Performance Analysis of Two-Step Bi-Directional Relaying with Multiple   Antennas
  In this paper we study decode-and-forward multi-antenna relay systems that achieve bi-directional communication in two time slots. We investigate different downlink broadcast schemes which employ binary or analog network coding at the relay. We also analyze and compare their performances in terms of diversity order and symbol error probability. It is shown that if exact downlink channel state information is available at the relay, using analog network coding in the form of multi-antenna maximal-ratio transmit beamforming to precode the information vectors at the relay gives the best performance. Then, we propose a Max-Min antenna selection with binary network coding scheme that can approach this performance with only partial channel state information. 
Mahshad Eslamifar, Woon Hau Chin, Chau Yuen and Yong Liang Guan
cs.IT math.IT