Spectral Efficiency of Multipair Massive MIMO Two-Way Relaying With Imperfect CSI

We consider a two-way half-duplex relaying system where multiple pairs of single-antenna users exchange information assisted by a multiple-antenna relay. Taking into account the practical constraint of imperfect channel knowledge, we study the achievable sum spectral efficiency (SE) of the amplify-and-forward protocol, assuming that the relay employs maximum ratio processing. We derive a closed-form expression for the sum SE for arbitrary system parameters and a large-scale approximation for the sum SE when the number of relay antennas M becomes sufficiently large. In addition, we study how the transmit power reduces with M to maintain a desired SE. 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
^α
, 1/M
^β
, and 1/M
^γ
for certain combinations of α, β, and γ, 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 SE, novel power allocation schemes are designed to further improve the sum SE.