Joint Estimation of Time Delay and Clock Error in the Incoherent Reception Systems

The assumption that observed signals are ideally received is commonly used in the literature on time-delay estimation. However, for practical digital receivers, the received radio-frequency signals are usually downconverted to the baseband and digitized by analog-to-digital converters. Because inaccurate and unstable system clocks are used, frequency and phase offsets are usually induced by the frequency-mixing procedure, whereas a time stretch may ensue from the sampling procedure. The aforementioned problems are almost inevitable for incoherent reception systems. Therefore, the neglect of imperfect reception for incoherent systems may reduce the performance of conventional time-delay estimation methods. In this paper, employing refined signal models developed specifically for incoherent time-delay estimation in active and passive systems, the corresponding joint maximum likelihood estimates of time delay and system-clock frequency error are proposed. The Cramér–Rao lower bounds (CRLBs) on time-delay and clock frequency error estimations are also derived. The performance of the proposed time-delay estimators can be improved for frequency/phase offsets and time stretches, approaching the performance of the CRLBs in scenarios of moderate and high signal-to-noise ratios. Furthermore, both CRLBs analysis and simulation results verify that the accuracy of the proposed time-delay estimator is unaffected by the performance of the system clock in moderate scenarios.