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The book is about performances assessment of different schemes of MIMO decoders in terms of quality and complexity. At the end, an optimum MIMO decoder has been found with quality performances near to Maximum Likelihood decoder with reasonable complexity. By combining pre-processing techniques with sub-optimal decoders has lead to a good performance/complexity trade-off. Pre-processing techniques include left pre-processing (GDFE) and the right pre-processing (lattice reduction). GDFE pre-processing transforms the original system into a non equivalent one which is more conditioned than the original. The impact of GDFE pre-processing on the tree search stage has been highlighted when used with optimal decoders. Same applies for lattice reduction. Lattice reduction aims to reduce the basis of the channel matrix, since sub-optimal decoders perform very well with roughly orthogonal matrices. Two lattice reduction algorithms have been used (LLL and Seysen) which are characterized by their polynomial time. The use of both GDFE and Seysen reduction with the ZFDFE decoder has given very good performance and reasonable complexity.