Signal to Noise Ration (SNR) is not an unknown terminology for Engineers and Tech professionals who are dealing with Digital or Analog form of Communication.Here we will explore the aspect of SNR in Optical Fiber Communication space known as Optical Signal to Noise Ratio(OSNR).
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Some handy definition of OSNR to pick :
 OSNR [dB] is the measure of the ratio of signal power to noise power in an optical channel .
 OSNR is the short form of Optical Signal to Noise Ratio. It is key parameter to estimate performance of Optical Networks. It helps in BER calculation of Optical System.
 OSNR is important because it suggests a degree of impairment when the optical signal is carried by an optical transmission system that includes optical amplifiers.
 If we know the OSNR and the bandwidths, we can find Q and the BER
 It can be seen as the QoS at the physical layer of optical networks. OSNR is directly related to biterror rate, which will lead to packet losses seen by higher layers.
 OSNR indirectly reflects BER and can provide a warning of potential BER deterioration.
 OSNR has long been recognised as a key performance indicator for amplified highspeed transmission networks to ensure network performance and reliability and it is related to many design parameter such as number or repeater/amplifiers ,reach ,available modulation formats etc.
Now let's explore it in more detail:
Optical signaltonoise ratio (OSNR) is used to quantify the degree of optical noise interference on optical signals. It is the ratio of service signal power to noise power within a valid bandwidth.When the signal is amplified by the optical amplifier (OA), like EDFA, its optical signal to noise ratio (OSNR) is reduced, and this is the primary reason to have limited number of OAs in a network.
The OSNR values that matter the most are at the receiver, because a low OSNR value means that the receiver will probably not detect or recover the signal. The OSNR limit is one of the key parameters that determine how far a wavelength can travel prior to regeneration.
OSNR serves as a benchmark indicator for the assessment of performance of optical transmission systems. DWDM networks need to operate above their OSNR limit to ensure error – free operation. There exists a direct relationship between OSNR and bit error rate (BER), where BER is the ultimate value to measure the quality of a transmission.
The value of OSNR_{out} that is needed to meet the required system BER depends on many factors such as the bit rate, whether and what type of FEC is employed, the magnitude of any crosstalk or nonlinear penalties in the DWDM line segments, etc.Below picture highlights OSNR as one of the important parameter in a DWDM link.
Optical amplifiers such as erbiumdoped fiber amplifiers (EDFAs) are normally employed in optical networks to compensate for the transmission losses over long distances. However, besides providing optical gain, EDFAs also add unwanted amplified spontaneous emission (ASE) noise into the optical signal. Furthermore, the cascading of EDFAs results in accumulation of ASE noise. ASE noise is typically quantified by OSNR and is one of the most important parameters to be monitored in optical networks since the BER is directly related to the signal OSNR Furthermore, it also plays a pivotal role in fault diagnosis and as a measure of general health of links in an optical network.
OSNR may change due to signal power changes or higher repeater noise levels due to aging.
Now lets read the Legacy method to measure it:
The traditional method to measure OSNR is defined in the IEC 6128029 standard and is known as the interpolation or outofband method, as shown in Figure1 below
OSNR for a PointtoPoint Link
NF_{stage} 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).
OSNR =158.9+ Pin.dBm −NF−10log(Br )
where OSNRdB = optical signal to noise ratio of the optical amplifier, dB
Pin.dBm = average amplifier input signal power (DWDM systems use singlechannel power), dBm
NF = amplifier noise figure, dB
h = Planck's constant 6.626069 ◊ 10−34, Js
f = signal center frequency, Hz
Br = optical measurement bandwidth RBW, Hz
If the measurement optical bandwidth can be assumed to be 0.1 nm (12.48 GHz),
OSNR = 58 + Pin.dBm − NF
OSNRF.dB =158.9+Psource.dBm −Γ−NF−10log(Br)−10logN
where OSNRF.dB = final OSNR seen at the receiver, dB
Psource.dBm = average source signal power into the first span
(DWDM systems use singlechannel power), dBm NF = amplifier noise figure, the same for all EDFAs, dB Br = optical measurement bandwidth, Hz
N = number of amplifiers in the fiber link excluding the booster
Γ = span loss, the same for all spans, dB
Above equation 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.
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).
Now see what bliss Raman Amplifier can do here:
Addition of Raman and OSNR change:
As we can see from above equation the factor G_{RA }in the numerator actually enhances the OSNR of the system.(stages) could be considered as EDFA hops here.
OSNRbased design essentially means whether the OSNR at the final stage (at the receiver) is in conformity with the OSNR that is desired to achieve the required BER. This also guarantees the BER requirement that is essential for generating revenue.
This method works well for networks up to 10G, without any Reconfigurable Optical AddDrop Multiplexers (ROADM).
But traditional way of measurement don’t work anymore in High Speed Communications:
However, IEC 6128029 isn’t feasible for 100G+ signals as well as ROADM networks.
Figure 2 illustrates 100G channels spaced 50GHz apart, which is a common spacing in modern submarine (and terrestrial) networks. PolarizationMultiplexed (PolMux) 100G+ signals are typically wider (require more optical spectrum) than legacy OnOffKeyed (OOK) 10G signals, meaning they could overlap with neighboring channels. Accordingly, the midpoint between channels no longer consists only of noise, but rather of signal plus noise. Thus, the IEC method applied to 100G+ PolMux signals will therefore lead to an overestimation of noise and inaccurate measurement date leading to incorrect decisions.
Figure 2: IEC 6128029 Method Fails with Dense PolMux 100G+ signals
Figure 3 illustrates a 100G signal that has gone through a ROADM, with the green area showing the channel bandwidth. Given filters inside a ROADM, the noise at the midpoint between channels will be carved (or filtered), leading to an underestimation of the noise level, if the IEC 6128029 method is used, meaning this method is not feasible in ROADMenabled coherent submarine networks.
Figure 3: IEC 6128029 Method Fails in ROADM 100G+ PolMux Networks
To address the issues described in Figures 2 and 3, inband OSNR was introduced around 2009 to support OSNR measurements of 10G signals in ROADM networks and 40G OOK signals. However, this method can’t be applied to coherent, PolMux 100G+ signals, because of technical reasons beyond the scope of this blog. Consequently, PolMux OSNR techniques have been introduced to support 100G+ signals, which is the topic of the latest standards.
Appropriate standards for PolMux OSNR measurements?
There are two standards providing relevant guidelines for OSNR measurements of PolMux signals. They are the China Communications Standards Association (CCSA) YD/T 21472010 standard and the IEC 6128212 standards, which was recently introduced in February 2016. Both standards provide a futureproof definition of OSNR, which can be applied to any type of signal, at any data rate, including superchannels and flexiblegrid signals. Specifically, the IEC6128212 standard specifies that:
where:
 s(λ) is the timeaveraged signal spectral power density, not including ASE, expressed in W/nm
 ρ(λ) is the ASE spectral power density, independent of polarization, expressed in W/nm
 Br is the reference bandwidth expressed in nm (usually 0.1nm if not otherwise stated)
 and the integration range in nm from λ1to λ2is chosen to include the total signal spectrum

The only drawback of these two standards is that a careful application of their formulae requires turning off channels, to access the Amplified Spontaneous Emission (ASE) noise floor, which isn’t possible on an inservice lest we upset endusers! Fortunately, inservice PolMux OSNR methods have been introduced.
below table summarizes the correct OSNR method for each type of signal.
Data Rate

ROADM Present?

OSNR Method

Works on inservice network?

≤10G signals

No

IEC 6128029

Yes

≤10G signals

Yes

Inband OSNR

Yes

Noncoherent 40G signals

Yes or No

Inband OSNR

Yes

Coherent 100G+ signals

Yes or No

PolMux OSNR (IEC and CCSA standards)

No

Coherent 100G+ Signals

Yes or No

InService PolMux OSNR

Yes

Table 1: OSNR Measurement Methods for Various Signal Types
Using the wrong OSNR measurement method for a given signal can have a significant impact on results, as it can lead to errors ranging from a few dBs up to 10dB, potentially leading to future outages. Using the proper method guarantees the right OSNR measurements are achieved leading to accurate network modeling, link simulation, and maintenance of ongoing submarine cable network performance.
Summarizing the importance of OSNR and its proper measurement method?
Some of the benefits of OSNR testing, including avoiding network outages, optimizing troubleshooting times, and ensuring optimal terrestrial and submarine cable performance. OSNR will become even more critical at data rates beyond 100G, because of the more stringent OSNR thresholds that will be required. Several OSNR methods have been introduced over the years, so the key takeaway is that the right OSNR measurement method must be used on a specific signal type to get accurate results.
Introduction to OSNR for high speed communication
The OSNR is the signaltonoise ratio (SNR) measured in a reference optical bandwidth, where frequently a bandwidth Bref of 12.5 GHz is used corresponding to 0.1 nm wavelength. The OSNR relates to the Es ∕N0 and Eb ∕N0 as
where Bref is the previously introduced reference bandwidth, RS corresponds to the symbol rate of the transmission, r is the aforementioned rate of the code with r = k∕n, and qcorresponds to the number of bits mapped to each modulation symbol.
The use of highorder modulation formats requires a higher optical signaltonoise ratio (OSNR), which may result in a significantly reduced achievable transmission distance .Following diagram shows the OSNR estimation stage for High Speed Optical Communication.
Lets talk about OSNR Penalty now:
OSNR penalty is obtained from the BER curves and determined at a particular BER. A value of the OSNR penalty is obtained by comparing the values of OSNR before and after the change of the parameters, which are under test, as given by
Gripple = penalty due to DWDM amplifier gain ripples
OSNRpenalties = various transmission penalties due to CD, PMD, PDL, etc. (note these penalties maybe different for 100G vs. 400G)
Calculation of QFactor 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 Qfactor.
The logarithmic value of Q (in dB) is related to the OSNR
In the equation, B_{0} is the optical bandwidth of the end device (photodetector) and B_{c} is the electrical bandwidth of the receiver filter.
Q is somewhat proportional to the OSNR
BER FORMULAS FOR THE MOST COMMON QAM SYSTEMS
Gray coding is assumed for all formats. For PMBPSK the exact formula is:
For PMQPSK the exact formula is:
For PM16QAM and PM64QAM, respectively, the following formulas are approx imate, but their accuracy is better than ±0.05 dB of OSNRNL over the range
10−1– 10−4:
EDFA Noise – Why Input Power Matters
Optical signal suffers more than only attenuation. In amplitude, spectrally, temporally signal interaction with light matter, light light, lightmatterlight leads to other signal disturbances
such as :
 Power reduction
 Dispersion
 Polarization
 Unbalanced amplification
Thus leading to random noise, which causes misalignments, jitter and other disturbances resulting in erroneous bits, the rate of which is known as biterrorrate
Because of all possible influences outlined bits transmitted by source and bits arriving at the receiver may not have the same value. In actuality a threshold value is set at the receiver, above the threshold refers to a logic “one” and below threshold refers to a logic “zero”.
In order to measure BER in photonic regime, the optical signal is converted to electrical signal.
Example: Assuming a confidence level of 99%, BER threshold set at 1010 and a bit rate of 2.5 Gb/s the required number n is 6.64 x 1010
Given the OSNR, the empirical formula to calculate BER for single fiber is
Log10 (BER) = 10.71.45 (OSNR)
In an experimental environment where factors such as loss, dispersion, and nonlinear effects are excluded, if the OSNR is less than the specified threshold, the preFEC BER will be excessively large and uncorrectable bit errors will be generated. The OSNR threshold in this case is called B2B OSNR tolerance.
Some mathematical aspects of OSNR:
Calculating OSNR:
As can be seen from the definitions above, two quantities must be known to compute OSNR: the Total Signal Power, and the amount of ASE Noise Power present in a 0.1nm bandwidth.
Measuring the ASE power:
When the ASE noise floor is clearly visible left and right of the optical signal, the ASE Noise Power at the signal wavelength can be interpolated from two measurements made left and right of the signal.
Alternately, when the noise floor is not visible left and right, the optical signal needs to be removed temporarily in order to allow the measurement of the ASE Noise Power at the signal wavelength.
▪ This is the case when some filtering devices implemented somewhere in line are removing some of the noise between channels (Example = WSS).
▪ This could also be the case if the modulated signal bandwidth is so large so that the tail of adjacent signals overlaps the open space between them – masking the noise floor.
Note that power values are frequently provided in dBm by the OSA  whether the measurements is made using integrated power function or a userspecified resolution bandwidth. To convert the values in dBm to mW, the following relation must be used:
Measuring the Total Signal Power:
When making this measurement it is important to use a bandwidth that is large enough to capture the entire signal:
▪ If using an OSA with variable resolution bandwidth, this means that the resolution bandwidth has to be set larger than the width of the signal.
▪ If using a integrated power function between vertical markers, the markers have to be set to include the entire signal bandwidth.
Note that when measuring a DWDM spectrum, the power of each DWDM signal cannot be measured independent of ASE noise present in the measurement bandwidth.
Ie., the value that is actually measured is: Total Signal Power + ASE Noise Power.
To get the Total Signal Power only, the ASE noise content (measured separately in the previous step) must be subtracted from the measurement. Since the measurement bandwidth used to measure the noise on its own (ASE BW) may be different from the bandwidth used to measure the signal (Signal BW), a factor is added to the equation. This removes the correct amount of noise from the measurement.
where:
Signal BW is the bandwidth used to measured the signal,
ASE BW is the bandwidth used to measure the ASE Noise Power only (e.g., 0.1nm).
Calculating OSNR from measurements:
Since OSNR must be reported as signal power with respect to 0.1nm worth of ASE noise, the denominator of the OSNR equation also includes a factor. This adjusts the amount of ASE noise measured to an amount expected inside a 0.1nm bandwidth:
Thus
In a transmission chain, the relative evolution of the optical signal and noise levels is usually characterized by the optical signaltonoise ratio (OSNR). The OSNR, in a given optical bandwidth, is defined as
The optical signal may be polarized, but the noise is usually not and, depending on the receiver polarization sensitivity, the noise must be considered with a single or two polarizations. Any active (or passive) linear optical device amplifies (or attenuates) simultaneously the incoming signal and the incoming noise
Accordingly with the fluctuation dissipation theorem, it also adds noise, making its output OSNR lower than its input one. This OSNR degradation is expressed in terms of noise factor (NF) defined as:
where G is the optical power gain (or the attenuation coefficient) of the device which is larger (or smaller) than 1. NF is denoted noise figure when it is expressed in dB. Because the relative importance of the added noise strongly depends on the input noise level, NF is only an intrinsic parameter of the optical device (i.e. independent of the input signal and noise) when an input reference noise is defined.
For polarization insensitive devices, input noise and output noise usually do depend on polarization, making noise figure independent of polarization considerations.
Single amplifier noise factor
OSNR at the output of an optical amplifier with an output power Pout and for an optical bandwidth B0 is expressed as:
where m=1 or 2 is the number of polarization modes contributing to noise. It is usual to consider the two polarization modes (m=2) of the noise and to make reference to an optical bandwidth equal to 0.1 nm corresponding to Bo = 12.5GHz at a wavelength of 1550 nm. In this particular situation, the OSNR is expressed in dB as:
Noise factor of a cascade of fibers and amplifiers
Let us consider now the cascade of spans displayed in Figure 3.8 and including NAMP11 optical fiber spans with an attenuation coefficient A5expð2αALÞ and NAMP lumped linear phase insensitive amplifiers with a gain net G and a noise factor NF. For each span a near compensation of the signal attenuation by the gain is assumed, making its net gain GSPAN 5 GA close to 1. Each fiber reduces the sig nal level and reduces the noise level nearly in the same way. Since the input noise level is far above the appropriated reference level, the attenuation noise of the fiber is negligible and the OSNR is kept nearly unchanged. Each amplifier output POUT restores the input noise of the link but adds the amplifier noise.
The accumulated noise is Namp times larger than single amplifier and we have:
To bridge transoceanic distances while keeping a high OSNR (optical SNR), it is crucial to limit the noise contribution added by the successive amplifiers. The impact of the added noise on the output OSNR can be calculated with:
This equation can also be expressed in a more physical manner:
where N is the amplifier count, and Δλ the width of the filter where the OSNR is expressed. The number “30” at the end of Equation corresponds to the conversion of signal input power from units in watts into units scaled in milliwatts.
Note: Now try to utilise the above concepts and equations whatever way you want .