This papers considers the design of a mutiple-input multiple-output (MIMO) communication system with channel knowledge at the transmitter and receiver. The design methods available in the literature have addressed the following two aspects of the problem: a) choice of the symbol constellations for a given transmission scheme or b) choice of the optimal (linear) precoder and equalizer for a given choice of the constellations. More specifically, the choice of the constellations has been made enforcing a diagonal, or parallel, transmission. However, in practice, the two problems of choosing the constellations and the linear precoder/equalizer are clearly coupled, and the diagonal structure may not be necessarily the best. This paper attempts to provide a global view of the problem by bridging the gap between the existing results on the selection of the constellations and on the design of the signal processing in the form of a linear transceiver (i.e., precoding at the transmitter and equalization at the receiver).