Loss of Lock Analysis of a First-Order Digital Code Tracking Loop and Comparison of Results to Analog Loop Theory for BOC and NRZ Signals

A. Robert Golshan

Abstract:	Non-return to zero (NRZ) and binary offset carrier (BOC) are two waveform modulation schemes which are to be utilized in the modernized GPS and Galileo systems. Implications of signaling waveforms on code acquisition and tracking in the presence of white Gaussian noise have already been addressed in the literature. Recently, one measure of tracking performance, the mean time to loss of lock (MTLL), has been analyzed for the NRZ and BOC signals in the context of analog code tracking loops [1]. Analog loop theory has often been used in practice to assess the performance of digital loops; yet, with regards to the loss of lock behavior of loops, it is not clear under which conditions the performances of the analog and digital loops coincide. In this paper, a nonlinear (Markov chain) analysis technique is presented for evaluating MTLL of a digital code tracking loop with an arbitrary time separation or spacing between its early and late correlators. Digital loop results are then compared to existing results of analog loop theory for both NRZ and BOC signals by plotting the MTLL of a first-order digital and analog loop operating over a range of loop bandwidths and correlator spacings. Results indicate that in some cases, the analog and digital loop MTLL performances do not coincide, most notably in the case of NRZ signals, at larger loop bandwidths for a given fixed correlator spacing, or at narrower correlator spacings for a given fixed loop bandwidth. Finally, the Markov chain digital loop results are validated via a floating-point multiple samples per chip Monte-Carlo simulation that simulates the actual operation of the digital loop until loss of lock is detected.
Published in:	Proceedings of the 2005 National Technical Meeting of The Institute of Navigation January 24 - 26, 2005 The Catamaran Resort Hotel San Diego, CA
Pages:	299 - 305
Cite this article:	Golshan, A. Robert, "Loss of Lock Analysis of a First-Order Digital Code Tracking Loop and Comparison of Results to Analog Loop Theory for BOC and NRZ Signals," Proceedings of the 2005 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2005, pp. 299-305.
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