# Packet TDEV, MTIE, and MATIE - for Estimating the Frequency and Phase Stability of a Packet Slave Clock. Antti Pietiläinen

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1 Packet TDEV, MTIE, and MATIE - for Estimating the Frequency and Phase Stability of a Packet Slave Clock Antti Pietiläinen Soc Classification level 1 Nokia Siemens Networks

2 Expressing performance of clocks TIE = Time interval error MTIE = Maximum time interval error MTIE/ = Maximum frequency error estimate from MTIE TDEV = Time deviation MDEV = Modified Allan deviation MATIE = Maximum average time interval error (proposal) MAFE = Maximum average frequency error (proposal)

3 TIE [s] Time interval error (TIE) Indicates the phase of a clock compared with the phase of a reference clock. For example if the frequency of a clock is 10 ppb too large, TIE will increase by 10 ns every second. The quantities considered of interest in standardization bodies for characterization of time and frequency stability are calculated from TIE, e.g. MTIE, TDEV, and MDEV TIE of a packet clock synchronized over a DSL connection Time [s]

4 MTIE - maximum time interval error MTIE defines maximum wander within an observation window. The observation window is slid over the TIE data. The sizes of the observation windows are indicated by the x-axis values of the MTIE curve. MTIE is specified in G.810. MTIE masks have been specified, for example, in G.812, G.813, G.823, G.824, and G.8261 T = (N - 1) 0 x(t) Time error = n0 xppk (from G.810) k k + n N i T

5 MTIE [s] MTIE of a practical packet clock Each observation window scanned over the TIE curve (see previous slide) will produce one point on the MTIE or MRTIE curve. MTIE of a TCXO based packet clock synchronized over a production network and DSL connection shoots about one order of magnitude over the PDH specifications. Does one need to average this clock for seconds to go below 16 ppb? 1E-3 1E-4 MTIE of clock MTIE of a packet clock synchronized over a DSL connection. 1E-5 G Mbit/s traffic interf. G Mbit/s network interf. 1E-6 15 ppb 16 ppb OBSAI RP1 1E tau [s]

6 TIE [s] MTIE is a pessimistic estimator when used to indicate achievable frequency stability MTIE predicts a stability of 127 ppb. However, by passing the signal through a 1 st order low-pass filter with time constant of 1000 s, the maximum frequency error drops to 67 ppb. With a better filter, the frequency error could be further reduced without widening the window. 60.0µs 40.0µs 20.0µs 0.0s -20.0µs -40.0µs -60.0µs MTIE(1000 s) =127 µs s MTIE/ = 127 ppb f max = 500 ppb Time [s] Original TIE MTIE(1000 s) = 12.8 µs. MTIE/ = 12.8 ppb f max = 67 ppb After passing low-pass filter of time constant = 1000 s

7 TDEV [s] Time deviation (TDEV) TDEV indicates phase variation of a clock as a function of averaging time. TDEV masks have been specified in various ITU- T recommendations. TDEV averages out extremes. TDEV and MDEV (on following slide) are closely related, see formula. MDEV 3 TDEV 1E-4 1E-5 1E-6 1E-7 1E-8 1E-9 TDEV of a packet clock synchronized over a DSL connection tau [s]

8 Modified Allan deviation Modified Allan deviation (MDEV) (root of modified Allan variance) Is used to indicate frequency variation and frequency uncertainty of clocks. Because frequency variation is built up from various noise phenomena, the fundamental accuracy limits of a clock can be determined by averaging the clock frequency over a period of time. Consequently, Allan variance is indicated in graphs as a function of averaging window size. Allan variance is an averaging function and hides occasional bad performance. 1E-8 16 ppb 1E-9 MDEV of a packet clock synchronized over a DSL connection. 1E Averaging window, tau [s]

9 MATIE (maximum average time interval error), MAFE (maximum average frequency error) A new metric has to be defined. The target: a metric that Describes the upper bound of the phase or frequency error of a clock. Is presented as a function of averaging window width, similar to TDEV or MDEV. The averaging window size at which the metric drops below required level corresponds to the required local oscillator stability. Can be calculated from packet delay of fastest packets and from the phase (TIE) of a clock. Solution : Calculate average phase (or packet delay) difference between two windows next to each other. Find the maximum value of the difference over the whole data.

10 Calculating Maximum average time interval error Calculate x i = abs[average(blue)-average(purple)] Slide the windows over the data and find max(x i ) Change the window size and start over until all window sizes of interest have been covered. MATIE can be calculated from time interval error (TIE) of a clock, as well as from packet delays. In case of packet delays, a percentile selection is done first. In the figure, 10 fastest of each 1000 consecutive samples have been preselected and averaged.

11 TIE [s] Average TIE [s] Determining the maximum average time interval error MATIE and max. average frequency error MAFE at = 3000s. TIE (time interval error) is averaged over observation window and maximum change between two consecutive windows is determined Note, this is a simplification. In reality the adjacent averaging windows slide over the data The example shows how MATIE MATIE at and = MAFE 3000 s are calculated at observation window of 3000 s. = 3000 s The metric is calculated at different window sizes. MATIE and MAFE are plotted as a function MATIE of observation window =53 µs MATIE = 53 µs size. (Max average freq. err. MAFE = MATIE/ =18 ppb) The function estimates achievable worst-case stability over the whole TIE measurement as a function of the averaging time of the clock algorithm Time [s]

12 MDEV, MAFE, max freq error, MTIE/ [relative] TIE [s] TIE Comparison between frequency stability estimations of MDEV, MTIE/, and MAFE (corresponds to TDEV, MTIE, and MATIE in phase domain) MDEV varies depending on fill ratio and is optimistic. MTIE/ is too pessimistic. The different metrics estimate very different frequency stability. It is expected that low-pass filtered max. frequency error will approach MAFE when the filter is more optimal. 1E-6 80µs 40µs 1E-7 0s -40µs -80µs 1E µs 80.0µs 60.0µs 40.0µs 20.0µs 1E-9 0.0s -20.0µs -40.0µs -60.0µs -80.0µs µs Time [s] 1 Time [s] st order low-pass filtered maximum frequency error. Time constant = tau 16 ppb tau [s] MDEV MTIE/ MAFE

13 MATIE follows quite closely the framework set by TDEV and MTIE MATIE nk 1 ik n max x x 0 1k N2n1 1 n in i, n = 1, 2,..., integer part (N/2) TDEV n N 3n1 n j xi2n 2xin xi 6n N 3n 1 j1 i j 2, n = 1, 2,..., integer part N 3 MTIE( n 0 ) max max x x, n, N 1 k N n k i k n i min k i k n i 1, 2,... 1 n 0 is the observation window length, n is the number of samples in the window, 0 is the sample interval, N is the number of samples in the data set. Index variable i is incremented to scan across the window and k or j is incremented for sliding the window.

14 Estimating packet clock performance from packet delay variation Packet delay variation is not a good indicator of expected packet clock properties because the time interval error of a packet clock is a small and unknown fraction of the packet delay variation. Black: Timing packet delay Yellow: TIE of the packet clock

15 Describing packet networks capability to support packet timing: Proposals Measurement Author Published Time Minimum TDEV Symmetricom ITU contrib. accepted Minimum picking TDEV June 2007 Semtech ITU contrib. June 2007 Percentile TDEV Symmetricom No public or standards documents Fixed selection window percentile TDEV & MDEV Fixed selection window percentile MTIE Nokia Siemens Networks Nokia Siemens Networks Not published Taken into discussion in ~December 2007 ITU contrib. May 2008 MATIE, MAFE Nokia Siemens Networks ITU contrib. Sep 2008

16 Modified Allan deviation Comparing modified Allan deviation of packet clock and packet MDEV of delay values At small averaging windows the short-term stability of the local oscillator dominates the packet clock performance. At certain point the curves almost combine. TDEV (and MDEV) first showed the link between packet delay variation and packet clock performance! 1E-4 1E-5 1E-6 1E-7 Packet delay MDEVs 0.1 % 1 % fastest packets selected from various window sizes 1E-8 16 ppb 1E-9 Packet clock MDEV 1E-10 1E Averaging window, tau [s]

17 MTIE [s] Packet MTIE vs. packet clock MTIE Packet MTIE would allow setting a performance limit mask. However, in addition to being pessimistic considering frequency stability, it is difficult to find parameters for packet MTIE that would accurately describe the performance of a packet clock. 1E-3 1/100 Minimum picking (6-s window) 1E-4 1/1000 Minimum picking (60-s window) 1-% averaging in 60-s window 1/10000 Minimum picking (600-s window) 1-% averaging in 300-s window 1-% averaging in 600-s window 1-% averaging in 1200-s window SLA requirement: Best at 60 s Best at 300 s Best at 600 s 1E-5 Slave clock 16 ppb Observation interval [s]

18 MAFE [relative] Maximum average frequency error (MAFE) Regardless of the exact packet selection method used in calculating packet MAFE the curves remain within a reasonably small range. The packet MAFE and MAFE of the clock coincide at large averaging windows. 1E-4 1E-5 1E-6 fpmafe, 1 %, 6-s selection window (minimum picking) pmafe, 1-% percentile packet MAFE fpmafe, 1 %, 60-s selection window A candidate mask for reaching 15 ppb with 6000-s averaging 1E-7 MAFE of packet clock 1E-8 1E tau [s]

19 Conclusions of packet timing metrics The introduction of packet TDEV in the form of mintdev was the longawaited breakthrough in correlating packet delay variation with packet clock performance. TDEV and MDEV describe average performance. Therefore, not accurately usable as limit values when occasionally protruding packet delay variations determine the boundary values of the performance. MTIE has been used traditionally also for defining frequency accuracy limits. However, in this use gives usually worse estimation than actual performance, incorporating thus unnecessary and variable safety margin. Further, it is difficult to match packet MTIE with packet clock MTIE. MATIE and MAFE seem to avoid these issues and the first analysis considering them as performance estimators and as limiting values have been promising. More analysis with various TIE data and reference slave clocks are still needed.

20 Backup formulas as pictures p. 7. p. 13. MATIE MDEV nk 1 ik n max x x 0 3 TDEV 1k N 2n1 1 n in i, n = 1, 2,..., integer part (N/2) TDEV n N 3n1 n j xi2n 2xin xi 6n N 3n 1 j1 i j MTIE( n 0 ) max max x x, n, N 1 k N n k i k n i min k i k n i 1, 2, , n = 1, 2,..., integer part N 3 n 0 is the observation window length, n is the number of samples in the window, 0 is the sample interval, N is the number of samples in the data set. Index variable i is incremented to scan across the window and k or j is incremented for sliding the window.

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