Bicomplex Representation and Processing of GNSS Signals

Generalized binary offset carrier (BOC) modulations and global navigation satellite system (GNSS) meta-signals require advanced processing algorithms to overcome problems associated with their multi-peaked correlation functions. In this paper, bicomplex numbers are introduced for GNSS signal representation and for algorithm development. Bicomplex numbers generalize complex numbers and are characterized by four real components. These numbers have the potential to represent multicomponent signals, such as GNSS meta-signals, leading to a compact notation that allows effective derivations and algorithm development. Moreover, bicomplex numbers allow one to express a meta-signal as the product of a code, a carrier, and a subcarrier component: this representation leads to acquisition and tracking algorithms that are capable of effectively processing GNSS meta-signals, thus solving the code ambiguity problem. Theoretical developments are demonstrated using real data collected using software-defined radio front-ends for the Galileo alternative BOC modulation and the BeiDou B1I/B1C meta-signal.