Constellation space invariance of orthogonal space-time block codes

In this correspondence, we prove an interesting property of orthogonal space-time block codes (OSTBCs). For flat block-fading channels, it is shown that the internal structure of the vector space of the input constellation remains invariant to the effects of both the OSTBC and the channel except for certain scaling factors. This property sheds light on the mechanism of maximum-likelihood (ML) decoding of OSTBCs and, in particular, provides an alternative explanation of why optimal decoding can be reduced to symbol-by-symbol decoding. New simple expressions for the ML decoder are obtained which clarify its intrinsic structure.