Date:	Tue, April 22, 2014
Time:	11:15
Place:	Research I Seminar Room

Abstract: A simple scheme that allows placing two antennas within a single device and using the channel diversity that this provides, without suffering from interference, has been discovered by Alamouti in late 1990s. It was quickly discovered that Hurwitz's 1-2-4-8 theorem restricts the existence of higher-order schemes of this kind, namely, that schemes with linear processing exist for two antennas maximum. However, weakening some of the restrictions, higher-order schemes have been shown to exist.
Since then, the theory of Space-Time Block Codes has flourished, producing a variety of alternative schemes of higher order, with different transmission rates and construction algorithms, including ones based on cyclic division algebras and Clifford algebras.
We find that the correct way to generalize the scheme of Alamouti to arbitrarily large dimensions is to use the so-called Generalized ABBA codes, introduced by Abreu in 2005. A doubling construction of the Cayley-Dickson kind allows us to build a space-time block code of an arbitrary size. A viable transmission scheme using multiple antennas on each device can help us take advantage of the fact that due to central limit theorem, the interference grows slower than the diversity gain from multiple users.
We discover that the GABBA code is closely related to the multicomplex numbers, a family of commutative non-division algebras of which tessarines, bi-complex and tri-complex numbers are examples.