||Recently, adaptive resource allocation, OFDM MIMO systems and V-BLAST detection algorithm in frequency selective fading channel attract a lot of interests because they can significantly improve the system performance. In particular, we study the system design of the single user as well as the multi-user environment in an OFDM MIMO system. We analyze the properties of the wireless MIMO channels and develop effective algorithms to utilize and allocate the resources in real-time communication applications. Assuming the knowledge of the instantaneous channel gains for all spatial channels at all the sub-carriers in the receiver, several types of algorithms have been proposed to assign the bit and/or the transmit power level to each sub-carriers in each spatial channel to minimize the total transmission power for a given bit error rate. The optimal solutions to these problems in both the single user and the multi-user environment are very complicated and involve combinatorial search over a very large space. In our approach, we study the trade-off between the amount of information needed to be fed back to the transmitter and the system performance. Moreover, several proposed algorithms provide different tradeoffs between the system performance and the amount of channel feedback, allowing the user to optimize the system to obtain the desired system performance to channel feedback ratio. In the second part of the thesis, we analyze and demonstrate the effectiveness of our proposed algorithms by computer simulation for different channel configurations. Assuming prefect synchronization and channel estimation, we find that the proposed allocation algorithms can significantly improve the system performance and still maintain a reasonable computational complexity compared to the traditional V-BLAST for OFDM MIMO system in a frequency selective fading channel model.