Performance analysis of ZF and MMSE receivers in uplink of MU-MIMO system

For uplink of Multiuser (MU) Multiple-Input, Multiple-Output (MIMO) system with M receive antennas at base station and one transmit antenna at each user, in this paper, performances of linear decoders, namely Zero-Forcing decoder and Minimal Mean-Square Error (MMSE) decoder, are investigated. Differing from existing results which mainly describe various asymptotic properties, this paper gives analytical formulas of estimating pair-wise error probabilities (PEP) of ZF and MMSE decoders for given parameters M, K (number of users), and ρ (Signal-to-Noise Ratio, SNR). Furthermore, a formula estimating MMSE decoder dB gain over ZF decoder is given. Based on this formula, an analytical formula calculating the gain when ρ goes to infinite is also presented, which is almost the same as one given in the paper. At last, simulations to confirm these formulas are shown.