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For an $n_t$ transmit, $n_r$ receive antenna system ($n_t \times n_r$system), a {\it{full-rate}} space time block code (STBC) transmits $n_{min} =min(n_t,n_r)$ complex symbols per channel use and in general, has anML-decoding complexity of the order of $M^{n_tn_{min}}$ (considering squaredesigns), where $M$ is the constellation size. In this paper, a scheme toobtain a full-rate STBC for $2^a$ transmit antennas and any $n_r$, with reducedML-decoding complexity of the order of $M^{n_t(n_{min}-3/4)}$, is presented.The weight matrices of the proposed STBC are obtained from the unitary matrixrepresentations of a Clifford Algebra. For any value of $n_r$, the proposeddesign offers a reduction from the full ML-decoding complexity by a factor of$M^{3n_t/4}}$. The well known Silver code for 2 transmit antennas is a specialcase of the proposed scheme. Further, it is shown that the codes constructedusing the scheme have higher ergodic capacity than the well known puncturedPerfect codes for $n_r < n_t$. Simulation results of the symbol error rates areshown for $8 \times 2$ systems, where the comparison of the proposed code iswith the punctured Perfect code for 8 transmit antennas. The proposed codematches the punctured perfect code in error performance, while having reducedML-decoding complexity and higher ergodic capacity.

Reduced ML-Decoding Complexity, Full-Rate STBCs for $2^a$ Transmit Antenna Systems