Novel quaternion matrix factorisations

The recent introduction of η-Hermitian matrices A = A
^ηH
has opened a new avenue of research in quaternion signal processing. However, the exploitation of this matrix structure has been limited, perhaps due to the lack of joint diagonalisation methodologies of these matrices. As such, we propose novel decompositions of η-Hermitian matrices to address this shortcoming in the literature. As an application, we consider a blind source separation problem in the form of an Alamouti-based communication system. Simulation studies demonstrate the effectiveness of our proposed joint diago-nalisation technique and indicate that our approach is particularly useful when the sources are correlated.