IEEE 1588, built on the classical two-way message exchange scheme, is a popular clock synchronization protocol for packet-switched networks. Due to the presence of random queuing delays in a packet-switched network, the joint recovery of the clock skew and offset from the timestamps of the exchanged synchronization packets can be treated as a statistical estimation problem. In this paper, we address the problem of clock skew and offset estimation for IEEE 1588 in the presence of possible unknown asymmetries between the deterministic path delays of the forward master-to-slave path and reverse slave-to-master path, which can result from incorrect modeling or cyber-attacks. First, we develop lower bounds on the mean square estimation error for a clock skew and offset estimation scheme for IEEE 1588 assuming the availability of multiple master-slave communication paths and complete knowledge of the probability density functions (pdf) describing the random queuing delays. Approximating the pdf of the random queuing delays by a mixture of Gaussian random variables, we then present a robust iterative clock skew and offset estimation scheme that employs the space alternating generalized expectation-maximization (SAGE) algorithm for learning all the unknown parameters. Numerical results indicate that the developed robust scheme exhibits a mean square estimation error close to the lower bounds.

This paper addresses the problem of clock skew and offset estimation (CSOE) for the IEEE 1588 precision time protocol. Built on the classical two-way message exchange scheme, IEEE 1588 is a prominent synchronization protocol for packet switched networks. Due to the presence of random queuing delays in a packet switched network, the joint recovery of clock skew and offset from the received packet timestamps can be viewed as a statistical estimation problem. Recently, assuming perfect clock skew information, minimax optimum clock offset estimators were developed for IEEE 1588. Building on this work, we first develop joint optimum invariant clock skew and offset estimators for IEEE 1588 for known queuing delay statistics and unlimited computational complexity. We then show that the developed estimators are minimax optimum, i.e., these estimators minimize the maximum skew normalized mean square estimation error over all possible values of the unknown parameters. Minimax optimum estimators that utilize information from past timestamps to improve accuracy are also introduced. The developed optimum estimators provide useful fundamental limits for evaluating the performance of CSOE schemes. These performance limits can aid system designers to develop algorithms with the desired computational complexity that achieve performance close to the performance of the optimum estimators. If a designer finds an approach with a complexity they find acceptable and which provides performance close to the optimum performance, they can use it and know they have near optimum performance. This is precisely the approach used in communications when comparing to capacity.

In this letter, we address the problem of target detection in passive multiple-input multiple-output radar networks. A generalized likelihood ratio test is derived, assuming prior knowledge of the signal format used in the noncooperative transmit stations. The performance of the generalized likelihood ratio test in the known signal format case is often significantly more favorable when compared to the case that does not exploit this information. Further, the performance improves with increasing number of samples per symbol and for a sufficiently large number of samples per symbol, the performance closely approximates that of an active radar with a known transmitted signal.

This paper addresses the problem of robust clock phase offset estimation for the IEEE 1588 precision time protocol in the presence of unknown asymmetric network path delays. The presence of an unknown asymmetry between the path delays can lead to significant degradation in the performance of a phase offset estimation scheme. Assuming multiple master-slave communication paths are available, we first provide lower bounds on the best achievable performance for a phase offset estimation scheme in the presence of asymmetric master-slave communication paths. We then present a novel phase offset estimation scheme that employs the expectation-maximization algorithm to identify the asymmetric master-slave communication paths. After discarding information from these paths, we employ the minimax optimum vector location parameter estimator for estimating the phase offset. Simulation results are presented to show that the proposed phase offset estimation scheme exhibits performance close to the lower bounds in a wide variety of network scenarios.