNC) method is proposed, referred to as channel-quantized PNC (CQ-PNC), that can achieve full diversity gain of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> . The proposed method converts <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> received signals at the relay into two signals by a QR decomposition. The first one is a weighted summation of the two users' messages and the second one is a scaled version of one user's message. Then, the first signal is quantized at the relay by using the channel coefficient and the quantization error is cancelled by using the side information of the second signal. Finally, a Gaussian-integer weighted summation of the two users' messages is obtained, mapped to network codeword, and then broadcast to the two users. It is proved that the proposed CQ-PNC can achieve the full diversity gain of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="TeX">$K$</tex-math></inline-formula> with receiver side channel information, low computational complexity and symbol level synchronization. Simulation results demonstrate that the proposed method obtains optimum performance results with negligible gap.