  In this paper, we consider a two-way or bidirectional communications system
with a relay equipped with multiple antennas. We show that when the downlink
channel state information is not known at the relay, the benefit of having
additional antennas at the relay can only be obtained by using decode and
forward (DF) but not amplify and forward (AF). The gain becomes significant
when we employ transmit diversity together with wireless network coding. We
also demonstrate how the performance of such system can be improved by
performing antenna selection at the relay. Our results show that if downlink
channel state information is known at the relay, network coding may not provide
additional gain than simple antenna selection scheme.
