Generalized Theory of BOC Signal Unambiguous Tracking With Two-Dimensional Loops

The multipeaked correlation functions of binary offset carrier (BOC) modulated signals introduce an ambiguity threat into the code tracking. Several techniques have been proposed to solve this problem, such as a class of two-dimensional (2-D) tracking techniques, in which the spreading code and the subcarrier are tracked separately. In this paper, the key properties of correlation functions and the theoretical tracking performance analysis considering noise and multipath environments of the general 2-D tracking loop are studied. Exact explicit expressions, taking into account the effects of local subcarrier waveform mismatching and the front-end bandlimiting, are provided for the correlation function employed in 2-D tracking. From these expressions, the key characteristics of 2-D correlation functions such as the shape, coupling relation between dimensions, and the effects of bandlimiting can be clearly seen. Moreover, general theoretical methods to predict the performance of the 2-D tracking techniques under the multipath and noise environments are provided. The results obtained in this paper can facilitate investigations in the area of 2-D tracking technique parameter optimization and performance assessment.