On modal subspaces of extended Alamouti space-time block codes

In this paper, two fundamental subspace invariances of quasiorthogonal space-time block codes recursively derived from the Alamouti code (Jafarkhani codes, extended Alamouti codes) are proven: (i) an eigenbasis of the code word distance matrices can be found which is invariant with respect to the chosen modulation alphabet and (ii) the eigenspaces of the virtual channel matrices are invariant with respect to the channel state realization. These subspace invariances lead to important conclusions: The subspace invariance (i) enables efficient transmission schemes with very small amount of channel state feedback. As a corollary of (ii), an extremely tight analytical bound for the bit error rate can be obtained.