In this thesis, we studied the efficient non-diagonal precoder based on the maximization of the minimum Euclidean distance (max-dmin) between two received data vectors. Because the complexity of the optimized solutions depends on the number of antennas and the modulation order, the max-dmin precoder was only available in closed-form for two independent data-streams with low-order modulations. Therefore, we firstly extended this solution for two 16-QAM symbols and then generalized the concept to any rectangular QAM modulation. By using trigonometric functions, a new virtual MIMO channel representation thanks to two channel angles, allows the parameterization of the max-dmin precoder and the optimization of the distance for three parallel data streams. Thanks to this scheme, an extension for an odd number of data-streams using QAM modulations is obtained. Not only the minimum Euclidean distance but also the number of neighbors providing it has an important role in reducing the error probability when an ML detection is considered at the receiver. Aiming at reducing this number of neighbors, a new precoder in which the rotation parameter has no influence is proposed, leading to less complex processing and a smaller space of solutions. Finally, an approximation of the minimum distance was derived by maximizing the minimum diagonal element of the SNR-like matrix. The major advantage of this design is that the solution can be available for all rectangular QAM-modulation and any number of datastreams
