BER Evaluation of Linear Detectors in Massive MIMO Systems Under Imperfect Channel Estimation Effects

New perspectives for wireless communications have brought new techniques, such as a very large number of antennas at a base station (BS) serving multiple user terminals (UTs) with a single antenna each, known as massive MIMO (M-MIMO). M-MIMO linear detectors, such as maximal-ratio combining (MRC), zero-forcing (ZF) or minimum-mean-square error (MMSE) can achieve excellent performance with low complexity due to the channel hardening property. However, imperfect channel estimation produces a penalty in the performance. An average bit error rate (BER) performance analysis over time-invariant channel is presented for M-MIMO systems under imperfect channel estimation in contrast with most of M-MIMO literature that uses the ergodic capacity approach. Closed-form expressions and bounds to evaluate the average BER are derived for MRC, ZF and MMSE detectors in a unicellular environment considering
$M$
-QAM modulation. Furthermore, an expression to evaluate the normalized signal-to-noise ratio (
$E_{b}/N_{0}$
) penalty due to the imperfect channel estimation is presented. Montecarlo numerical simulations are used to verify the tightness of the derived equations which are a function of the number of BS antennas, number of users, coherence time interval, number of pilot symbols and the
$E_{b}/N_{0}$
of pilot and data symbols used for channel estimation and data detection.