General analytical models characterizing MBOC modulated signal

The modernized Global Positioning System (GPS) and Galileo satellite navigation systems have recommended the interoperable Multiplexed-Binary Offset Carrier (MBOC) modulation on L1C/E1 frequency band for their open service signals. MBOC signal multiplexes BOC(6,1) and BOC(1,1) according to a certain proportion, and can be implemented in a number of ways, including Composite BOC (CBOC) and Time-Multiplexed BOC (TMBOC). The complexity and the accuracy of the theoretical signal modeling pose a growing concern to scrutinize and to optimize signal characteristics and receiver performances. In this paper, the analytical expressions of the optimal correlation function (CF) for the new modernized MBOC signal are proposed. Also derived are the analytical models of the discriminator functions (DFs) and the multipath error envelopes (MEEs) in both coherent and non-coherent code tracking configurations. The validation of the proposed models is performed and the simulation results show that the proposed analytical models coincide with the numerical ones.