1、 International Telecommunication Union ITU-T O.182TELECOMMUNICATION STANDARDIZATION SECTOR OF ITU Amendment 1(01/2009) SERIES O: SPECIFICATIONS OF MEASURING EQUIPMENT Equipment for the measurement of digital and analogue/digital parameters Equipment to assess error performance on Optical Transport N
2、etwork interfaces Amendment 1: An additional evaluation procedure Recommendation ITU-T O.182 (2007) Amendment 1 ITU-T O-SERIES RECOMMENDATIONS SPECIFICATIONS OF MEASURING EQUIPMENT General O.1O.9 Maintenance access O.10O.19 Automatic and semi-automatic measuring systems O.20O.39 Equipment for the me
3、asurement of analogue parameters O.40O.129 Equipment for the measurement of digital and analogue/digital parameters O.130O.199 Equipment for the measurement of optical channel parameters O.200O.209 Equipment to perform measurements on IP networks O.210O.219 Equipment to perform measurements on lease
4、d-circuit services O.220O.229For further details, please refer to the list of ITU-T Recommendations. Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) i Recommendation ITU-T O.182 Equipment to assess error performance on Optical Transport Network interfaces Amendment 1 An additional evaluation procedure Summa
5、ry Amendment 1 to Recommendation ITU-T O.182 adds an additional evaluation procedure using the goodness of the fit to the exponential distribution for the random error generator (clause C.6) and the detailed description of this evaluation method (Appendix II). Source Amendment 1 to Recommendation IT
6、U-T O.182 (2007) was approved on 13 January 2009 by ITU-T Study Group 15 (2009-2012) under Recommendation ITU-T A.8 procedures. ii Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) FOREWORD The International Telecommunication Union (ITU) is the United Nations specialized agency in the field of telecommunicati
7、ons, information and communication technologies (ICTs). The ITU Telecommunication Standardization Sector (ITU-T) is a permanent organ of ITU. ITU-T is responsible for studying technical, operating and tariff questions and issuing Recommendations on them with a view to standardizing telecommunication
8、s on a worldwide basis. The World Telecommunication Standardization Assembly (WTSA), which meets every four years, establishes the topics for study by the ITU-T study groups which, in turn, produce Recommendations on these topics. The approval of ITU-T Recommendations is covered by the procedure lai
9、d down in WTSA Resolution 1. In some areas of information technology which fall within ITU-Ts purview, the necessary standards are prepared on a collaborative basis with ISO and IEC. NOTE In this Recommendation, the expression “Administration“ is used for conciseness to indicate both a telecommunica
10、tion administration and a recognized operating agency. Compliance with this Recommendation is voluntary. However, the Recommendation may contain certain mandatory provisions (to ensure e.g. interoperability or applicability) and compliance with the Recommendation is achieved when all of these mandat
11、ory provisions are met. The words “shall“ or some other obligatory language such as “must“ and the negative equivalents are used to express requirements. The use of such words does not suggest that compliance with the Recommendation is required of any party. INTELLECTUAL PROPERTY RIGHTS ITU draws at
12、tention to the possibility that the practice or implementation of this Recommendation may involve the use of a claimed Intellectual Property Right. ITU takes no position concerning the evidence, validity or applicability of claimed Intellectual Property Rights, whether asserted by ITU members or oth
13、ers outside of the Recommendation development process. As of the date of approval of this Recommendation, ITU had received notice of intellectual property, protected by patents, which may be required to implement this Recommendation. However, implementers are cautioned that this may not represent th
14、e latest information and are therefore strongly urged to consult the TSB patent database at http:/www.itu.int/ITU-T/ipr/. ITU 2009 All rights reserved. No part of this publication may be reproduced, by any means whatsoever, without the prior written permission of ITU. Rec. ITU-T O.182 (2007)/Amd.1 (
15、01/2009) iii CONTENTS Page 1) Clause 10.2, Error generation . 1 2) Annex C 1 3) Clause C.1. 1 4) Clause C.5. 1 5) Clause C.6. 1 6) New Appendix II 3 Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) 1 Recommendation ITU-T O.182 Equipment to assess error performance on Optical Transport Network interfaces Amen
16、dment 1 An additional evaluation procedure 1) Clause 10.2, Error generation Change the first paragraph of clause 10.2 to: Figure 10-1 presents the error generator. To measure the FEC performance, ME sender inserts symbol errors after FEC computation. Errors are inserted following a Poisson process l
17、aw. Annex C defines the parameters and the procedure for testing the goodness of fit of a Poisson process. 2) Annex C Change the title of Annex C to: Procedure of goodness of fit for Poisson process by 2test 3) Clause C.1 Change clause C.1 to: C.1 Introduction A “Poisson error generator“ used for pe
18、rformance tests of digital communications systems should generate random errors satisfying the Poisson process. However, the distribution of the random errors generated from such equipment may not necessarily fit a Poisson process. Therefore, an objective method to evaluate the distribution characte
19、ristic of the random errors is needed. Although there are many methods for testing goodness of fit for Poisson process, this annex describes a method using the 2test. Both Annexes C.5 and C.6 explain the concrete test procedure. Refer to Appendices I and II for the detailed explanation of this metho
20、d. 4) Clause C.5 Change the title of clause C.5 to: C.5 Procedure for test of goodness of fit for Poisson distribution by 2test 5) Clause C.6 Insert the following new clause: C.6 Procedure for test of goodness of fit for exponential distribution by 2 test The test of goodness of fit for exponential
21、distribution by 2 test is performed by the following steps. Refer to Appendix II for the detailed explanation of this method. 1) Measure the nearest neighbouring error intervals, tn= in+1 in1, n =1, ., N. 2 Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) 2) Find tmaxfor sample 1,=nNnt . 3) Determine divisor
22、 M for interval 0, tmax. Recommended 5 M 50 Example M = 30 4) Determine interval width when creating histogram T as T = tmax/M. Where x is the minimum integer value of x. 5) Using 1,=nNnt , determine the sample size (namely observation frequency fi, i = 0, ., M 1) for interval iT, (i +1) T. 6) Find
23、the average error interval, t , using the following equation: =NnntNt117) Find the maximum likelihood estimator of pe, ep, using the following equation: ,11tpe+=epq1= 8) Find the theoretical frequency ei, i = 0, , M 1 for iT, (i +1) T using the following equation: =+=1)1(1)1(TiTixxeTTiiqpNqqNe 9) Us
24、ing the observed frequency 01,=iMif and the theoretical frequency 01,=iMie , check the 2 goodness of fit as described in items 7 to 11 of clause C.5. .O.182.Amd.1(09)_FC.2Observed interval tErrorRandomerrorgeneratorIntervalmeasureClockHistogramReadTest of goodnessof fit by test2 DecisionErrorClockOb
25、servedintervalt1t2t3t4t5tNi1Occurrencetime of errori2i3i4i5iN+1Figure C.2 Error interval property block diagram Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) 3 6) New Appendix II Add the following new appendix. Appendix II Test of goodness of fit for exponential distribution by 2test (This appendix does n
26、ot form an integral part of this Recommendation) This appendix describes the detail of the evaluation method for exponential distribution described in clause C.6. Furthermore, this appendix describes why this method is used. II.1 Introduction An ideal error generator with error rate peis a device th
27、at repeats independently the Bernoulli process at some given period with the parameter pe. Consequently, the error generator performance can be evaluated by using the following two statistical methods: 1) Binomial distribution of errors occurring within some observation interval: Error frequency pro
28、perty. 2) Time interval error distribution: Error interval property. Appendix I describes an evaluation method based on the error frequency property in method 1 above; it assumes that when the observation interval n is sufficiently long and peis sufficiently small, the binomial distribution becomes
29、asymptotic and approaches the Poisson distribution where parameter = npe. On the other hand, this appendix describes a 2 goodness of fit evaluation method for the error interval property in method 2 above, where the error generation interval (error interval below) follows the exponential distributio
30、n. Clause II.2 describes that the nearest neighbouring error interval follows an exponential distribution and describes the theoretical frequency required for performing the 2goodness of fit test. Clause II.3 describes a 2goodness of fit test using actual measured data. II.2 Nearest neighbouring err
31、or interval distribution and theoretical values A sample Bernoulli procedure with population parameter peis represented as: xi 0,1, i = 1,2, where error occurrence time which becomes “xi= 1“ is represented by i1, i2, , iN+1. When the nearest neighbouring error interval tnis defined as tn= in+1 in1,
32、n =1, ., N, the probability of tn= t, t = 0,1,. is the probability of 1 appearing after t continuous 0s, or, in other words, etpq . Here, q is defined as q = 1 pe. Therefore, sample 1,=nNnt is the sample extracted from the population according to the geometrical distribution of parameter pe. The the
33、oretical frequency of the geometric distribution is calculated as follows, where the sample average t is defined as: =NnntNt114 Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) By solving eeppt/)1( = for the maximum likelihood estimator of pe, epis defined as: eepqtp1,11=+= The maximum value T for 1,=nNnt is
34、 defined as T= T/M, using the appropriate divisor M. x is the minimum integer value x. The theoretical frequency ei, i = 0, , M 1 for interval iT, (i +1) T is given by the following equation, using the sum of the geometric progression: ).1(1)1(TTiTiTixxeiqpNqpNe+=(II-1) The theoretical frequency of
35、equation (II-1) when ab= exp(b log a) has the following asymptotic form when pe1 and the logq = log(1pe) peapproximation is used. ()+=TiTieeeeidttppNTpTpiNe)1()exp()exp(1)exp( (II-2) The integer expression for ei on the right side of equation (II-2) is the theoretical frequency for the relevant inte
36、rval corresponding to the exponential distribution of parameter ep. This corresponds to an asymptotic Poisson process when the Bernoulli process is pe1. II.3 Goodness of fit test results The error generator operation period and the error rate, pe, were set to 10 ns and 102, respectively, and a goodn
37、ess of fit test described in clause C.6 was performed on data obtained using three different types of generator. Table II.1 shows the goodness of fit test results, and Figure II.1 shows the theoretical and observed frequency histograms with the number of errors on the left and the intervals between
38、nearest neighbouring errors on the right. Although errors generated by the type A generation method are evaluated as not fitting the Poisson distribution for error frequency properties, neither is there a fit with the exponential distribution for the error interval property. Actually, from Figure II
39、.1, it is clear that errors generated by the type A method are concentrated in a narrower interval than is ideal. Next, using the type B method unlike the fit of the error frequency property, the interval property does not fit the geometric distribution. However, type B is closer to the exponential
40、distribution than type A, as shown by the 2values (Table II.1) and the decrease in the difference between the observed and theoretical frequencies (Figure II.1). Last, the error generated by the type C generation method fits the distribution for both the error frequency and error interval properties
41、. Error frequency property: Poisson distribution of goodness of fit Error interval property: exponential distribution goodness of fit Error generation method df 2value 2 M,0.05Fit/No Fit df 2value 2 M,0.05Fit/No Fit Type A1) 28 5330.841.3 No Fit 26 14341.6 38.9 No Fit Type B2) 18 19.6 28.9 Fit 25 17
42、3.0 37.7 No Fit Type C3) 18 18.7 28.9 Fit 25 18.2 37.7 Fit 1)Type A is the generation method used in the example 2, described in clause I.4.2. 2)Type B is the generation method used in the example 1, described in clause I.4.1. 3)Type C is a new generation method improving randomness. Rec. ITU-T O.18
43、2 (2007)/Amd.1 (01/2009) 5 O.182.Amd.1(09)_FII.1Error frequency propertyType AType BError interval propertyFrequencyNumber of errorsInterval between the nearest neighbouring errors ( s)0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.08000700060005000400030002000100009000FrequencyInterval between the nearest neigh
44、bouring errors ( s)0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.040003000200010000FrequencyInterval between the nearest neighbouring errors ( s)0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0400030002000100005 1015202530120100806040200Number of errors5 10152025 4030 35120100806040200Type CNumber of errors5 101520253012010
45、0806040200Observed frequency Theoretical frequencyFrequencyFrequencyFrequencyFigure II.1 Observed and theoretical frequency histograms for three types of error generators 6 Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) Tables II.2, II.3 and II.4 show the sample data for the error frequency property of typ
46、es A, B and C, respectively. Table II.2 Sample data for the error frequency property (type A) k Observed frequency fkExpected frequency kknpe =Deviation ()kkkeef /23 8 0.093 668.636 4 9 0.315 239.538 5 9 1.008 63.395 6 25 2.687 185.303 7 20 6.141 31.277 8 38 12.281 53.860 9 54 21.832 47.398 10 45 34
47、.929 2.904 11 60 50.802 1.665 12 69 67.732 0.024 13 67 83.358 3.210 14 58 95.260 14.574 15 72 101.605 8.626 16 55 101.599 21.373 17 69 95.617 7.409 18 52 84.987 12.804 19 51 71.564 5.909 20 36 57.248 7.886 21 32 43.615 3.093 22 33 31.718 0.052 23 27 22.063 1.105 24 21 14.708 2.692 25 24 9.412 22.608
48、 26 17 5.792 21.689 27 17 3.432 53.638 28 15 1.961 86.695 30 11 1.659 52.600 32 9 0.447 163.795 34 6 0.106 327.269 38 6 0.011 3219.725 Total kf = 1015 ke = 1023.982 ()kkkeef /22= = 5330.752 Rec. ITU-T O.182 (2007)/Amd.1 (01/2009) 7 Table II.3 Sample data for the error frequency property (type B) k O
49、bserved frequency fkExpected frequency kknpe =Deviation ()kkkeef /26 6 3.701 1.427 7 7 6.151 0.117 8 13 12.299 0.04 9 20 21.86 0.158 10 33 34.967 0.111 11 62 50.849 2.445 12 70 67.782 0.073 13 78 83.404 0.35 14 77 95.295 3.512 15 91 101.624 1.111 16 109 101.599 0.539 17 101 95.599 0.305 18 92 84.956 0.584 19 85 71.525 2.539 20 52 57.206 0.474 21 34 43.575 2.104 22 39 31.683 1.69 23 21 22.035 0.049 24 1
