Cellular wireless communication systems, based on the 3rd Generation Partnership Project (3GPP) termed as Long Term Evolution (LTE) are characterized by high mobility, efficient use of channel capacity even approaching Shannon Capacity and finally high potential to increase the cell coverage. Orthogonal Frequency Division Multiplex Access (OFDM) is a fundamental modulation technique considered in the LTE downlink transmission, while Single Carrier Frequency Division Multiplexing (SC-FDMA) is used in the uplink. To further improve the system performance provided by LTE, Multiple-Input Multiple-Output (MIMO) systems are also employed in this standard. However, the imperfections of the High Power Amplifier (HPA) have increasingly become the major bottleneck in the drive toward faster and more reliable system performance.Specially, the nonlinear amplification remains the key design issue to be solved in order to get improved overall performance. In this thesis, we give an comprehensive discussion concerning the nonlinear amplification in the multicarrier systems and state some important conclusions regarding SC-FDMA and MIMO-OFDM nonlinear detection.