Zero-bias Analysis and Mitigation for Band-limited PN Code Tracking

Zero-bias is one type of pseudo-noise (PN) code tracking error in digital receivers that use non-commensurate sampling and becomes dominant in scenarios with high signal-to-noise ratio (SNR) and small Doppler effects. Several theoretical models and error mitigation techniques have been proposed to solve this issue, yet are oversimplified due to the assumption of a receiver with an infinite front-end bandwidth. Taking the effect of band-limiting into account, this paper establishes a theoretical statistical model of zero-bias error in coherent PN code tracking using non-commensurate sampling. Analytical expression of the zero-bias variance is provided and some key characteristics of the relationship between zero-bias and receiver parameters are described. Based on the theoretical analysis, for typical early-late (E-L) digital receiver structures with non-commensurate sampling, a zero-bias mitigation method via iterative E-L correlation spacing optimization is presented. Results of simulation and experimental test show the proposed method has a superior performance for band-limited PN code signals in comparison with existing zero-bias mitigation methods under the infinite bandwidth assumption. The general practicality of the method under different Doppler and SNR conditions is verified. The theoretical analysis and simulation results of zero-bias can facilitate performance assessment and parameter design of receivers for high precision applications.