On error rate performance of multi-cell massive MIMO systems with linear receivers

For an uplink of multi-cell multiuser (MU) Multiple-Input, Multiple-Output (MIMO) system, where each cell has a Base Station (BS) with M antennas and K users with single antenna, the Zero-Forcing (ZF) decoder and the Minimal Mean-Square Error (MMSE) decoder are considered. Upper bounds, lower bounds on Pair-wise Error Probability (PEP) of these decoders are derived. Moreover, analytic expressions of approximations on PEP are given. These show that, if the BS knows Channel State Information (CSI) in its own cell only and does not have CSI in other cells, error floors will occur even when Signal-to-Noise Ratio (SNR) goes to infinity for both the ZF decoder and the MMSE decoder, while these error floors disappear when M goes to large. All theoretical results above are confirmed by simulations. Especially, the approximations of PEP match up with simulation results very well.