  We consider a two-way half-duplex relaying system where multiple pairs of
single antenna users exchange information assisted by a multi-antenna relay.
Taking into account the practical constraint of imperfect channel estimation,
we study the achievable sum spectral efficiency of the amplify-and-forward (AF)
and decode-and-forward (DF) protocols, assuming that the relay employs simple
maximum ratio processing. We derive an exact closed-form expression for the sum
spectral efficiency of the AF protocol and a large-scale approximation for the
sum spectral efficiency of the DF protocol when the number of relay antennas,
$M$, becomes sufficiently large. In addition, we study how the transmit power
scales with $M$ to maintain a desired quality-of-service. In particular, our
results show that by using a large number of relay antennas, the transmit
powers of the user, relay, and pilot symbol can be scaled down proportionally
to $1/M^\alpha$, $1/M^\beta$, and $1/M^\gamma$ for certain $\alpha$, $\beta$,
and $\gamma$, respectively. This elegant power scaling law reveals a
fundamental tradeoff between the transmit powers of the user/relay and pilot
symbol. Finally, capitalizing on the new expressions for the sum spectral
efficiency, novel power allocation schemes are designed to further improve the
sum spectral efficiency.
