Frequency-domain equalization (FDE) based on minimum mean square error (MMSE) criterion can significantly improve the BER performance of DS- and MC-CDMA signal transmissions in a severe frequency-selective fading channel. However, since the frequency-distorted signal cannot be completely equalized, the residual inter-code interference (ICI) limits the BER performance improvement. In 4G systems, much higher variable rate data services than in the present 3G systems are required. Orthogonal multicode transmission technique has flexibility in offering variable rate services. However, the BER performance degrades as the number of parallel codes increases. In this paper, we propose a frequency-domain soft interference cancellation (FDSIC) for multicode DS- and MC-CDMA signal transmissions and their achievable BER performances are evaluated by computer simulation.