Space-Time Block Codes with Symbol-by-Symbol Maximum Likelihood Detections
Coding for multiple-input multiple-output (MIMO) channels can significantly increase the transmit diversity of communication systems in fading environments . Among various MIMO transmission and receiving techniques, the rate-1 orthogonal space-time block codes constitute a powerful scheme to achieve full diversity and decouple the received signals into parallel channels . The optimal decoders can therefore be realized through symbol-by-symbol maximum likelihood (ML) detections. Nevertheless, Tarokh, Jafarkhani, and Calderbank  proved that the well-known Alamouti scheme for two transmit antennas  is the only existing rate-1 complex orthogonal space-time block code, wherefore quasi-orthogonal space-time block codes (QOSTBCs) are proposed to have better spectral efficiency with four transmit antennas [4, 5, 6]. A complete list of QOSTBCs that can be identified as rings is given jointly in  and . Including those of [4, 5, 6], each of the QOSTBCs in  and  can achieve full diversity and the optimal coding gains with possibly having to rotate half of the transmitted symbols' constellations, as quadrature amplitude modulations (QAMs)  or phase-shift keying (PSK) modulations  are utilized. A common character for those QOSTBCs is that the corresponding optimal decoders can only be implemented via complex symbol pairwise ML detections. Motivated by this, Yuen, Guan, and Tjhung  re-stacked the Alamouti schemes with different input symbols into another QOSTBC that is symbol-by-symbol ML detectable. This QOSTBC is different from the traditional ones merely in that the transmitted symbols are precoded by coordinate-interleavers before transmissions occur. In , Wang, Wang, and Xia further used two coordinate-interleavers involving two real symbols together with other two involving four real symbols to achieve the maximum coding gains over general QAM constellations. A QOSTBC with coordinate-interleavers is no longer linear over the field of all complex numbers with respect to the input symbols so rotating all constellations with the same angle usually varies the corresponding normalized diversity product. An optimal rotation that provides the maximum normalized diversity product is then always embedded with the code. Subsequently, both  and  claim by numerical simulation that their performance of bit error rates (BERs) is identical with the rate-1 coordinate-interleaved orthogonal design (CIOD) of  over the 4-QAM constellation. By applying matrix representations of Clifford algebras, Karmakar and Rajan  presented codes with the similar properties.
The ultimate goals of this project are summarized as follows.
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