In this paper, we evaluate the performance of single- and multi-antenna multi-carrier code division multiple access (MC-CDMA) downlink (base station to mobile terminal) systems in single- and multi-cell environments. We first propose a minimum mean square error (MMSE) filter with a Gaussian approximation for a single input single output (SISO) MC-CDMA downlink system. Then, we apply it to a SIMO (single input multiple output) system with a conventional turbo coding. Furthermore, we compare the performance of SISO (11) and SIMO (12) MC-CDMA systems with that of a multiple input multiple output (MIMO) (22) system employing space-time turbo coded modulation (STTuCM) in a multi-cell environment with 7 cells by computer simulation. Based on the computer simulation results, it is found that the considered MIMO system can achieve twofold capacity with the same transmission power in the multi-cell environment.