Ergodic Rate Analysis for Multipair Massive MIMO Two-Way Relay Networks

This paper considers a multipair massive multiple-input–multiple-output two-way relay network, in which multiple pairs of users are served by a relay station with a large number of antennas, which uses maximum ratio combining/maximum ratio transmission and a fixed amplification factor for reception/transmission. First, the users' ergodic rates are derived for the case with a finite number of antennas, and then, the rate gain is analyzed when the transmit power of the senders and the relay is sufficiently large. We show that the ergodic rates increase with the number of antennas at the relay, i.e., $N$ , but decrease with the number of user pairs, i.e., $K$ , both logarithmically. The energy efficiency for the network is also investigated when the number of antennas grows to infinity. It is further revealed that the ergodic sum-rate can be maintained while the users' transmit power is scaled down by a factor of $1/N$ or the relay power by a factor of $2K/N$ . This indicates that users obtain an energy efficiency gain of $N$ , but the relay has an energy efficiency gain of $N$ divided by the number of users, i.e., $2K$ .