On constructions of algebraic space-time codes with AM-PSK constellations satisfying rate-diversity tradeoff

Constructions of space-time codes having amplitude-modulated phase-shift keying (AM-PSK) constellations are presented in this paper. The first construction, termed ℘-radii construction, is obtained by extending Hammons' dyadic dual-radii construction to the cases when the size of the constellation is a power of a prime ℘,℘ ≥ 2. The resultant code is optimal with respect to the rate-diversity tradeoff and has an AM-PSK constellation with signal points distributed over ℘-concentric circles in the complex plane, i.e., there are ℘ radii. Also contained in this paper is the identification of rich classes of nontrivial subset-subcodes of the newly constructed space-time codes and it is shown that these subset-subcodes are again, all optimal. Finally, a new generalization of the super-unified construction by Hammons is presented. It is shown that codes obtained from several previously known constructions are subset-subcodes of the one derived from this generalized construction.