On the BER Gap Between Optimal and Near-Optimal Detectors on Massive MIMO Systems

On massive MIMO (maMIMO) systems with a large number of antennas at the base station (BS) to serve singleantenna users, linear detectors, as zero forcing (ZF), can achieve the near-optimal bit error rate (BER) performance due to the asymptotically orthogonal maMIMO channel property. However, it is necessary to know under what circumstances, linear detectors can be considered as near-optimal for the design of maMIMO systems. To solve this problem, in this paper, we find out an upper bound for the BER performance gap between the optimal and the near-optimal detectors. This upper bound is a function of the maMIMO channel condition number and it only depends according to the relation between the number of BS antennas and users. Simulation results are used to demonstrate the validity of the upper bound for the BER gap between near-optimal and optimal detectors on maMIMO systems.