STBC-schemes with non-vanishing determinant for certain number of transmit antennas

This paper presents a systematic technique for constructing STBC-schemes (space-time block code schemes) with non-vanishing determinant, based on cyclic division algebras. Prior constructions of STBC-schemes with non-vanishing determinant are available only for 2,3,4 and 6 transmit antennas. In this paper, by using an appropriate representation of a cyclic division algebra over a maximal subfield, we construct STBC-schemes with non-vanishing determinant for the number of transmit antennas of the form 2k or 3middot2k or 2middot3k or qk(q - 1)/2, where q is a prime of the form 4s + 3 and s is any arbitrary integer. In a recent work, Elia et. al. have proved that non-vanishing determinant is a sufficient condition for STBC-schemes from cyclic division algebra to achieve the optimal diversity-multiplexing gain (D-MG) tradeoff; thus proving that the STBC-schemes constructed in this paper achieve the optimal D-MG tradeoff