Orthogonal frequency division multiplexing (OFDM) systems with cyclic prefix (CP) can be used to protect signal from the time-variant multipath channel induced distortions. However, the presence of CP could greatly decrease the effective data rate, thus many recent research works have been focused on the multiple-input multiple-output (MIMO) OFDM systems without CP (CP-free), equipped with the space-time block codes (ST-BC). The constraint of the conventional MIMO-OFDM (without using the ST-BC) system is that the number of receive-antenna has to be greater than the transmit-antenna. In this thesis, we first consider the ST-BC MIMO-OFDM system and show that the above-mentioned constraint can be removed, such that the condition become that the receive antenna should be greater than one, that is the basic requirement for MIMO system. It is particular useful and confirm to the recently specification, e.g., 3GPP LTE (Long Term Evolution) where the system deploy the 2¡Ñ2 or 4¡Ñ4 antennas systems. This thesis also considers the effects of peak-to-average power ratio (PAPR) in the transmitter and In-phase/ Quadrature-phase (IQ) imbalance in the receiver, and solves them by using the adaptive Volterra predistorter and blind adaptive filtering approach of the nonlinear parameters estimation and compensation, along with the power measurement, respectively. After the compensator of IQ imbalance in the receiver, an equalizer under the framework of generalized sidelobe canceller (GSC) is derived for interference suppression. To further reduce the complexity of receiver implementation, the partially adaptive (PA) scheme is applied by exploiting the structural information of the signal and interference signature matrices. As demonstrated from computer simulation results, the performance of the proposed CP-free ST-BC MIMO-OFDM receiver is very similar to that obtained by the conventional CP-based ST-BC MIMO-OFDM system under either the predistortion or compensation scenario.