This research is mainly concerned with the performance analysis of multicarrier code-division multiple-access (MC-CDMA) systems over frequency-selective fading channels. The performance of MC-CDMA systems with space time block codes is investigated in conjunction with a new transmit diversity scheme for MC-CDMA systems by exploiting some intrinsic properties of MC-CDMA systems. The channel estimation algorithms for multicarrier systems are also considered. To analyze the performance of MC-CDMA systems over fading channels a Gaussian approximation of the multiple-access interference is commonly adopted with the assumption that the fading among subcarriers is independent of each other. However, the accuracy of Gaussian approximation depends on system configurations, especially on the number of users and their powers. It is well known that the Gaussian approximation is not accurate when the number of users is small or power control is inaccurate. Furthermore, the assumption of independent fading is usually not practical since the fading of the subcarrier is highly correlated due to insufficient subcarrier spacing. Therefore, an exact bit-error rate (BER) analysis is always desirable. In this thesis, we propose performance analysis methods for MC-CDMA systems over downlink transmission. The analysis assumes the two most popular fading statistics, namely Rayleigh and Rician. An exact BER formula is obtained