  Zero-forcing (ZF) precoding plays an important role for massive MIMO downlink
due to its near optimal performance. However, the high computation cost of the
involved matrix inversion hinders its application. In this paper, we adopt the
first order Neumann series (NS) for a low-complexity approximation. By
introducing a relaxation parameter jointly with one selected user's
interference to others into the precondition matrix, we propose the
identity-plus-column NS (ICNS) method. By further exploiting the multi-user
diversity gain via choosing the user with the largest interference to others,
the ordered ICNS method is also proposed. Moreover, the sum-rate approximations
of the proposed ICNS method and the competitive existing identity matrix based
NS (INS) method are derived in closed-form, based on which the performance loss
of ICNS due to inversion approximation compared with ideal ZF and its
performance gain over INS are explicitly analyzed for three typical massive
MIMO scenarios. Finally, simulations verify our analytical results and also
show that the proposed two designs achieve better performance-complexity
tradeoff than ideal ZF and existing low-complexity ZF precodings for practical
large antenna number, correlated channels and not-so-small loading factor.
