Analysis of Spectral Efficiency for Multi-Pair Users Massive MIMO Relaying Systems

Based on the massive multiple-input multiple-output (MIMO) relaying system with multi-pair users, an analytical expression of the spectral efficiency was derived by virtue of the law of large numbers when the maximum ratio combining/maximum ratio transmission (MRC/MRT) precoding was adopted at the relay. The closed-form expression gave an explicit relation between the spectral efficiency and the number of relay antennas and user-pairs, as well as the transmit power at the source users and the relay. Using this expression, we analyzed the asymptotic performance of spectral efficiency and the transmit power gain when the number of relay antennas became large with the number of user-pairs keeping fixed or proportionally increasing. It was shown that the spectral efficiency increased with the number of relay antennas and decreased with number of user-pairs, both logarithmically. Moreover, when the number of served user-pairs increased proportionally to the number of relay antennas, arbitrary spectral efficiency per user could be achieved by adjusting the ratio of antenna number and user-pair number with no extra power cost. Numerical simulations validate the accuracy of the proposed closed-form expression of spectral efficiency and verify all the analytical results in the manuscript.