Non-deterministic approach for hypercomplex orthogonal design (NAHOD)

The Alamouti scheme is a well known coding form for providing transmit diversity in wireless communication scenarios and is, for example, used in the 3G standard. The generalization of this technique using quaternions, allowing to use e.g. polarization as another signal attribute for diversity, has been discussed in several publications. However, there is still the open question how to design such coding matrices. In this paper, we present a generalized form of hypercomplex numbers used as basis for our computation allowing to generalize the notation of complex numbers and quaternions. Moreover, we will discuss the structure of generalized orthogonal designs allowing us to realize a non-deterministic approach for generating such code matrices.