Complex Step-Shape Binary Offset Carrier Modulation for a Unitary Analytical Framework of GNSS Signals

The Binary Offset Carrier and Binary Coded Symbol modulation family is widely used in the existing Global Navigation Satellite Systems (GNSS). There are several modulation types in this family and new types are still being developed. However, the analysis of these modulations is still scarce of uniform theoretical frame. This paper presents a novel Complex Step-shape Binary Offset Carrier (CSBOC) modulation to build a unitary analytical framework for all these modulation types. This framework contains a unified signals expression based on the extended concept of step-shape symbols bits vector. It can denote sine and cosine phase, odd and even order, time division multiplex and complex modulations. Moreover, the unified formulas of important signal characteristics which include the power spectral density, the auto-correlation function, and the cross-correlation function are derived. The proposed formulas are verified through comparing with the results came from existing theories and signal simulations. The applications of the CSBOC in analyzing side-peaks cancellation methods of GNSS signals are also provided to show that this framework is a useful tool to analyze and design locally generated signals of side-peaks cancellation methods.