Zero-forcing Precoding for the MU-MISO Downlink: How Many Antennas Do We Need?

In this study, we consider zero-forcing (ZF) precoding under uncorrelated Rayleigh channels with both perfect channel state information (CSI) and pilot-based CSI in a multi-user multiple-input single-output (MU-MISO) system. Using perfect CSI, we first demonstrate that the needed number of the transmit antennas for ZF precoder to achieve a certain percentage of the maximal achievable sum-rate monotonically decreases with the increase of the transmit signal-to-noise ratio (SNR). In addition, the analysis of the needed transmit antennas shows that an upper bound of the required number of antennas for easy calculation only relates to the number of users and the target percentage. For completeness of the research, the pilot-based case is analyzed to examine that how pilots will affect the aforementioned results. Finally, the concept of massive MIMO for practical deployment is discussed via simulation results.