  Full-rate STBC (space-time block codes) with non-vanishing determinants
achieve the optimal diversity-multiplexing tradeoff but incur high decoding
complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an
STBC structure with special QR decomposition characteristics. In this paper, we
adopt a simplified form of this fast-decodable code structure and present a new
way to optimize the code analytically. We show that the signal constellation
topology (such as QAM, APSK, or PSK) has a critical impact on the existence of
non-vanishing determinants of the full-rate STBC. In particular, we show for
the first time that, in order for APSK-STBC to achieve non-vanishing
determinant, an APSK constellation topology with constellation points lying on
square grid and ring radius $\sqrt{m^2+n^2} (m,n\emph{\emph{integers}})$ needs
to be used. For signal constellations with vanishing determinants, we present a
methodology to analytically optimize the full-rate STBC at specific
constellation dimension.
