Algebraic Approaches to Space-Time Code Construction for Multiple-Antenna Communication

A major challenge in wireless communications is overcoming the deleterious effects of fading, a phenomenon largely responsible for the seemingly inevitable dropped call. Multiple-antennas communication systems, commonly referred to as MIMO systems, employ multiple antennas at both transmitter and receiver, thereby creating a multitude of signalling pathways between transmitter and receiver. These multiple pathways give the signal a diversity advantage with which to combat fading. Apart from helping overcome the effects of fading, MIMO systems can also be shown to provide a manyfold increase in the amount of information that can be transmitted from transmitter to receiver. Not surprisingly,MIMO has played, and continues to play, a key role in the advancement of wireless communication.Space-time codes are a reference to a signalling format in which information about the message is dispersed across both the spatial (or antenna) and time dimension. Algebraic techniques drawing from algebraic structures such as rings, fields and algebras, have been extensively employed in the construction of optimal space-time codes that enable the potential of MIMO communication to be realized, some of which have found their way into the IEEE wireless communication standards. In this tutorial article, reflecting the authors’interests in this area, we survey some of these techniques.