On the Matrix Inversion Approximation Based on Neumann Series in Massive MIMO Systems

Zero-Forcing (ZF) has been considered as one of the potential practical precoding and detection method for massive MIMO systems. One of the most important advantages of massive MIMO is the capability of supporting a large number of users in the same time-frequency resource, which requires much larger dimensions of matrix inversion for ZF than conventional multi-user MIMO systems. In this case, Neumann Series (NS) has been considered for the Matrix Inversion Approximation (MIA), because of its suitability for massive MIMO systems and its advantages in hardware implementation. The performance-complexity trade-off and the hardware implementation of NS-based MIA in massive MIMO systems have been discussed. In this paper, we analyze the effects of the ratio of the number of massive MIMO antennas to the number of users on the performance of NS-based MIA. In addition, we derive the approximation error estimation formulas for different practical numbers of terms of NS-based MIA. These results could offer useful guidelines for practical massive MIMO systems.