The IEEE 1588 protocol has received recent interest as a means of delivering sub-microsecond level clock phase synchronization over packet-switched mobile backhaul networks. Due to the randomness of the end-to-end delays in packet networks, the recovery of clock phase from packet timestamps in IEEE 1588 must be treated as a statistical estimation problem. A number of estimators for this problem have been suggested in the literature, but little is known about the best achievable performance. In this paper, we describe new minimax estimators for this problem, that are optimum in terms of minimizing the maximum mean squared error over all possible values of the unknown parameters. Minimax estimators that utilize information from past timestamps to improve accuracy are also introduced.Simulation results indicate that significant performance gains over conventional estimators can be obtained via such optimum processing techniques. These minimax estimators also provide fundamental limits on the performance of phase offset estimation schemes.

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In this paper, we describe new lower bounds on error variance of phase offset estimation schemes used in IEEE 1588 based synchronization. The motivation for this study is to determine the feasibility of providing microsecond-level time synchronization over mobile backhaul networks for the backend in 4G cellular systems. Many packet filtering/selection techniques for phase offset estimation have been proposed in synchronization literature, however, lower limits on the performance of such estimators have not yet been described. In this paper, we re-derive two Bayesian estimation bounds, namely the Ziv-Zakai and Weiss-Weinstien bounds, for use under a non-Bayesian formulation. This enables us to apply these bounds to the problem of phase offset estimation. Simulation results compare the performance of existing estimation schemes against these lower bounds under a variety of different network scenarios.

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The ambiguity function is an important tool to study the performance of radar detectors. In this paper, motivated by Neyman-Pearson testing principles, we propose an alternative definition of the ambiguity function that directly associates with each pair of true and assumed target parameters the probability that the radar will declare a target present. We show that the original ambiguity function definition of Woodward and Davies for single antenna systems (and its extensions to multichannel systems that use coherent processing) are essentially equivalent to the proposed definition. Further, for radars that perform non-coherent processing, we show the extensions to Woodward's ambiguity function proposed in literature are not equivalent to our proposed definition -and therefore may not accurately reflect detection performance. Simulations results demonstrate the differences between these different ambiguity function definitions for non-coherent radars.