||Wireless multiple-input-multiple-output (MIMO) antenna systems offer significant improvements in performance and capacity when used in wireless communications, and have received much attention recently. However, there exist a number of challenges, including their application to the frequency selective fading environment. In this thesis, a number of solutions are investigated for MIMO systems, with a focus on frequency selective fading channels. In the first contribution, two narrow-band structures are investigated in both MIMO flat (frequency nonselective) fading and frequency selective fading channels. The first one is the optimum maximum likelihood detection (MLD), and a tight union bound is derived with an asymptotic form on the symbol error probability, which provides a comprehensive performance analysis for MLD. The second one is a generalized Bell Laboratory Layered Space-Time (BLAST) structure, which allows tradeoffs between performance and complexity. In frequency selective channels, however, these narrow-band structures suffer from severe performance loss and this motivates the research on equalization for MIMO frequency selective channels. In the second contribution, a general layered space-time equalization (LSTE) structure is therefore proposed, by employing the MIMO delayed decision feedback sequence estimator (DDFSE) at each layer of detection. It is shown that the proposed LSTE significantly outperforms the flat fading case in a range of small delay spread, by achieving path diversity. The third contribution of this work is to propose a layered space-frequency equalization (LSFE) structure, where frequency-domain equalization (FDE) is introduced to the layered architecture. Simulation results show that LSFE provides much better performance than uncoded OFDM and LSTE, especially with a higher delay spread and a smaller number of receive antennas. Additionally, FDE at each layer of LSFE is incorporated with time-domain decision feedback (referred to as FD-DFE), which yields great contributions to further performance enhancement. In the fourth contribution, two power allocation (PA) schemes are incorporated with LSTE (LSFE), including min-BER PA and EQ-BER PA. It is shown that both the PA schemes provide significant performance gain over the uniform-power case, especially at higher SNR. Intensive performance analysis is provided, including closed-form PA results, BER analysis and discussion on detection ordering. In the future, MIMO OFDM systems with insufficient cyclic prefix will be studied, to enhance the bandwidth efficiency with little/no performance loss. Also, improved PA will be investigated and PA will be incorporated with adaptive modulation for MIMO frequency selective channels.