Analysis of Clock Synchronization Approaches for Residential Ethernet

Transcription

1 Analyss of Clock Synchronzaton Approaches for Resdental Ethernet Geoffrey M. Garner Kees den Hollander SAIT / SAMSUNG Electroncs gmgarner@comcast.net denhollander.c.j@samsung.com 5 Conference on IEEE 1588 October 1 1, 5 Wnterthur, Swtzerland

2 Outlne Introducton Applcaton reference models End-to-end requrements Synchronzaton approaches for ResE Synchronzaton model Smulaton cases and results Conclusons Future work References Appendx I Clock nose model Appendx II Defnton of MTIE 5 Conference on IEEE 1588 /39

3 Introducton Resdental Ethernet (ResE) s a new standardzaton actvty n IEEE 8 that s consderng extensons to Ethernet to allow the transport of tme-senstve traffc (e.g., hgh qualty audo and vdeo (A/V)) A/V applcatons have tght jtter and wander requrements that must be met end-to-end To meet these requrements, synchronzaton s requred at ResE ngress and egress ponts Ths analyss nvestgates f and how synchronzaton approaches based on IEEE 1588 can meet the ResE requrements 5 Conference on IEEE /39

4 Applcaton Reference Models Example Reference Model for Transport of MPEG- Vdeo over Servce Provder Networks and Resdental Ethernet [] System Clock (Vdeo Source Clock) Ref. Pt. A Interworkng Functon (IWF) between successve transport networks MPEG- PES Ref. Pt. B MPEG- TS Ref. Pt. C MPEG- Encoder or Source MPEG- TS Mux MPEG-/ Transpt Netwk 1 Mapper Transpt Netwk 1 Transpt Netwk Transpt Netwk N - Map MPEG- packets from Transpt Netwk N nto ResE frames (may create ResE applcaton tme stamps) Transpt Netwk N/ ResE IWF Synchronzed ResE Clocks ResE Network MPEG-/ ResE Demapper - Demap MPEG- packets from ResE frames - Recover MPEG- TS Tmng (may have PLL functon) MPEG- TS Ref. Pt. D MPEG- TS Demux MPEG- PES Ref. Pt. E MPEG- Decoder Recover System Clock (may have PLL functon; see example on earler slde) Decoded Vdeo Ref. Pt. F Vdeo Dsplay 5 Conference on IEEE /39

5 End-to-End Requrements Summary of End-to-End Applcaton Jtter and Wander Requrements (see[] and references gven there) Requrement Uncompressed SDTV Uncompressed HDTV MPEG-, wth network transport MPEG-, no network transport Dgtal audo, consumer nterface Dgtal audo, professonal nterface Wde-band jtter (UIpp) Wde-band jtter meas flt (Hz) Hgh-band jtter (UIpp) µs peak-to-peak phase varaton requrement (no measurement flter specfed) 1 ns peak-to-peak phase varaton requrement (no measurement flter specfed) No requrement Hgh-band jtter meas flt (khz) (approx) No requrement Frequency offset (ppm) ± (NTSC) ±.5549 (PAL) ±1 ±3 ±3 ±5 (Level 1) ±1 (Level ) ±1 (Grade 1) ±1 (Grade ) Frequency drft rate (ppm/s).7937 (NTSC).5549 (PAL) No requrement No requrement No requrement 5 Conference on IEEE /39

6 End-to-End Requrements End-to-End Applcaton Jtter and Wander Requrements Expressed as MTIE Masks [] (see Appendx II for MTIE defnton) Uncompressed SDTV (SDI sgnal) Uncompressed HDTV (SDI sgnal) MPEG-, after netwk transport (Ref. Pts. D and E) MPEG-, no netwk transport (Ref. Pts. B and C) Dgtal Audo, Consumer Interfaces (S/P-DIF) Dgtal Audo, Professonal Interfaces (AES3) 1e+1 1e+11 1e+1 1e+9 1e+8 1e+7 Network Interface MTIE Masks for Dgtal Vdeo and Audo Sgnals MTIE (ns) 1e+6 1e+5 1e+4 1e+3 1e+ 1e+1 1e+ 1e-1 1e- 1e-9 1e-8 1e-7 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ 1e+3 1e+4 1e+5 1e+6 1e+7 Observaton Interval (s) 5 Conference on IEEE /39

7 Synchronzaton Approaches Basc -Way Tme Stamp Approach used n IEEE 1588 ResE wll use ths basc approach; however, a number of varatons are possble Generally assumed a flterng functon wll be present at the endpont May be present at ntermedate nodes (.e., n some varatons) Master f f 1 3) Master sends kth response tmestamp at T M 3,k contanng T S 1,k,T M,k, T M 3,k 4) Slave receves kth response tmestamp at T S 4,k contanng T S 1,k,T M,k, T M 3,k T S 1,k TM,k T M 3,k T S 1,k TM,k T M 3,k Slave N M k y M k Local Counter Offset 5) Slave computes kth clockdelta u k M S S ( T, k T1, k ) ( T 4, k T 3, = M k ) N S k y S k Local Counter Offset ) Master receves kth tmestamp at T M,k contanng T S 1,k T S 1,k T S 1,k 1) Slave sends kth tmestamp at T S 1,k contanng T S 1,k 6) Slave computes current offset y k n terms of current and possbly past clockdelta's u k 5 Conference on IEEE /39

8 Synchronzaton Approaches Varatons/Choces 1) Use one-way tme stamp scheme wth less frequent two-way exchange; obtan delay from two-way exchange and assume delay s fxed untl next two-way exchange ) Instantaneous phase adjustments at ntermedate nodes 3) Instantaneous phase and frequency adjustments at ntermedate nodes (wth nstantaneous frequency adjustments possbly less frequent) Descrbed n [4] 4) Fltered phase adjustments at ntermedate nodes, usng dgtal flter runnng at local clock rate (wth or wthout nstantaneous frequency adjustments) 5) Full phase-locked loops (PLLs) at ntermedate nodes (.e., fltered phase and frequency adjustments) 6) Use of transparent clock nodes a) End-to-end versus peer-to-peer b) Whether or not to adjust rate of local oscllator n transparent clock and, f so, whether to do flterng 7) Tme stamp reflects current tme versus delay by some number of frames 8) Tme stamp reflects local free-runnng clock tme versus latest corrected tme based on most recent tme stamps and possble flterng) 5 Conference on IEEE /39

9 Synchronzaton Model Grand Master y b (t), n (t) y b1 (t), n 1 (t) y b (t), n (t) y b +1 (t), n +1 (t) y bm (t), n M (t) Node Number 1 +1 M x ( t) = phase offset of clock relatve to UTC (ns) b y ( t) = b frequency offset (pure fracton) of n ( t) = phase nose of clock (ns) x ( ) = b t y ( t) dt + n ( t) = y t + n ( t) b - Assumes the frequency offset s constant over tme - Assumes the phase offsets are zero at - We are nterested n tmng relatve to the GM; therefore, can set y ( t) = n b b ( t) = clock relatve to UTC t = Message Exchanges between clock (master) and clock +1 (slave) -Note that messages from master to slave and slave to master do not necessarly occur at the same tmes -Note that messages from master to slave and slave to master may not occur at the same rates 5 Conference on IEEE /39

10 Synchronzaton Model Clock (m a ste r) Clock + 1 (sla ve ) T T T T T 1,k T,k T 3,k T 4,k 1, k + 1, k + 1 T T T 3, k + 1 4, k + 1 1, k + 1, k + 3, k + D D T m T m x T k ' 1, T, k ' T 3, k ' T k ' 4, T 1, k + 1 ' T, k + 1 ' T 3, k + 1 ' T 4, k + 1 ' T 1, k + ' T, k + ' T 3, k + ' T x m D = propaton delay between master and slave b, k = tme between successve messages from master to slave, measured relatve to UTC x = tme offset between master and slave (wll be ntalzed randomly between and T kept constant or allowed to change by frequency offset between master and slave multpled by T - Assume = y D << T ndex; UTC tme at step k = kt ) Tmk + b n k m from master to slave and slave to master overlap n tme s neglgble - Unprmed quanttes are relatve to master clock - Prmed quanttes are relatve to slave clock Then, can express, and therefore probablty that messages the phase offset n dscrete tme ( k = tme m m and ether m T 4, k + T 4, k + ' 5 Conference on IEEE /39

11 Synchronzaton Model Outlne of model dervaton For varatons (3) and (4), express frequency offset estmate of slave relatve to master over P tme steps n terms of the x b,k and x b,k +1 (tlde denotes relatve frequency offset between current and prevous node) Compare tme dfferences n free-runnng master and slave clocks over PT m ~ y ~ y kp = kp ( PT + x x ) ( PT + x x ) = ~ y m kp+ b, kp PT = L = ~ y b,( k 1) P + 1 m + xb, kp kp+ P 1 x = ~ y kp m b, kp + 1 b,( k 1) P b,( k 1) P For varatons (3) and (4), calculate cumulatve frequency offset of current j node relatve to GM y = ~ k yk For varaton (3) and (4), express corrected phase error estmate x j n terms cumulatve frequency offset estmate and free-runnng clock phase error x b,j Choose phase error estmate at all tme steps between frequency updates to be consstent wth current frequency offset estmate ( j kp) T x ( j kp) T j = x kp + m m + x + x ( x x )( 1+ y ) + ( j kp) T y b, j j b, j j= 1 x x b, kp kp b, kp = 1+ y k k m k 5 Conference on IEEE /39

12 Synchronzaton Model For varatons () (4), calculate clock delta n terms of ether corrected phase error estmates (for cases where frequency adjustments are made) or free-runnng clock phase errors Apply result for clock delta n step (5) on slde 7 Need phase error values at ntermedate tmes T 1, k', T, k, T3, k Obtan these by nterpolaton; result depends on x and D Take lmt D Note: assumpton s beng made that we can nterpolate on the nose Reasonable as long as the desred nose level s chosen for samplng rate T m See paper for detals Calculate cumulatve clock delta for all nodes up to the current one (GM clock delta s zero) Add cumulatve clock delta to corrected or free-runnng clock phase error to obtan unfltered phase estmate Flter the unfltered phase estmate wth a dgtal flter that runs at the local clock rate 5 Conference on IEEE /39

13 Synchronzaton Model Snce the flter s lnear, the result s the same for the case where each clock delta s fltered at each respectve ntermedate node versus flterng the cumulatve clock delta If synchronzaton s needed at each node, the work s the same n ether case Flter model s a dgtal mplementaton of standard nd order, lnear flter wth db/decade roll-off H ( s) = s ςωns + ωn + ςω s + ω ω = undamped natural frequency ς = dampng rato f n H n = 3 db bandwdth = p = gan peakng = whereα = 1/(4ς ) n ( ω / π ) ( ς + 1) + ( ς + 1) [ 1 α α + α α + α ] The dgtal mplementaton s obtaned by expressng the flter n state varable form (See [6] and [7] for detals) State vector at current tme step s wrtten as convoluton ntegral of nput vector and mpulse response matrx Impulse response matrx s calculated exactly and ntegral s evaluated usng trapezodal approxmaton for nput Output s wrtten n terms of states n n 1/ Conference on IEEE /39

14 Synchronzaton Model Addtonal aspects of model Clock nose model s descrbed n appendx Smulaton tme step s a sub-multple of the nter-message tme T m (cannot exceed T m ) Tme between frequency estmate updates s a multple of T m Tme offset between master slave and slave master messages may be ntalzed randomly or ntalzed wth user-specfed values Tme offset between master slave and slave master messages may reman constant over the smulaton or vary over T m by the relatve frequency offset between master and slave, multpled by T m Former requres that the master and slave send messages at the same rate Latter corresponds to messages beng sent at the free-runnng clock rates Fnte precson of clock s modeled Granularty, n unts of tme, s suppled as nput parameter 5 Conference on IEEE /39

15 Parameters Common to All Cases 1 hops GM followed by 1 slave clocks, n chan Slave clock frequency tolerance = ± 1 ppm Flter bandwdth = 1 Hz Flter gan peakng =.1 db Smulaton tme step =.1 ms Used small tme step to ensure phase peaks were captured 5 Conference on IEEE /39

16 Smulaton Cases 1 and Assumptons No clock phase nose Granularty of clock = No frequency adjustments (Case 1); Instantaneous frequency adjustments (Case ) Inter-message tme (T m ) = 1 ms Tme between frequency offset updates = 1 ms (Case ) Offset between master slave and slave master messages set to T m at each node (determnstc and constant) Results (see plots on next slde) Wth nstantaneous phase adjustments (no flterng) and no frequency adjustments, steady-state peak-to-peak phase error can be large (tens of ns) and depends on frequency offsets Wth 1 Hz flter and no frequency adjustments, steady-state peak-to-peak phase error s reduced to a few tenths of a ns Wth nstantaneous frequency adjustments, steady state peak-to-peak phase error s very small Approxmately.7 ns wth no flterng Approxmately.55 ns (.55 ps) wth flterng Wth no clock nose and zero phase granularty, frequency offsets can be measured very accurately Phase varaton does not ncrease monotoncally wth number of clocks n chan 5 Conference on IEEE /39

17 Smulaton Cases 1 and Node 1 Instantaneous Phase Adjustments Case 1 - No Frequency Adjustments Case - Instantaneous Frequency Adjustments Case 1 Case Node 1 Instantaneous Phase Adjustments Case 1 - No Frequency Adjustments Case - Instantaneous Frequency Adjustments Case 1 Case Unfltered Phase Error (ns) Unfltered Phase Error (ns) Tme (s) Tme (s) Node 1 Fltered Phase Adjustments Case 1 - No Frequency Adjustments Case - Instantaneous Frequency Adjustments (Intal transent s ncluded) Case 1 Case Node 1 Fltered Phase Adjustments Case 1 - No Frequency Adjustments Caes - Instantaneous Frequency Adjustments (Plot begns after ntal transent has decayed) Case 1 Case Fltered Phase Error (ns) 6 4 Case 1Fltered Phase Error (ns) Case Fltered Phase Error (ns) Tme (s) Tme (s) 5 Conference on IEEE /39

18 Smulaton Cases 3 and 4 Assumptons Wth clock phase nose (model descrbed n Appendx) Granularty of clock = 1 ns No frequency adjustments (Case 3); Instantaneous frequency adjustments (Case 4) Inter-message tme (T m ) = 1 ms (suggested n [4]) Tme between frequency offset updates = 1 ms (Case 4) (suggested n [4]) Offset between master slave and slave master messages ntalzed randomly at each node All nodes send messages at the same rate (offsets reman constant over smulaton) Results (see plots on next slde) Wth 1 Hz flter, MTIE s consderably smaller wth frequency adjustments (compared to wthout frequency adjustments), at longer observaton ntervals Approxmately ns wth frequency adjustments Approxmately 1 5 ns wthout frequency adjustments Wthout flterng, MTIE ranges from approxmately 16 6 ns wthout frequency adjustments and 4 ns wth frequency adjustments Phase varaton does not ncrease monotoncally wth number of clocks n chan (n all cases) Note that the results exhbt large statstcal varablty Must run multple, ndependent replcatons of the smulatons to obtan confdence ntervals for the results 5 Conference on IEEE /39

19 Smulaton Cases 3 and 4 Node 1 Instantaneous Phase Adjustments Case 3 - No Frequency Adjustments Case 4 - Instantaneous Frequency Adjustments 5 Case 3 Case 4 Node 1 Instantaneous Phase Adjustments Case 3 - No Frequency Adjustments Case 4 - Instantaneous Frequency Adjustments Case 3 Case 4 Unfltered Phase Error (ns) Unfltered Phase Error (ns) Tme (s) Node 1 Fltered Phase Adjustments Case 3 - No Frequency Adjustments Case 4 - Instantaneous Frequency Adjustments (plot begns after ntal transent has decayed) 35 Case 3 Case 4 Tme (s) Node 1 Fltered Phase Adjustments Case 3 - No Frequency Adjustments Case 4 - Instantaneous Frequency Adjustments (Plot begns after ntal transent has decayed) Case 3 Case Fltered Phase Error (ns) Fltered Phase Error (ns) Tme (s) Tme (s) 5 Conference on IEEE /39

20 Smulaton Case 4 (Detaled Vew) 5 Case 4, Node 1 Instantaneous Phase Adjustments Instantaneous Frequency Adjustments 3 Case 4, Node 1 Instantaneous Phase Adjustments Instantaneous Frequency Adjustments (Plot begns after ntal transent has decayed) Unfltered Phase Error (ns) Unfltered Phase Error (ns) Tme (s) Tme (s).6 Case 4, Node 1 Fltered Phase Adjustments Instantaneous Frequency Adjustments (plot begns after ntal transent has decayed).8 Case 4, Node 1 Fltered Phase Adjustments Instantaneous Frequency Adjustments (Plot begns after ntal transent has decayed).4.6 Fltered Phase Error (ns).. -. Fltered Phase Error (ns) Tme (s) Tme (s) 5 Conference on IEEE 1588 /39

21 Smulaton Cases 3 and 4 1e+7 Case 3 Instantaneous Phase Adjustments No Frequency Adjustments 1e+7 Case 3 Fltered Phase Adjustments No Frequency Adjustments 1e+6 1e+6 1e+5 1e+5 1e+4 1e+4 1e+3 1e+3 MTIE (ns) 1e+ 1e+1 1e+ MTIE (ns) 1e+ 1e+1 1e+ 1e-1 1e-1 1e- 1e- 1e-3 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ 1e+7 1e+6 1e+5 1e+4 Observaton Interval (s) Case 4 Instantaneous Phase Adjustments Instantaneous Frequency Adjustments 1e-3 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ 1e+7 1e+6 1e+5 1e+4 Observaton Interval (s) Case 4 Fltered Phase Adjustments Instantaneous Frequency Adjustments Node 1 Node Node 3 Node 5 Node 7 Node 1 Uncompressed SDTV Uncompressed HDTV Dgtal Audo, Consumer Interface Dgtal Audo, Professonal Interface MPEG-, After Network Transport MPEG-, Before Network Transport MTIE (ns) 1e+3 1e+ 1e+1 1e+ 1e-1 1e- 1e-3 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ Observaton Interval (s) MTIE (ns) 1e+3 1e+ 1e+1 1e+ 1e-1 1e- 1e-3 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ Observaton Interval (s) 5 Conference on IEEE /39

22 Smulaton Cases 5 and 6 Assumptons Wth clock phase nose (model descrbed n Appendx) Granularty of clock = 1 ns No frequency adjustments (Case 5); Instantaneous frequency adjustments (Case 6) Inter-message tme (T m ) = 1 ms; tme between frequency offset updates = 1 ms (Case 6) Offset between master slave and slave master messages ntalzed randomly at each node All nodes send messages at local free-runnng clock rate (offsets vary over smulaton) Results (see plots on followng sldes) If frequency adjustments are not made, phase steps occur due to varaton n tme offset between master slave and slave master messages Ths tme offset results n a phase error on the order of the sze of the offset (n unts of tme) multpled by the fractonal frequency dfference between the free-runnng master and slave clocks As the tme offset ncreases from to T m (or decreases from T m to ) phase offset changes When the tme offset reaches T m (or ) t jumps to (or T m ) as one message walks past the other Ths produces a step change n phase error of order yt m, where y s the relatve frequency offset between the master and slave E.g., for T m =.1 s and y = 1 ppm, the phase error jump s on the order of 1 ns 5 Conference on IEEE 1588 /39

23 Smulaton Cases 5 and 6 Results (Cont.) The 1 Hz flter removes the fast phase varaton due to nstantaneous phase adjustments, clock phase nose, and non-zero granularty; however, t cannot remove the phase varaton due to varaton n the tme offset between the master slave and slave master messages as ths varaton s much slower The effect does not occur when frequency adjustments are made because the error n phase correcton due to the frequency offset between the nodes s corrected for MTIE for the case wth frequency adjustments s roughly the same as n the correspondng case where the master slave and slave master message tme offset does not vary (Case 4) Phase varaton does not ncrease monotoncally wth number of clocks n chan (n all cases) Note that the results exhbt large statstcal varablty Must run multple, ndependent replcatons of the smulatons to obtan confdence ntervals for the results 5 Conference on IEEE /39

24 Smulaton Case 5 5 Case 5, Node 1 Instantaneous Phase Adjustments No Frequency Adjustments 4 Case 5, Node 1 Instantaneous Phase Adjustments No Frequency Adjustments Unfltered Phase Error (ns) Unfltered Phase Error (ns) - -4 Fltered Phase Error (ns) Tme (s) Case 5, Node 1 Fltered Phase Adjustments No Frequency Adjustments Note: Peak-to-peak phase varaton for Case 5 s much larger than for Cases 3, 4, and 6. Fltered Phase Error (ns) Tme (s) Case 5, Node 1 Fltered Phase Adjustments No Frequency Adjustments Tme (s) Tme (s) 5 Conference on IEEE /39

25 Smulaton Case 6 5 Case 6, Node 1 Instantaneous Phase Adjustments Instantaneous Frequency Adjustments 3 Case 6, Node 1 Instantaneous Phase Adjustments Instantaneous Frequency Adjustments (Plot begns after ntal transent has decayed) 4 Unfltered Phase Error (ns) 3 1 Unfltered Phase Error (ns) Tme (s) Case 6, Node 1 Fltered Phase Adjustments Instantaneous Frequency Adjustments (plot begns after ntal transent has decayed) Tme (s) Case 6, Node 1 Fltered Phase Adjustments Instantaneous Frequency Adjustments (plot begns after ntal transent has decayed).6.4 Fltered Phase Error (ns) Fltered Phase Error (ns) Tme (s) Tme (s) 5 Conference on IEEE /39

26 Smulaton Cases 5 and 6 1e+7 Case 5 Instantaneous Phase Adjustments No Frequency Adjustments 1e+7 Case 5 Fltered Phase Adjustments No Frequency Adjustments 1e+6 1e+6 1e+5 1e+5 1e+4 1e+4 MTIE (ns) MTIE (ns) 1e+3 1e+ 1e+1 1e+ 1e-1 1e- 1e-3 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ 1e+7 1e+6 1e+5 1e+4 1e+3 1e+ 1e+1 1e+ 1e-1 1e- 1e-3 Observaton Interval (s) Case 6 Instantaneous Phase Adjustments Instantaneous Frequency Adjustments 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ Observaton Interval (s) MTIE (ns) MTIE (ns) 1e+3 1e+ 1e+1 1e+ 1e-1 1e- 1e-3 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ 1e+7 1e+6 1e+5 1e+4 1e+3 1e+ 1e+1 1e+ 1e-1 1e- 1e-3 Observaton Interval (s) Case 6 Fltered Phase Adjustments Instantaneous Frequency Adjustments 1e-4 1e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ Observaton Interval (s) Node 1 Node Node 3 Node 5 Node 7 Node 1 Uncompressed SDTV Uncompressed HDTV Dgtal Audo, Consumer Interface Dgtal Audo, Professonal Interface MPEG-, After Network Transport MPEG-, Before Network Transport 5 Conference on IEEE /39

27 Conclusons In deal case of no clock nose, zero phase granularty, and no varaton n the tme offset between the master slave and slave master messages, can acheve extremely small peak-to-peak phase varaton n steady state.7 ns wth no flterng and frequency adjustments (Case, node 1).55 ns wth flterng and frequency adjustments (Case, node 1).1 ns wth flterng and no frequency adjustments (Case 1, node 1) However, wth clock nose (usng the model of the appendx) and 1 ns phase granularty, peak-to-peak phase varaton n steady state s larger 4 ns wth no flterng and frequency adjustments, whether or not tme offset between the master slave and slave master messages vary ns wth flterng and frequency adjustments, whether or not tme offset between the master slave and slave master messages vary 1 5 ns wth flterng and no frequency adjustments f tme offset between the master slave and slave master messages does not vary 35 6 ns wth flterng and no frequency adjustments f tme offset between the master slave and slave master messages does vary 5 Conference on IEEE /39

28 Conclusons The cases wth clock nose and 1 ns phase granularty ndcate that MTIE masks for uncompressed dgtal vdeo are exceeded f flterng s not done Ths ndcates that flterng s necessary, whether or not nstantaneous frequency adjustments are made The end-to-end dgtal audo masks are met for ths case only f frequency adjustments are made The uncompressed dgtal vdeo masks are slghtly exceeded wth 1 Hz,.1 db flterng f frequency adjustments are made; they and the consumer nterface audo mask are exceeded f frequency adjustments are not made Note that the masks apply to the end-to-end applcaton ResE gets only a budget allocaton of the total Get some addtonal phase varaton (lkely small) due to the fnte granularty of the applcaton tme stamps relatve to the synchronzaton sgnals descrbed here Ths means t s lkely that the flter must have BW that s somewhat narrower than 1 Hz Results show that f nstantaneous frequency adjustments are not made, must ensure that master slave and slave master messages are sent at nomnally the same rate, to avod varaton of ther tme offset and resultng large phase varaton for ths case Note that only varatons () (4) (see slde 8) have been addressed here 5 Conference on IEEE /39

29 Future Work Analyss of addtonal parameter varatons Flter BW Tme between messages Tme between frequency adjustments Larger clock nose level Choose level that bounds nose n oscllators expected to be used n ResE Clock phase granularty Consderaton of error n measurement of tmes the tme stamps are sent and receved, for mplementaton of the measurement n dfferent layers Determnaton of statstcal confdence ntervals for MTIE (and possbly TDEV) by runnng multple, ndependent replcatons a smulaton case Analyss of other varatons/choces (slde 8) 5 Conference on IEEE /39

30 References 1. Geoffrey M. Garner and Felx Feng, Delay Varaton Smulaton Results for Transport of Tme-Senstve Traffc over Conventonal Ethernet, Samsung presentaton at July, 5 IEEE 8.3 ResE SG meetng, San Francsco, CA, July 18, 5. Avalable va Geoffrey M. Garner, End-to-End Jtter and Wander Requrements for ResE Applcatons, Samsung presentaton at May, 5 IEEE 8.3 ResE SG meetng, Austn, TX, May 16, 5. Avalable va 3. Ralf Stenmetz, Human Percepton of Jtter and Meda Synchronzaton, IEEE JSAC, Vol. 14, No. 1, January, 1996, pp Resdental Ethernet (RE) (a workng paper), Draft.136, mantaned by Davd V. James and based on work by hm and other contrbutors, August 1, 5. Avalable va 5. ITU-T Recommendaton G.81, Defntons and Termnology for Synchronzaton Networks, ITU-T, Geneva, August, 1996, Corrgendum 1, November, ITU-T Recommendaton G.851, The Control of Jtter and Wander wthn the Optcal Transport Network (OTN), ITU-T, Geneva, November, 1, Amendment 1, June,, Corrgendum 1, June,. 7. Geoffrey Garner, Jtter Analyss for Asynchronous Mappng of a Clent Sgnal nto an OCh, Lucent Contrbuton to ITU-T Q 11/15 Interm Meetng, Ottawa, ON, July,. 8. Phase Nose, Vectron Internatonal, Applcaton Note, avalable at 5 Conference on IEEE /39

31 References 9. Jtter and Sgnal Nose n Frequency Sources, Raltron, Applcaton Note, avalable at 1. Davd W. Allan, Marc A. Wess, and James L. Jespersen, A Frequency Doman Vew of Tme Doman Characterzaton of Clocks and Tme and Frequency Dstrbuton Systems, Forty-Ffth Annual Symposum on Frequency Control, Los Angeles, CA, May 9 31, 1991, pp Stefano Bregn, Synchronzaton of Dgtal Telecommuncatons Networks, Wley,. 1. J.A. Barnes and Stephen Jarvs, Jr., Effcent Numercal and Analog Modelng of Flcker Nose Processes, Natonal Bureau of Standards, NBS Techncal Note 64, June, James A. Barnes and Charles A. Greenhall, Large Sample Smulaton of Flcker Nose, 19 th Annual Precse Tme and Tme Interval (PTTI) Applcatons Plannng Meetng, December, Govann Corsn and Roberto Salett, A 1/f γ Power Spectrum Nose Sequence Generator, IEEE Transactons on Instrumentaton and Measurement, Vol. 37, No. 4, December, 1988, pp Alexe Belaev, Latency Senstve Applcaton Examples, Gbson Labs, part of Resdental Ethernet Tutoral, IEEE 8.3 meetng, March, 5. 5 Conference on IEEE /39

32 Appendx I Clock Nose Model Clock phase nose may be modeled as a sum of random processes wth power spectral densty (PSD) of the form Af -α In practce, the PSD has 3 terms (see [8] and [9]) α =, Whte Phase Modulaton (WPM) α = 1, Flcker Phase Modulaton (FPM) α = 3, Flcker Frequency Modulaton (FFM) Can wrte the PSD, S x (f) as A B S x ( f ) = + + C, where S ( f 3 x f f Often express as ) has unts of An example PSD specfcaton s gven n Fgure 1 of [8], and reproduced on the next slde Data n [8] s gven n dbc/hz; data has been converted to rad /Hz Data n [8] s gven only for frequences below 1 khz; here, we assume the PSD s flat above 1 khz Dotted curve on the next slde s the converted data of [8]; sold lne s a conservatve ft of the above power law sum The specfcatons for the ndvdual products of [7] and [8] are below ths example, at least for those products where phase nose specfcatons are provded ns /Hz ( πν ) S ( f ), where unts of S ( ) are rad /Hz Sφ ( f ) = x φ f 5 Conference on IEEE /39

33 Appendx I Clock Nose Model 1e-3 1e-4 1e-5 1e-6 Example Clock Phase Nose Specfcaton Provded n [9] (data n [9] does not extend above 1 khz; PSD s assumed flat for hgher frequences wth the 1 khz value) analytc form of PSD specfcaton n [9] Note: Data n [8] s gven n dbc/hz; data has been converted to rad /Hz PSD (rad^/hz) 1e-7 1e-8 1e-9 1e-1 1e-11 1e-1 1e-13 1e+ 1e+1 1e+ 1e+3 1e+4 1e+5 1e+6 1e+7 1e+8 Frequency (Hz) 5 Conference on IEEE /39

34 Appendx I Clock Nose Model Another measure for clock nose, whch s more convenent because t s a tme doman parameter, s Tme Varance (TVAR) Tme Devaton (TDEV) s the square root of TVAR TVAR s 1/6 tmes the expectaton of the square of the second dfference of the phase errror averaged over an nterval TVAR( τ ) where E [] and [( x) ] 1 = E 6 denotes expectaton, x denotes average over the ntegraton tmeτ, denotes second dfference TVAR may be estmated from measured or smulated data usng [5] 1 TVAR( nτ ) whereτ s the samplng nterval and τ N 3n 1 n j 1 = 6n ( N 3n 1) j= 1 = j ( x x + x ), n = 1,,..., nteger part( N/ 3) = nτ + n + n 5 Conference on IEEE /39

35 Appendx I Clock Nose Model TVAR s equal to τ /3 multpled by the Modfed Allan Varance For power-law noses wth PSD proportonal to f -α, TVAR s proportonal to τ β, where β = α -1 The magntude of TVAR may be related to the magntude of PSD for power-law noses; see [1] and [11] for detals FFM ( π ) 9ln A S x ( f ) = TVAR( τ ) = Aτ 3 f FPM (result s from [1]; a more exact expresson s gven n [11]) WPM B 3.37 S x ( f ) = TVAR( τ ) = B f 3 τ fh S x ( f ) = C TVAR( τ ) = C τ f h = nose bandwdth 5 Conference on IEEE /39

36 Appendx I Clock Nose Model Smulaton of WPM WPM s smulated as a sequence of ndependent, dentcally dstrbuted random samples Nose dstrbuton s taken as Gaussan wth zero mean Varance and samplng tme determne TDEV level Choose varance such that, wth gven samplng tme, the computed TDEV from a sample hstory s close to value obtaned from above relaton between TDEV and PSD Assume nose bandwdth s equal to lne rate (1 MHz) Smulaton of FPM FPM s smulated by passng a sequence of ndependent, dentcally dstrbuted random samples through a Barnes/Jarvs flter [1] [14] If whte nose s nput to a flter wth frequency response H(f) = f 1/, the output s a random process wth PSD proportonal to 1/f The Barnes/Jarvs flter approxmates an f 1/ frequency response usng a bank of lead/lag flters The actual frequency response of ths flter s a starcase The spacngs of the poles and zeros are chosen such that the average slope s 1 db/decade 5 Conference on IEEE /39

37 Appendx I Clock Nose Model Smulaton of FPM (Cont.) Nose dstrbuton s taken as Gaussan wth zero mean Varance determnes TDEV level Choose varance such that the computed TDEV from a sample hstory s close to value obtaned from above relaton between TDEV and PSD Smulaton of FFM Input a sequence of ndependent, dentcally dstrbuted random samples through a Barnes/Jarvs flter followed by an ntegrator (accumulator) Nose dstrbuton s taken as Gaussan wth zero mean Varance determnes TDEV level Choose varance such that the computed TDEV from a sample hstory s close to value obtaned from above relaton between TDEV and PSD Next slde shows TDEV for smulated data sample (1-5 s tme step) and analytc form equvalent to PSD (sold curve on slde 35) 5 Conference on IEEE /39

38 Appendx I Clock Nose Model Clock Phase Nose Model Smulaton Data Sample Analytc Form Equvalent to PSD 1 1 TDEV (ns) e-6 1e-5 1e-4 1e-3 1e- 1e-1 1e+ 1e+1 1e+ Integraton Tme (s) 5 Conference on IEEE /39

39 Appendx II Defnton of MTIE Jtter and wander requrements can be expressed n terms of Maxmum Tme Interval Error (MTIE) masks MTIE s peak-to-peak phase varaton for a specfed observaton nterval, expressed as a functon of the observaton nterval An estmate of MTIE may be computed by (see [5]) MTIE( nτ ) whereτ x( ) s the ( Nτ s max 1 k N n ( ) max x( ) mn x( ), s the samplng nterval, nτ s th k k + n phase sample, and N the measurement nterval) k k + n the number of phase samples The dervaton of the MTIE masks on slde 6 from the jtter and wander requrements s gven n [] s n = 1,,..., N 1 the observaton nterval, 5 Conference on IEEE /39