In this thesis, a novel detection in multicarrier code-division multiple-access (MC-CDMA) system by using adaptive widely linear algorithm is proposed. The proposed method utilizes the time-multiplex-pilot symbols as the reference symbol due to the frequency selective fading channel. In addition, this algorithm jointly elaborate the received signal and its complex conjugate. To verify the performance of the algorithms, the proposed techniques are used for the uplink channel response of MC-CDMA systems. The simulation results show that this algorithm has a very good capability of suppressing multiple access interference (MAI), resulting in a MC-CDMA system in multi-path Rayleigh fading channel. Our performance analysis and simulation results are compared and shown to be in good agreement that the widely linear detection stochastic gradient algorithm has important advantages over their linear counterparts.