A family of cyclic division algebra based fast-decodable 4×2 space-time block codes

Multiple-input double-output (MIDO) codes are important in future wireless communications, where the portable end-user device is physically small and will typically contain maximum two receive antennas. Especially tempting is the 4×2 channel, where the four transmitters can either be all at one station, or separated between two different stations. Such channels optimally employ rate-two space-time (ST) codes consisting of 4×4 matrices. Unfortunately, such codes are in general very complex to decode, the worst-case complexity being as high as N⁸, where N is the size of the complex signaling alphabet. Hence, constructions with reduced complexity are called for. One option, of course, is to use the rate-one codes such as the quasi-orthogonal codes. However, if full multiplexing, i.e., transmission of two symbols per channel use is to be maintained, this option has to be put aside. Recently, some reduced complexity constructions have been proposed, but they have mainly been based on ad hoc methods and have resulted in a specific code instead of a more general class of codes. In this paper, it will be shown that cyclic division algebra (CDA) based codes satisfying certain criteria will always result in at least 25% worst-case complexity reduction, while maintaining full diversity and even the non-vanishing determinant (NVD) property. The reduction follows from the fact that the codes will consist of four Alamouti blocks allowing simplified decoding. At the moment, such reduction is the best known for rate-two MIDO codes,. The code proposed in was the first one to provably fulfill the related algebraic properties, and shall be repeated here as an example. Further, a new low-complexity design resulting from the proposed criteria is presented, and shown to have excellent performance through simulations.