Wireless communications systems use a multiple user scheme such as time- or frequency-division, but these do not allow truly simultaneous use of the spectrum. By deploying multiple antennas and beamforming, it is possible, in principle, for users to share the spectrum simultaneously, and this scenario is called the multiuser MIMO interference channel. In this modern age of high speed wireless data communication, Multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) schemes have recently drawn wide interests due to their capability of high data rate transmission over multipath fading channels. This thesis work introduces the study of multi-user and multi-antenna MIMO-OFDM systems. In this work, the performances of two main classes of MIMO-OFM system i.e. multi-user and multi-antenna MIMO-ODM techniques have been studied. In the existing system, the system exploited uplink-downlink SINR duality. Joint transmit-receive optimization based on null space constraint was introduced. But none of the existing system can be applied to the more complicated interference channel. In this project the system proposed a three beamforming designs for multiuser multiple-input and multiple-output with orthogonal frequency-division multiplexing. All the solutions of the proposed system allow for exploiting multipath diversity where the complexity of the decoder is independent of the number of antennas. The proposed methods are also computationally simpler, but at the price of one more antenna element at each terminal.