  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.
