A finite group of complex integers and its application to differentially coherent detection of QAM signals
R.G. Egri, F.A. Horrigan · IEEE Transactions on Information Theory · 1994
A finite multiplicative group of complex integers is constructed and its application to differential detection of 16 QAM signals is given. In this group the algebraic properties of regular complex multiplication, such as commutativity, associativity, and conjugation are preserved. The challenge in finding such a group lies in the requirements for the existence of multiplicative inverses for numbers that have magnitudes different from 1, and for maintaining associativity. The group properties are used to demodulate 16 QAM signals in a differentially coherent way.>