On Low Complexity ML Decoder for Quaternion Orthogonal Designs

Quaternion orthogonal designs (QODs) provide an efficient way of constructing orthogonal space time polarization block codes to achieve larger transmit diversity gains without substantial increase in antenna dimensions. However, their optimal decoding remains a big challenge. This letter introduces an important constraint, which has not been emphasized before, for decoupled decoding of QODs and proposes a generalized low complexity maximum-likelihood decoder for QODs based on symmetric-paired designs. The main contribution of this letter is to explore the benefits of QODs for smaller as well as higher order designs without compromising system performance. Results show that the proposed decoder yields optimal decoupled decoding with remarkably low complexity. This letter also compares the performance of quaternion coordinate interleaved orthogonal designs (QCIODs), which provide full diversity, with proposed symmetric-paired designs and shows that proposed designs significantly outperform QCIODs.