High-rate full-rank space-time block codes from Cayley algebra

For a quasi-static, multiple-input multiple-output (MIMO) Rayleigh fading channel, high-rate space-time block codes (STBCs) with full-diversity have been constructed in B. A. Sethuraman et al., (2003) for arbitrary number of transmit antennas, by using the regular matrix representation of an associative division algebra. While the 2/spl times/2 as well as 4/spl times/4 real-orthogonal design (ROD) V. Tarokh et al., (1999) and Alamouti code S. M. Alamouti (1998) were obtained as a special case of this construction, the 8/spl times/8 ROD could not be obtained. In this paper, starting with a non-associative division algebra (Cayley algebra or more popularly known as octonion algebra) over an arbitrary characteristic zero field F, a method of embedding this algebra into the ring of matrices over F is described, and high-rate full-rank STBCs for 8m (m, an arbitrary integer) antennas are obtained. We also give a closed form expression for the coding gain of these STBCs. This embedding when specialized to F=/spl Ropf/ and m=1, gives the 8/spl times/8 ROD.