Further results on differential space-time modulation

A general approach to differential modulation using multiple transmit and receive antennas was proposed independently by Hughes (see IEEE Trans. on Commun., 1999), and by Hochwald and Sweldens (see IEEE Trans. on Inform. Theory, 1999, and Proc. IEEE Wireless Networking and Communications Conf. (WCNC ´99), vol.l, p.145-49, 1999). In this approach, data are differentially encoded using a special class of space-time block codes called unitary group codes. Unitary group codes are block codes with a group structure in which each code matrix is square and has equal-energy, orthogonal rows. In this paper, we show that every full-rank unitary group code is equivalent to one of two very simple block codes, called cyclic and dicyclic group codes. This reduces the set of possible optimal codes to a finite set, which can be exhaustively searched by computer. Thus, we have characterized all optimal differential space-time modulation techniques that fit within the framework of Hughes, Hochwald and Sweldens