Division Algebras and Wireless Communication

The aim of this note is to bring to the attention of a wide mathematical audience the recent application of division algebras to wireless communication. The application occurs in the context of communication involving multiple transmit and receive antennas, a context known in engineering as MIMO, short for multiple input, multiple output. While the use of multiple receive antennas goes back to the time of Marconi, the basic theoretical framework for communication using multiple transmit antennas was only published about ten years ago. The progress in the field has been quite rapid, however, and MIMO communication is widely credited with being one of the key emerging areas in telecommunication.