Multiuser precoding scheme and achievable rate analysis for massive MIMO system

We analyze the downlink multiuser precoding of massive multiple input multiple output (MIMO) system, where the base station (BS) has ideal channel state information (CSI) and adopts three types of different linear precoding schemes, i.e., maximum ratio transmission (MRT), zero-forcing (ZF), and minimum mean squared error (MMSE). Under a Rayleigh fading channel, we attain the exact expressions on the achievable rate for these three precoding schemes. Moreover, we provide several insights on the achievable rates and reveal the relation of the number of BS antennas, the number of users, and the input signal-to-noise ratio (SNR) with the achievable rates respectively. It is found in general that the achievable rate increases with the number of BS antennas and the input SNR. To be more specific, the MRT precoding scheme is much inferior to the ZF and MMSE precoding schemes and tends to be at a fixed rate at the high SNR case. On the contrary, the MRT precoding scheme outperforms ZF precoding schemes at the low SNR case. Moreover, the total achievable rate always does not increase with the number of users and the optimal number of users always exists for the ZF and MMSE precoding schemes.