Novel rotation angle for quasi-orthogonal space-time block codes

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Recently, various space-time block coding (STBC) schemes have been developed to take advantage of the MIMO communication channel. The code designs using the pair-wise error probability of the maximum likelihood (ML) detector are based mainly on the rank and the determinant criteria. In particular, the current STBC designs focus on full diversity and the non-vanishing determinant, since such codes enable the optimal tradeoff of diversity and multiplexing gains. In this paper, we consider a coherent communication system equipped with multiple transmitter antennas and a single receiver antenna, i.e., a MISO system. For such systems, Afarkhani, Tirkkonen-Boariu-Hottinen, and Papadias-Foschini proposed the quasi-orthogonal STBC designs with fast ML decoding. Su and Xia designed the rotated quasi-orthogonal STBCs enabling full diversity and optimal coding gain. However, the nearest neighbor number per symbol for this code tends to infinity when the size of constellation is large. Here, we explore a novel criterion to design rotated quasi-orthogonal STBCs. In addition to both maximizing the rank and the coding gain, our design attempts to make the average number of the nearest neighbors as small as possible.