As one of the major breakthroughs in the physical layer evolution, multiple-input multiple-output (MIMO) is a promising technology in present and future wireless communication systems, boosting up the overall throughput/reliability by opening up the spatial dimension.MIMO systems can be used to achieve diversity gain, multiplexing gain or a combination of the two. For MIMO systems seeking multiplexing gain, an essential objective is to cancel the interference among antenna pairs in order to obtain the original transmitted data. This interference-cancelling process can be viewed as decomposing the channel into multiple independent subchannels, each transmitting its own data without intruding on one another. This research focuses on the realizations and applications of MIMO channel decomposition algorithms. The first part of the work, Chapters 2 and 3, are based on three channel decomposition methods proposed by Yi Jiang et. al., including the Geometric Mean Decomposition (GMD), the Uniform Channel Decomposition (UCD) and the Tunable Channel Decomposition (TCD). We first present hardware design of closed-loop MIMO transceivers based on the GMD and the UCD, which can both decompose the communications channel into identical subchannels, but the UCD is superior in that it is capacity lossless. We then discuss the application of the TCD in cognitive radio systems, which can control the individual gains of the decomposed subchannels and is suitable for satisfying different quality-of-service (QoS) constraints. We present a reconfigurable MIMO transceiver design based on the TCD. In the second part of this dissertation, Chapter 4, we investigate MIMO transceiver designs over channels where inter-symbol interference (ISI) is present. We propose a new fast iterative algorithm to obtain the minimum-mean-square-error decision feedback equalizer (MMSE-DFE) for MIMO single carrier systems. This algorithm is based on the QR decomposition of an augmented channel matrix. It outperforms other time domain MMSE-DFE algorithms in terms of complexity and flexibility; moreover, it can be converted into hybrid DFE where the feedforward part is in frequency domain, which makes it especially suitable for heterogeneous networks.