Papers in the literature dealing with the Ethernet network characterize packet delay variation (PDV) as a long-range dependence (LRD) process. Fractional Gaussian noise (fGn) or generalized fraction Gaussian noise (gfGn) belong to the LRD process. This paper proposes a novel clock skew estimator for the IEEE1588v2 applicable for the white-Gaussian, fGn, or gfGn environment. The clock skew estimator does not depend on the unknown asymmetry between the fixed delays in the forward and reverse paths nor on the clock offset between the Master and Slave. In addition, we supply a closed-form-approximated expression for the mean square error (MSE) related to our new proposed clock skew estimator. This expression is a function of the Hurst exponent H, as a function of the parameter a for the gfGn case, as a function of the total sent Sync messages, as a function of the Sync period, and as a function of the PDV variances of the forward and reverse paths. Simulation results confirm that our closed-form-approximated expression for the MSE indeed supplies the performance of our new proposed clock skew estimator efficiently for various values of the Hurst exponent, for the parameter a in gfGn case, for different Sync periods, for various values for the number of Sync periods and for various values for the PDV variances of the forward and reverse paths. Simulation results also show the advantage in the performance of our new proposed clock skew estimator compared to the literature known ML-like estimator (MLLE) that maximizes the likelihood function obtained based on a reduced subset of observations (the first and last timing stamps). This paper also presents designing graphs for the system designer that show the number of the Sync periods needed to get the required clock skew performance (MSE = 10–12). Thus, the system designer can approximately know in advance the total delay or the time the system has to wait until getting the required system’s performance from the MSE point of view.

Papers in the literature dealing with the Ethernet network characterize packet delay variation (PDV) as a long-range dependence (LRD) process. The fractional Gaussian noise (fGn) or the generalized fractional Gaussian noise (gfGn) belong to the LRD process. The IEEE1588v2 is a two-way delay (TWD) protocol that uses the messages from the Forward (Master to Slave) and the Reverse (Slave to Master) paths. Suppose we have a significant difference between the PDV variances of the Forward and the Reverse paths. Thus, if we can use only the path with the lowest PDV variance (namely, only the one-way delay (OWD) technique), we might get a better clock skew performance from the mean square error (MSE) point of view compared with the traditional TWD method. This paper proposes two OWD clock skew estimators, one for the Forward path and one for the Reverse path applicable for the white-Gaussian, fGn and gfGn environment. Those OWD estimators do not depend on the unknown asymmetry between the fixed delays in the Forward and Reverse paths and nor on the clock offset between the Master and Slave. We also supply two closed-form approximated expressions for the MSE related to our new proposed OWD clock skew estimators. In addition, we supply some conditions, summarized in a table, guiding us whether we should use the OWD clock skew estimator for the Forward path or for the Reverse path, or just use the TWD algorithm. Simulation results confirm that our new proposed OWD clock skew estimators achieve better clock skew performances from the MSE point of view, compared with the TWD clock skew estimator recently proposed by the same authors and compared with two literature known OWD methods (the maximum likelihood and Kalman clock skew estimators).

Recently, the same authors provided a switching algorithm for the preferred clock skew estimator appropriate for the precision time protocol (PTP) scenario. The algorithm chooses the one-way delay (OWD) clock skew estimator for the Forward path or the Reverse path or the two-way delay (TWD) clock skew estimator that has the best performance in the mean square error (MSE) perspective. However, the switching algorithm applies only to the Gaussian scenario. In a real system, the packet delay variation (PDV) can be characterized as an fractional Gaussian noise (fGn) process where the Hurst exponent parameter can also have values higher than 0.5. Thus, the Gaussian case-switching algorithm may not apply in a real system where after a small set of PTP measurements, the switching algorithm should be able to switch effectively to the preferred clock skew estimator with the best performance in the MSE perspective. In this paper, the PDV is characterized as an fGn process where the Hurst exponent (H) is in the range of 0.5 ≤ H < 1 . We estimate the unknown PDV variances and the Hurst exponent parameters of the Forward and Reverse paths. These estimated parameters are used for switching to the preferred clock skew estimator from the MSE perspective, even in the presence of asymmetry in the PDV or in the Hurst exponent parameters. We also detect and alarm for the unexpected load, cyber-attack, or clock skew deviation that can occur in a real system.

Precision Time Protocol (PTP) is a time protocol based on the Master and Slave exchanging messages with time stamps. In practical PTP systems, we have packet loss, a phenomenon where some of the PTP messages get lost in the Network. Packet loss may reduce the performance of the clock skew estimator from the mean square error (MSE) perspective. Recently, the same authors presented simulation results that show the clock skew performance of the three clock skew estimators (the two-way delay (TWD) clock skew estimator and the one-way delay (OWD) clock skew estimator for the Forward and Reverse paths) under the packet loss case in the fractional Gaussian noise (fGn) environment with Hurst exponent parameter (H) in the range of 0.5 ≤ H &lt; 1, where indeed the clock skew performance was degraded compared to the non-packet loss case. Please note that for 0.5 &lt; H &lt; 1, the corresponding fGn is of long-range dependency (LRD). This paper proposes an algorithm that estimates the missing timestamps in the packet loss and fGn (0.5 ≤ H &lt; 1) case. We use those estimates to generate three modified clock skew estimators (the two-way delay (TWD) modified clock skew estimator and the one-way delay (OWD) modified clock skew estimator for the Forward and Reverse paths) applicable to the packet loss, non-packet loss, and fGn (0.5 ≤ H &lt; 1) case based on the same authors’ previously developed clock skew estimators. Those modified clock skew estimators led, based on simulation results, to an improved clock skew performance in the packet loss and fGn (0.5 ≤ H &lt; 1) case compared with the authors’ previously developed clock skew estimators and those known from the literature (the ML-like (MLLE) and Kalman clock skew estimators). With the MSE expression, the system designer can know how many Sync periods are needed for the clock skew synchronization task to reach the system’s requirements from the MSE perspective. But no MSE expression exists in the literature for the packet loss case. In this paper, we derive closed-form approximated expressions for the MSE upper bounds related to the modified TWD and OWD clock skew estimators valid for the packet loss and fGn (0.5 ≤ H &lt; 1) cases.

The National Institute of Standards and Technology (NIST) document is a list of fifteen tests for estimating the probability of signal randomness degree. Test number six in the NIST document is the Discrete Fourier Transform (DFT) test suitable for stationary incoming sequences. But, for cases where the input sequence is not stationary, the DFT test provides inaccurate results. For these cases, test number seven and eight (the Non-overlapping Template Matching Test and the Overlapping Template Matching Test) of the NIST document were designed to classify those non-stationary sequences. But, even with test number seven and eight of the NIST document, the results are not always accurate. Thus, the NIST test does not give a proper answer for the non-stationary input sequence case. In this paper, we offer a new algorithm or test, which may replace the NIST tests number six, seven and eight. The proposed test is applicable also for non-stationary sequences and supplies more accurate results than the existing tests (NIST tests number six, seven and eight), for non-stationary sequences. The new proposed test is based on the Wigner function and on the Generalized Gaussian Distribution (GGD). In addition, this new proposed algorithm alarms and indicates on suspicious places of cyclic sections in the tested sequence. Thus, it gives us the option to repair or to remove the suspicious places of cyclic sections (this part is beyond the scope of this paper), so that after that, the repaired or the shortened sequence (original sequence with removed sections) will result as a sequence with high probability of random degree.