Home > Articles > Networking > Network Design & Architecture

WDM Network Design

This chapter is from the book

Calculation of Q-Factor from OSNR

The OSNR is the most important parameter that is associated with a given optical signal. It is a measurable (practical) quantity for a given network, and it can be calculated from the given system parameters. The following sections show you how to calculate OSNR. This section discusses the relationship of OSNR to the Q-factor.

The logarithmic value of Q (in dB) is related to the OSNR by Equation 4-11.

Equation 4-11

In the equation, B0 is the optical bandwidth of the end device (photodetector) and Bc is the electrical bandwidth of the receiver filter.

Therefore, Q(dB) is shown in Equation 4-12.

Equation 4-12

In other words, Q is somewhat proportional to the OSNR. Generally, noise calculations are performed by optical spectrum analyzers (OSAs) or sampling oscilloscopes, and these measurements are carried over a particular measuring range of Bm. Typically, Bm is approximately 0.1 nm or 12.5 GHz for a given OSA. From Equation 4-12, showing Q in dB in terms of OSNR, it can be understood that if B0 < Bc, then OSNR (dB )> Q (dB). For practical designs OSNR(dB) > Q(dB), by at least 1–2 dB. Typically, while designing a high-bit rate system, the margin at the receiver is approximately 2 dB, such that Q is about 2 dB smaller than OSNR (dB).

Calculation of OSNR for a Point-to-Point Link

Consider a physical link AB, as shown in Figure 4-5. Assume this to be a long-haul fiber WDM link (a link that is several hundred kilometers). Amplifiers are placed periodically at repeated intervals to boost signal power. Therefore, a signal can reach much farther than the maximum allowable accumulated loss due to the fiber (υL). However, in doing so, each amplifier stage adds its own component of amplified spontaneous emission (ASE) noise and degrades the OSNR further. Moreover, every amplifier amplifies the already present noise. Note that noise is omnipresent throughout the spectra and almost impossible to be removed. Therefore, it is imperative to devise a method to calculate the OSNR (output) at the end of an N stage-amplified system and see if the value N is still valid.

Figure 4-5Figure 4-5 A Multiple Stage Amplified DWDM System Deployed in a Point-to-Point Topology

In an OSNR-based design, we must ensure that OSNR of the final stage is in compliance with system OSNR requirements and hence the BER requirements. To make the system support a particular BER, it is necessary to make the OSNR system design compliant.

The OSNR of each stage is shown in Equation 4-13.

Equation 4-13

In Equation 4-13, NFstage is the noise figure of the stage, h is Plank's constant (6.6260 × 10-34), ν is the optical frequency 193 THz, and Δf is the bandwidth that measures the NF (it is usually 0.1 nm).

The total OSNR for the system can be considered by a reciprocal method and is shown in Equation 4-14.

Equation 4-14

for the 'N' stage system. That summarizes to Equation 4-15.

Equation 4-15

A slight detailed analysis provides a more appropriate equation for OSNR. For a single amplifier of gain G, the OSNR is shown in Equation 4-16.

Equation 4-16

In Equation 4-16, nsp is the population inversion parameter that is shown in Equation 4-17 and is the ratio of electrons in higher and lower states.

Equation 4-17

In Equation 4-17, N2 is the number of electrons in a higher state and N1 is the number of electrons in the lower state. (Refer to Chapter 2 for more details.)

The population inversion parameter is also shown in Equation 4-18.

Equation 4-18

For an N amplifier stage system, with each amplifier compensating for the loss of the previous span where the span loss in dB is , you have the relationship for final stage OSNR in Equation 4-19.

Equation 4-19

Taking logarithm to the common base (10), we get Equation 4-20.

Equation 4-20

From the previous section, we get Δf = 0.1 nm, or 12.5 GHz. Substituting this, we get Equation 4-21.

Equation 4-21

The following is assumed:

  • The NF of every amplifier is the same. (we assume uniformity of products; therefore, NFs are the same for all amplifiers.)

  • is the span loss and is same. (This is a generic assumption and can be changed, as shown later in this section.)

  • Noise is totaled over both states of polarization. In short, it is unpolarized noise.

Equation 4-21 provides the actual mathematical calculation of OSNR. This calculation method has quite a few approximations in which we can still find the system OSNR to a great degree of accuracy. In a multichannel WDM system, the design should consider OSNR for the worst channel (the one that has the worst impairment). The worst channel is generally the first or last channel in the spectrum.

OSNR Improvements by Raman Amplification

If we look at Equation 4-21, we can see that the EDFA gain factor G is not considered. That is because OSNR is a ratio, and the gain acts equally on signal and noise, canceling the gain factor in the numerator and denominator. In other words, although EDFAs alleviate the upper bound on transmission length due to attenuation, by cascading EDFAs in a series, the OSNR is continuously degraded with transmission length and ASE (from EDFAs). This degradation can be lessened somewhat by distributed Raman amplifiers (DRAs). As can be seen from Chapter 3, "Networking with DWDM -2," Raman amplification is inherently a result of stimulated Raman scattering of a high intensity pump signal at a different frequency (compared to the signal frequency). This produces a gain because of creation of a Stokes wave, which in turn produces a gain feeding wave of a wide bandwidth.

Consider a hybrid system as shown in Figure 4-6.

Figure 4-6Figure 4-6 Multistage Raman Amplifier-Based System

From the preceding system, the OSNR of the final stage is shown as in Equation 4-22.

Equation 4-22

Equation 4-23 gives the OSNR value of each stage.

Equation 4-23

As we can see from Equation 4-23, the factor GRA in the numerator actually enhances the OSNR of the system. Figure 4-7 shows the variation of Raman gain with pump power.

Figure 4-7Figure 4-7 Variation of Raman Gain with Pump Power

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020