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We consider a two-way half-duplex relaying system where multiple pairs ofsingle 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 simplemaximum ratio processing. We derive an exact closed-form expression for the sumspectral efficiency of the AF protocol and a large-scale approximation for thesum spectral efficiency of the DF protocol when the number of relay antennas,$M$, becomes sufficiently large. In addition, we study how the transmit powerscales with $M$ to maintain a desired quality-of-service. In particular, ourresults show that by using a large number of relay antennas, the transmitpowers of the user, relay, and pilot symbol can be scaled down proportionallyto $1/M^\alpha$, $1/M^\beta$, and $1/M^\gamma$ for certain $\alpha$, $\beta$,and $\gamma$, respectively. This elegant power scaling law reveals afundamental tradeoff between the transmit powers of the user/relay and pilotsymbol. Finally, capitalizing on the new expressions for the sum spectralefficiency, novel power allocation schemes are designed to further improve thesum spectral efficiency.

Multipair Two-way Half-Duplex Relaying with Massive Arrays and Imperfect CSI