Multicarrier code-division multiple-access (MC-CDMA) is a potentially attractive multiple access technique for future wireless communication systems. A unified multirate MCCDMA system model able to fit different multirate transmission schemes is presented. The performance of the multicode system with the same processing gain and the variable spreading factor (VSF) system is compared. Based on the characteristic function (CF) of a complex Gaussian random vector (CGRV), we present a bit error rate (BER) analysis method. The accuracy of the method is verified by computer simulations in frequency selective Rayleigh fading channels. Different subcarrier interleaving schemes for VSF MC-CDMA are also investigated. It is shown that if the gain resulting from the subcarrier interleaving is taken into account, VSF MC-CDMA and multicode MC-CDMA offer quite similar performance.