Stbc-schemes with nonvanishing determinant for certain number of transmit antennas

Abstract — 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 2 k or 3 · 2 k or 2 · 3 k or q k (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