Modeling dual polarization wireless fading channels using quaternions

In the letter we describe signal transmitted between two dual-polarized antennas using a quaternion notation. The channel can then be modeled by a single quaternion gain, instead of a matrix of four complex gains as it is done in a classical approach. The model is very useful as it allows for a simple accommodation of any polarization twist between the transmit and receive antennas, as well as, modeling random fading in both polarizations with or without cross-polar scattering.