Sensitivity Characterization of Differential Detectors for Acquisition of Weak GNSS Signals

In this paper, we assess the potential of several forms of the postcoherent differential detectors for the detection of weak Global Navigation Satellite Systems (GNSS) signals. We analyze in detail two different detector forms, namely the pair-wise differential detector (PWD) and noncoherent differential detector (NCDD). First, we follow a novel approach to obtain analytic expressions to characterize statistically the PWD. Then, we use these results to propose a polynomial-like model fitted by simulation to the sensitivity loss experienced by the differential operation with respect to coherent summing. This sensitivity loss formula is also used to characterize the NCDD, which is shown to be more adequate than the PWD for the acquisition of GNSS signals. A comparison between the PWD, NCDD, and the traditional noncoherent detector (NCD) is also carried out in this study. The results highlight the superior performance of the NCDD over the NCD for the acquisition of weak signals. For the case of the PWD, its performance is sensitive to Doppler shift. The conclusions drawn from the simulation results are confirmed in the acquisition of real Global Positioning System L1 C/A signals.