STBC from field extensions of the rational field

The construction of space time block code (STBCS) over symmetric m-PSK (m-arbitrary) signal sets for a restricted set of number of antennas n is presented by Sethuraman and Sundar Rajan (see ICC 2002, New York, 2002), using cyclotomic field extensions of the field of rationals Q. We extend the method of Sethuraman et al. and achieve construction of minimal-delay, full-rank, rate-1 STBCs over (i) certain asymmetric m-PSK (m-arbitrary) signal sets, QAM and cross-constellations, (ii) certain rotationally invariant signal sets, for arbitrary number of antennas, using transcendental extensions of Q and (iii) using non-cyclotomic field extensions of Q for arbitrary number of antennas.