Statistical models help specify pmd

June 1, 1997

Statistical models help specify pmd

WILLIAM B. GARDNER

In September 1996, Lightwave reported on several standard test methods for characterizing polarization-mode dispersion (pmd) in fiber-optic cables and presented a Special Report article about pmd in the same issue (see pages 36 and 43, respectively). Since then, national and international standards bodies have been addressing the difficult issues of specifying the random variable pmd.

In contrast, another fiber-optic cable parameter, chromatic dispersion, is a deterministic variable. This attribute makes it practical to specify a maximum value that serves to minimize optical-system performance problems. Such values are given for various transmission bit rates in the "Application Codes" of the International Telecommunication Union`s (itu) system Recommendations.

When the same specification approach is tried with pmd, however, calculations indicate that an optical-fiber cable that has a pmd value of 0.5 psec/sq.-root km would allow a transmission rate of 10 Gbits/sec over a distance of 400 km without signal impairment.

In theory, this maximum pmd value appears applicable for high-end fiber-optic cable networks. In practice, however, a random variable such as pmd can easily vary by a factor of 3 or 4 on a single fiber production line. Some suppliers deliver fiber-optic cables that are specified as having a maximum pmd of 0.5 psec/sq.-root km. However, if a network planner or provider uses this "worst-case" value in designing an optical system, the resulting design does not use the full capability of the fiber.

To help specify pmd, Steve Jacobs, distinguished member of technical staff, Lucent Technologies, Norcross, GA, presented a pmd statistical model to the Telecommunications Industry Association`s (tia) Joint Subcommittee FO-2.1/6.6 last January and to the International Electrotechnical Commission`s (iec) Working Groups 1 and 3 of Subcommittee 86A last February.

Jacobs`s model demonstrates that a 10-Gbit/sec optical-fiber system encompassing a distance of 400 km in a worst-case design is actually capable of operating successfully for more than 10 times that distance. The exact distance depends on the statistical assumptions made, such as the length of individual fiber cables. Similarly, a 40-Gbit/sec transmission rate could be transmitted only 25 km for a worst-case calculation, but more than 100 km when the actual statistical distribution of pmd is taken into account, using Jacobs`s model.

This statistical design approach infers a small probability that the system pmd objective will not be met (1 in 10,000 in Jacobs`s calculations). The statistical design also requires some knowledge of the distribution of pmd values in the vendor`s cables. Once this distribution were determined for a stable manufacturing process, it would not be necessary to measure the pmd of every cabled fiber to use the statistical model. The resulting cost savings could benefit both buyers and sellers.

In Jacobs`s model, two parameters (alpha and beta) are required to characterize the pmd distribution. In alternative approaches, successful uses of a Monte Carlo-type of statistical model have been reported by Lucent Technologies (tia, June 1995) and by Corning Inc. and Siecor Corp. (International Wire & Cable Symposium, November 1996).

A statistical approach to optical-fiber system design is not new. Before pmd became a concern, the itu had already sanctioned the use of both Gaussian and Monte Carlo statistical design models for determining fiber path attenuation (as listed in Appendix 4 of itu`s Recommendation G.982, for example).

Given the advantages that statistical design has over worst-case design for pmd, Eric Loytty, manager, engineering services, Siecor Corp., Hickory, NC, has also presented a specific proposal to both the tia and iec. The tia and iec are currently evaluating his proposed methodologies for pmd. q

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