Euclidean-Geometry-Based Space-Time Block Coded Spatial Modulation

In this paper, we propose Euclidean geometric schemes to construct the codebooks for the space-time block coded spatial modulation system. The new codebook-constructing schemes are more efficient than the previous exhaustive searching scheme. The result system is referred to as Euclidean-geometry-based space-time block coded spatial modulation (EG-STBC-SM) system. To achieve transmit diversity, two different schemes are introduced to construct sub-codebooks for the EG-STBC-SM system. In the first scheme, active transmits are selected based on the points and
$\mu$
-flats of
$d$
-dimensional Euclidean geometry over the Galois field
$\text{GF}(p^s)$
. Furthermore, the extended orthogonal space-time block codes are used to support more than two active transmit antennas in the EG-STBC-SM system. In the second scheme, the flats of a Euclidean geometry are grouped into a cyclic structure, which makes the encoding of the EG-STBC-SM scheme very easy. In addition, a simple maximum-likelihood decoder is derived in this paper. Bit error rate performance of the EG-STBC-SM system is evaluated via computer simulation and theoretical upper bound. It is shown that the proposed EG-STBC-SM system outperforms various existing multiple-input multiple-output transmission counterparts of the same or lower spectral efficiencies.