《TIA-TSB107-1999.pdf》由会员分享，可在线阅读，更多相关《TIA-TSB107-1999.pdf（31页珍藏版）》请在三一文库上搜索。
1、c TINEIA TELECOMMUNICATIONS SYSTEMS BULLETIN Guideline for the Statistical Specification of Polarization Mode Dispersion on Optical Fiber Cables TSBl07 NOVEMBER 1999 TELECOMMUNICATIONS INDUSTRY ASSOCIATION Rcprtsenhg the tcleammuniutions industry ia assouation with the Elechonic hdustries Alliance E
2、lsetionic Industries Alliance Copyright Telecommunications Industry Association Provided by IHS under license with EIALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/29/2007 21:35:51 MDTNo reproduction or networking permitted without license from IHS -,-,- NOTICE TIA/EIA Engi
3、neering Standards and Publications are designed to serve the public interest through eliminating misunhtan between m a n d m and purchasers, facilitating interchangeabihty and improvement of products, and assisting the purchaser in selecting and obtaining with minimum delay the proper product for hi
4、s particular need. Existence of such Standards and miblications shall not in any respect preclude any member or nonmember of TJA/EIA Fom m a n M g or selling products not conforming to such Standards and Publications, nor shall the existence of such Standards and Publications preclude their voluntar
5、y use by those other than TLLvEIA members, whether the standard is to be used either domestically or internaiody. Standards, Publications and Bulletins are adopted by EIA in accordance with the American National Standards Institute (ANSI) patent policy. By such action, TIA/EIA does not assume any li
6、ability to any patent owner, nor does it assume any obligation whatever to parties adopting the Standard, Publication, o r Bulld = 1) To find the maximum DGD at a given probability level from a given PMD value, d, compute the value of S that satisfies equation 6 for the desired probability and multi
7、ply this value of S times d to obtain the maximum DGD value. The following table has some S values along with the associated probabilities. 7 Copyright Telecommunications Industry Association Provided by IHS under license with EIALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 0
8、3/29/2007 21:35:51 MDTNo reproduction or networking permitted without license from IHS -,-,- TINEIA-TSB-107 - 3.0 3.1 Table I Probability based on 4.2E-05 2.OE-05 I Wavelength Average I 3.2 3.3 I S I Probabilitv I 9.2E-06 4.1 E-06 3.775 6.5E-08 3.9 2.OE-08 4.0 7.4E-09 4.1 2.7E-09 4.3 3.3E-10 4.4 I 1
9、.1E-IO I 4.5 I 3.7E-1 I I I Note: If the PMD value is defined as the root mean square (rms) of the DGD values, the constant 4h should be replaced with 312 in equations 4 and 5. 4. Definition and calculations for Method I The maximum link PMD coefficient for a given process distribution, PMDQ, is def
10、ined in terms of a small probability value, Q, and an assumed number of cable sections in the link, M, such that if dc-link is a possible link PMD coefficient: Pr(dc-link PMD,) e Q for M or more cable sections (7) Note: This reads as: The probability that a link PMD coefficient is greater than PMDQ
11、is less than Q. The requirement is expressed by stipulating M and Q and requiring that PMDQ be less than some value, PMDmm. The default values are: Q 100ppm M 20 PMDQ I P M D , = 0.5 psldkrn 8 Copyright Telecommunications Industry Association Provided by IHS under license with EIALicensee=IHS Employ
12、ees/1111111001, User=Wing, Bernie Not for Resale, 03/29/2007 21:35:51 MDTNo reproduction or networking permitted without license from IHS -,-,- E b057743 0000455 709 W TINEIA-TSB-I 07 Note: For Q=lOO ppm, PMDQ is the 99.99 percentile of the link PMD coefficients. There are three techniques that may
13、be used to calculate PMDQ: Monte Carlo, Gamma model, and Generalized Central Limit Theorem 7,8,9,1 O. The Monte Carlo technique makes no assumptions about the distribution. It cannot, however, be used to extrapolate beyond the empirically sampled data. The gamma model allows extrapolation by using a
14、 model that has two parameters that can be related to average and standard deviation. The gamma model is more suited to PMD distributions than the gaussian distribution because the gamma model is skewed right and produces only non-negative outcomes. The Generalized Central Limit Theorem model has th
15、ree parameters that allow the skew to be set independently from average and standard deviation. At the I O0 ppm probability level one may question whether any modeling can be effective with the finite sample sizes that are practical. A more appropriate way of viewing the requirement is that while th
16、e form of the criterion is in terms of probability, the net effect is a boundary on the combination of process distribution parameters. To illustrate, consider the following example based on gaussian assumptions: The requirement is that the probability be less than 1 O 0 ppm that a sample mean of M
17、values, x, , exceeds a given maximum, X,: Pr(X, A-,) 5. If the inequality is not verified, repeat the Monte Carlo using a larger value of M. 4.2.2 Maximum likelihood estimate This technique does not require the use of Monte Carlo, so the M parameter is set to one. It does require an iterative optimi
18、zation procedure. Let d,-i represent N measurements on individual cable sections. Calculate the quadrature average, v, as: Choose the value of a that maximizes the following expression by iterative evaluation of the function or by iterative reduction of its derivative with respect to a to zero : Usi
19、ng the computed value of a, obtained from maximizing 14, calculate as: a =- V 2 4.3 Generalized central limit theorem This technique might be considered as “model independent” because it is derived from the Central Limit Theorem 9,10, adjusted to include a skew term. Let d,-i be N measured values on
20、 individual cable sections. Calculate the following moments 12 Copyright Telecommunications Industry Association Provided by IHS under license with EIALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/29/2007 21:35:51 MDTNo reproduction or networking permitted without license f
21、rom IHS -,-,- lN P3 = - c ( 4 - i - PI l3 N - 1 The cumulative probability density function for a link of M concatenated cable sections is given by: Where Note: Equations 20a and 20b are just the expressions for a gaussian probability density function and its integral, or cumulative probability dens
22、ity function. Note: The probability density function (histogram representation) may be obtained by taking the derivative of equation 19 with respect to u. The value for PMDQ is determined by setting it equal to the value of u that satisf es: The value of PMDQ can be approximated by: Where ZQ satisfi
23、es: (zQ)= I- Q Note: For Q=100 ppm, ZQ = 3.72. 13 Copyright Telecommunications Industry Association Provided by IHS under license with EIALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/29/2007 21:35:51 MDTNo reproduction or networking permitted without license from IHS -,-,-
24、 TINEIA-TSB-107 5. Assessment of Method 1 vs. DGD Method 1 results in a reduction in the variability of the link PMD coefficient. Compared to worst case approach it should provide either some reduction in the estimated maximum DGD or some decrease in the probability of exceeding a fixed maximum DGD
25、value. Figure 3 illustrates three cases: - The worst case assumption, that the distribution of link PMD coefficients is a “spike” or dirac function; - A distribution of the PMD coefficients of individual cable sections, with moderate probability of exceeding the worst case; - The distribution of lin
26、k PMD coefficients, with very low probability of exceeding the worst case. PMD Coefficient Distribution O 25 0.2 5r a , 3 U u . 0.15 e! 0.1 0.05 O O 0.1 0.2 0.3 0.4 0.5 0.6 ps/sqrt( kirn) Figure 3 The traditional means of determining the maximum DGD, DGD probability level, PDGD, and a worst case PMD
27、 coefficient is to: defined by a - - - Select the desired probability level from Table 1. Multiply the associated value of S with the maximum PMD coefficient Multiply the result with the square root of the link length Taking the substantially decreased probability that a link PMD coefficient exceeds
28、 PMD max into account, as illustrated in Figure 3, would surely either decrease D G D , , or the associated probability of exceeding a pre-fixed value of D G D , , . 14 Copyright Telecommunications Industry Association Provided by IHS under license with EIALicensee=IHS Employees/1111111001, User=Win
29、g, Bernie Not for Resale, 03/29/2007 21:35:51 MDTNo reproduction or networking permitted without license from IHS -,-,- TINEIA-TSB-107 The problem is illustrated in Figure 4, which shows a series of Gamma distributions of link PMD coefficient. All these distributions meet the default criterion of Me
30、thod I. The far right distribution is approaching the worst case dirac function, which would, in fact pass the Method 1 criterion. Clearly the far left distribution would yield better DGD performance than the far right distribution. The Method 1 criterion, while suitable as being a measurable attrib
31、ute, does not provide accurate information with regard to a key system design attribute: DGD. Various passing distributions 0.06 a , 2 0.05 0.04 t $ ! 0.03 m iu 0.02 PL 0.01 O 3 .- U O 0.1 0.2 0.3 0.4 0.5 0.6 Concatenated link PMD coefficient Figure 4 If one were to take an extreme view, the probabi
32、lity associated with multiplying the P M D m , value by an S multiplier should be somewhat larger than the probability found in Table I, which represents a “pure” worst case. This is due to the fact that there is theoretically some “tail” of the statistical representation that extends beyond P M D ,
33、 while the pure worst case has no such tail. Using a Maxwell adjustment factor S = 3, for example, in the pure worst case yields probability: PDGD = 4 . 2 . IO- . The statistical worst case has been estimated as PED = I .4*1 O-4. This same S multiplier applied to a maximum cable PMD link coefficient
34、 of 0.5 psldkm yields a maximum DGD value of 30 ps over 400 km. In effect, the application of the S multiplier resumes the assumption that the link PMD distribution is a spike. 5 Using the S multiplier approach with P M D m , does not reflect the realistic improvements that could be garnered from a
35、statistical design approach. This is especially true when one considers the realistic needs of system design. According to the ITU recommendation G.691 IO, an end-to-end DGD value of 30 ps will induce a maximum of 1 dB receive sensitivity penalty for an NRZ 15 Copyright Telecommunications Industry A
36、ssociation Provided by IHS under license with EIALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/29/2007 21:35:51 MDTNo reproduction or networking permitted without license from IHS -,-,- TINEIA-TSB-107 system operating at 10 Gbis. If the actual DGD exceeds this value the sys
37、tem could become unavailable. Various means of converting the DGD probability (PDGD) to system unavailability have been discussed in standards development groups. While none have been agreed, it has become clear that a PDGD value on the order of less than is desirable. Since the link DGD and probabi
38、lity include both optical fiber cable and components, the maximum DGD and probability for optical fiber cable must be reduced from the levels discussed above. IEC 61282-3 provides some guidance on these issues. Inclusion of components with PMD into the system will induce a need to: - Reduce the opti
39、cal fiber cable induced portion of D G D m , to a value less than 30 ps to allow components with PMD. - Reduce the optical fiber cable DGD probability, PDGD, to a value that is half of what is desired for the combined link. 6. Definition and calculations for Method 2 Method 2 is introduced to solve
40、the problems mentioned in clause 5. The specific values that are introduced were chosen to provide: - A statistical requirement that is nearly the same as the Method 1 specification - An indication of operability of 10 Gbis systems over 400 km. 6.1 Definition Method 2 is expressed in terms of a maxi
41、mum DGD value, D G D m , , and the probability that a DGD on a given link and wavelength exceeds this maximum. This probability is specified with a maximum, PDGDmax. A reference link length, Ld, and assumed cable length, Lcab, are also stipulated. The combination of these lengths implies a value of
42、M, the number of concatenated cable sections, following 3.1. The Method 2 probability criterion is stated as: Provide a distribution of PMD coefficient values so a concatenated link of length, Ld, composed of individual cable sections of length, Lcab in length, yields a probability, PDGD, less than
43、PDGDmax, that a given IinWwavelength DGD value exceeds DGD m. Default values for the four defining variables are: Copyright Telecommunications Industry Association Provided by IHS under license with EIALicensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 03/29/2007 21:35:51 MDTNo rep
44、roduction or networking permitted without license from IHS -,-,- TINEIA-TSB-107 Note that for Method 1, the probability level is set and PMDQ is calculated - and required to be less than P M D m , . For Method 2, D G D , is set and PDGD is calculated - and required to be less than PDGDma. The refere
45、nce link length is taken as 400 km to match certain ITU system assumptions I I. The I O km cable section length is taken as a conservative estimation because most installed lengths are from 2 km to 4 km. The values for D G D m , and PDGDma are derived from the discussion in clause 5. The value of D
46、G D , can safely be used for links of any length that is less than the reference length. That is, the probability that D G D , , is exceeded reduces with decreasing link length if the cable length assumption is maintained. For links with longer lengths, the DGD limit should be increased in proportio
47、n to the square root of the ratio of link length to reference length. 6.2 Calculation principle - convolution The calculation principle is derived from extending the worst case approach discussed in clause 5. With this approach, the link PMD value is assumed to be a dirac function and the DGD distri
48、bution is represented as a Maxwell distribution. The probability that the Maxwell distribution exceeds DGD yields PWD. These distributions are represented in Figure 5. Worst case approach assumption 0.07 0.06 005 0.04 al J g! IL 9 003 f 002 .- c E 0.01 O: O 10 20 30 40 DGDIPMD link value Figure 5 Note: Though not shown, the dirac function illustrated in Figure 5 extends to a relative frequency value of 1 .O. Suppose the link PMD value could be represented by two dirac functions, each with a magnitude of 0.5. This would r