Orthogonal frequency division multiplexing (OFDM) is discussed as a special form of multi-carrier modulation (MCM). One major problem of the OFDM system is the sensitivity to an unknown frequency offset at the receiver. To improve the performance of the OFDM system, correction of the frequency offset is required before decision making. An adaptive method of frequency offset correction is presented. The adaptation algorithm used here is based on the LMS and the estimation is proven unbiased. A multiuser communications system having similar signal structure to the OFDM system, termed as multi-carrier code division multiple access (MC-CDMA), is discussed. The MC-CDMA system is susceptible to multiuser interference. Although orthogonal multiuser codes are used, the frequency selective fading might destroy the orthogonality between different codes and result in multiuser interference. The conventional decorrelator can be used to cancel such interference completely but has the disadvantage of enhancing noise power. An adaptive decorrelation algorithm, known as the Bootstrap algorithm, is implemented to separate interference from the desired user's signal. Such algorithm is shown to perform better than the conventional decorrelator particularly in the low interference region.