The Theory of Quaternion Orthogonal Designs

Correction to "The theory of quaternion orthogonal designs"

Quaternion orthogonal designs from complex companion designs

The success of applying generalized complex orthogonal designs as space–time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space–timepolarization block codes. This paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs. One technique is used to build ...

Zero-Free and Redundant Quaternion Orthogonal Designs

The success of applying generalized complex orthogonal designs as space-time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space-time-polarization block codes. Since complex orthogonal designs with no zero entries have proven important in applications, this paper offers a construction for an infinite family of restricted quaterni...

A Construction for Quaternion Orthogonal Designs

This paper provides a general construction technique for rectangular matrices whose elements are quaternion variables and whose column vectors are formally orthogonal. These matrices are named quaternion orthogonal designs, in parallel with the well-known constructs of real and complex orthogonal designs. The proposed construction technique provides the first infinite family of this type of qua...

The amicable-Kronecker construction of quaternion orthogonal designs

Recently, quaternion orthogonal designs (QODs) were introduced as a mathematical construct with the potential for applications in wireless communications. The potential applications require new methods for constructing QODs, as most of the known methods of construction do not produce QODs with the exact properties required for implementation in wireless systems. This paper uses real amicable or...