Multi-Pair Two-Way Massive MIMO AF Relaying with ZFR/ZFT Beamforming and Imperfect CSI over Ricean Fading Channels

This paper investigates the spectral and energy efficiencies of a multi-pair two-way amplify-and-forward (AF) relay system over Ricean fading channels, where multiple user-pairs exchange information within pair through a relay with very large number of antennas, while each user equipped with a single antenna. Firstly, beamforming matrixe of zero-forcing reception/zero-forcing transmission (ZFR/ZFT) with imperfect channel state information (CSI) at the relay is given. Then, the unified asymptotic signal-to-interference-plus-noise ratio (SINR) expressions with imperfect CSI are obtained analytically. Finally, two power scaling schemes are proposed and the asymptotic spectral and energy efficiencies based on the proposed power scaling schemes are derived and verified by the Monte-Carlo simulations. Theoretical analyses and simulation results show that with imperfect CSI, if the number of relay antennas grows asymptotically large, we need cut down the transmit power of each user and relay to different proportion when the Ricean K-factor is non-zero and zero (Rayleigh fading) in order to maintain a desirable rate.