Modelagem de Sistema de Comunicação com Modulação Digital baseada em Quatérnios

Abstract

This paper presents the Quarternions algebraic and their computational advantages in function of the decreasing of the algebraic operations involving the usuals real products going against the matrix model. We propose a new modulation scheme, called QuatMod, for the digital communications systems and a new analytical formulation for the error probability for an AWGN quaternionic equivalent channel. The QuatMod is performed for quadrangular constellations represented geometrically by isomorphism by hypercubes classes in R4. We used the Cayley-Dickson representation, interpreted by a given quaternionic structure as an equivalent carrier for two complex numbers. This representation is applied in the transmission between two dual polarized antennas, reflecting in a comparison with the existing classic approach. Finally, we also study de quarternionic channel modeling by comparing with the classic model.