Reduced ML-decoding complexity, full-rate STBCs for 2a transmit antenna systems

For an nt transmit, nr receive antenna system (nt × nr system), a {\it{full-rate}} space time block code (STBC) transmits nmin = min(nt,nr) complex symbols per channel use and in general, has an ML-decoding complexity of the order of Mntnmin (considering square designs), where M is the constellation size. In this paper, a scheme to obtain a full-rate STBC for 2a transmit antennas and any nr, with reduced ML-decoding complexity of the order of Mnt(nmin−3/4)−0.5, is presented. The well known Silver code for 2 transmit antennas is a special case of the proposed scheme. Further, it is shown that the codes constructed using the scheme have higher ergodic capacity than the well known punctured Perfect codes for nr < nt. Simulation results of the symbol error rates are shown for 8×2 systems, where the comparison of the proposed code is with the punctured Perfect code for 8 transmit antennas. The proposed code matches the punctured Perfect code in error performance, while having reduced ML-decoding complexity and higher ergodic capacity