Performance Analysis of Two-Step Bi-Directional Relaying with Multiple Antennas

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In this paper, the authors study decode-and-forward multi-antenna relay systems that achieve bi-directional communication in two time slots. They investigate different downlink broadcast schemes which employ binary or analog network coding at the relay. They 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, they propose a Max-Min antenna selection with binary network coding scheme that can approach this performance with only partial channel state information.