Global Navigation Satellite System Meta-Signals with an Arbitrary Number of Components

Global Navigation Satellite System (GNSS) meta-signals are obtained when components from different frequencies are jointly processed as a single entity. While most research work has focused on GNSS meta-signals made of two side-band components, meta-signal theory has been recently extended to the case where the number of components is a power of two. This condition was dictated by the use of multicomplex numbers for the representation of GNSS meta-signals. Multicomplex numbers are multi-dimensional extensions of complex numbers whose dimension is a power of two. In this paper, the theory is further extended and a procedure for the construction of GNSS meta-signals with an arbitrary number of components is provided. Also in this case, multicomplex numbers are used to effectively represent a GNSS meta-signal. From this representation, multi-dimensional Cross Ambiguity Functions (CAFs) are obtained and used to derive acquisition and tracking algorithms suitable for the joint processing of components from different frequencies. The specific case with three components is analysed. Theoretical results are supported by experimental findings obtained by jointly processing Galileo E5a, E5b and E6 signals collected using three synchronized Software-Defined Radio (SDR) HackRF One front-ends. Experimental results confirm the validity of the developed theory.