a definition of fiber optics - ttu.ee 5 - 2016.pdf · fiber optical communication lecture 5, slide...

Fiber Optical Communication Lecture 5, Slide 1

Lecture 5

• Bit error rate

– The Q value

• Receiver sensitivity

• Sensitivity degradation

– Extinction ratio

– RIN

– Timing jitter

– Chirp

• Forward error correction


Bit error rate (4.6.1)• The bit error rate (BER) is the probability that a bit is incorrectly

identified by the receiver (due to the noise and other signal distortion)

– A better name would be bit error probability

– A traditional requirement for optical receivers is BER < 10–9

• The receiver sensitivity is the minimum averaged received optical power required to achieve the target BER

• Figure shows:

– A signal affected by noise

– The PDFs for the upper andlower current levels

– The decision threshold ID

– The dashed area indicateserrors

p1(I)

p0(I)

Probability density

functions due to

noise


BER calculation• Agrawal defines:

– p(1) is the probability to send a ”one”

– P(0|1) is the probability to detect a sent out ”one” as a ”zero”

• Assume that the noise has Gaussian statistics

– I1 (I0) is the upper (lower) current level

– σ1 (σ0) is the standard deviation of the upper (lower) level

)0|1()1|0(2/1)0()1( )0|1()0()1|0()1(BER21 PPppPpPp

2erfc

2

1

2

)(exp

2

1)1|0(

1

1

2

1

2

1

1

D

III

dIII

PD

2erfc

2

1

2

)(exp

2

1)0|1(

0

0

2

0

2

0

0

IIdI

IIP D

ID

x

dyyx )exp(2

)(erfc 2

The erfc function


BER calculationThese expressions give us the BER

• BER depends on ID

• Note: In general σ1 and σ0

are not equal

• Example: Shot noise depends on the current ⇒ σ1 > σ0 since I1 > I0

2erfc

2erfc

4

1BER

0

0

1

1

IIII DD

BER using assumptionsI0 = 0, σ1 = σ0


Optimal decision threshold• Minimize the BER using d(BER)/dID = 0

– Optimal value is the intersection of the PDF for the “one” and “zero” levels

• Exact expression is given in the book

• Choosing ID according to expression below is a good approximation

• Notice the definition of Q

– Often used as a measure of signal quality

• Thermal case: σ1 = σ0 and ID = (I1 + I0)/2

• When shot noise cannot be neglected, ID shifts towards the ”zero” level

QIIII DD 1100 /)(/)( 10

0110

IIID


• The Q value is a measure of the eye opening since

• The optimum BER is related to the Q value as

– If currents and noise levels are known, the BER can be found from Q

• Q is often defined in dB scale as

– Example: BER = 10-9 corresponds to Q = 6 or 15.6 dB

The Q value

01

01

IIQ

2

)2/exp(

2erfc

2

1BER

2

Q

QQ

QQ 10

2 log20)dBin (


• Consider the following case:

– NRZ data in which “zero” bits contain no optical power, neglect dark current

The average current for a “one” is

where the average received power is

• The Q value is

where the shot noise is

and the thermal noise is

• The receiver sensitivity is then

Minimum average received power (4.6.2)

rec11 2 PRPRI dd

2/2/)( 101rec PPPP

TTs

d PRIQ

2/122

rec

01

1

)(

2

fPqRds )2(2 rec

2

fFRTk nLBT )/4(2

T

d

fqQR

QP rec


Minimum average received power• When thermal noise dominates in a p–i–n receiver, we have

– This corresponds to

– Example: Q = 6, Rd = 1 A/W, σT = 0.1 μA ⇒Prec = 0.6 μW, SNR = 144 = 21.6 dB

• When shot noise dominates in a p–i–n receiver, we have

– This corresponds to

– Example: Q = 6 ⇒ SNR = 36 = 15.6 dB

22

1

2

1 4/SNR QI

22

1

2

1 /SNR QI

fRQP dT /)( pinrec

fQRfqP d 2

idealrec )/()(


Receiver characterization• Receivers are experimentally studied using a long pseudorandom

binary sequence (PRBS)

– Random data is hard to generate

– Random data is not periodic

– Typical length 215–1

• The BER is measured as a function of received average optical power

– Sensitivity = average power corresponding to a given BER (often 10–9)

PRBS generator

laser

optical attenuator

PRBS detector

decided sequence

transmitted sequence

XOR gate

receiver under test

error counter


• So far, we have discussed an ideal situation

– Perfect pulses corrupted only by (inevitable) noise

• In reality, the receiver sensitivity is degraded

– There are additional sources of signal distortion

• The corresponding necessary increase in average received power to achieve a certain BER is called the power penalty

• Also without propagation in a fiber, a power penalty can arise

• Examples of degrading phenomena include:

– Limited modulator extinction ratio

– Transmitter intensity noise

– Timing jitter

Sensitivity degradation


Extinction ratio (4.7.1)

• The extinction ratio (ER) is defined as rex = P0/P1

– P0 (P1) is the emitted power in the off (on) state

– Ideally, rex = 0

• Different for direct and external modulation

• We use that

– The average received power is Prec = (P1 + P0)/2

– The definition of the Q-parameter is Q = (I1 – I0)/(σ1 + σ0)

• We find the sensitivity degradation to be

01

2

1

1

recd

ex

ex PR

r

rQ


Extinction ratio (ER), power penalty• If thermal noise dominates, then σ1 = σ0 = σT, and the sensitivity is

• The power penalty is (in dB)

• Laser biased below threshold rex < 0.05 (–13 dB) ⇒ δex < 0.4 dB

• For a laser biased above threshold rex > 0.2 ⇒ δex > 1.5 dB

• The penalty is independent of Q and BER

• The penalty for APD receivers is larger than for p–i–n receivers

d

T

ex

exexrec

R

Q

r

rrP

1

1)(

ex

ex

rec

exrecex

r

r

P

rP

1

1log10

)0(

)(log10 1010


Intensity noise (RIN) (4.7.2)• Intensity noise in LEDs and semiconductor lasers add to the thermal and

shot noise

• Approximately, this is included by writing

where

• (The RIN spectrum was discussed earlier)

• The parameter rI is the inverse SNR of the transmitter

• Assuming zero extinction ratio and using that

we can now write the Q-value as

2222

ITs

IddI rPRPR in

2/12

in

drI )(RIN2

12

2/1

rec )4( fPqRds rec2 PRr dII

TITs

d PRQ

2/1222

rec

)(

2


Intensity noise (RIN), power penalty (4.7.3)• The receiver sensitivity is found to be

• The power penalty is

• Note that δI → ∞ when rI → 1/Q

– The receiver cannot operate at the specified BER

• A BER floor

)1()(

22

2

recQrR

fqQQrP

Id

TI

)1(log10)0(/)(log10 22

10recrec10 QrPrP III

BER Floors

Prec

BER


Receiver performance (4.8)• Real sensitivities are

– ≈ 20 dB above the quantum limit for APDs

– ≈ 25 dB above the quantum limit for p–i–n diodes

– Mainly due to thermal noise

• Figure shows

– Measured sensitivities for p–i–n diodes (circles) and APDs (triangles)

– Lines show the quantum limit

• Two techniques to improve this

– Coherent detection

– Optical pre-amplification

– Both can reach sensitivities of only 5 dB above the quantum limit


Loss-limited lightwave systems (5.2.1)• The maximum (unamplified)

propagation distance is

– Prec is receiver sensitivity

– Ptr is transmitter average power

– αf is the net loss of the fiber, splices, and connectors

• Prec and L are bit rate dependent

• Table shows wavelengths with corresponding quantum limits and typical losses

• Loss-limited transmission

– Transmitted power = 1 mW

• λ = 850 nm, Lmax = 10–30 km

• λ = 1.55 µm, Lmax= 200–300 km

rec

trlogdB/km

10km

P

PL

f


Dispersion-limited lightwave systems (5.2.2)• Occurs when pulse broadening is

more important than loss

• The dispersion-limited distance depends on for example

– The operating wavelength

• Since D is a function of λ

– The type of fiber

• Multi-mode: step-index or graded-index

• Single-mode: standard or dispersion-shifted

– Type of laser

• Longitudinal multimode

• Longitudinal singlemode

– large or small chirp

• λ = 850 nm, multimode SI-fiber

– Modal dispersion dominates

– Disp.-limited for B > 0.3 Mbit/s

• λ = 850 nm, multimode GI-fiber

– Modal dispersion dominates

– Disp.-limited for B > 100 Mbit/s

kmMbit/s)(102 1 ncBL

kmGbit/s)(22 2

1 ncBL


• Long systems often use in-line amplifiers

– Loss is not a critical limitation

– Dispersion must be compensated for

– Noise and nonlinearities are important

– PMD can be a problem

Dispersion-limited lightwave systems• λ = 1.3 µm, SM-fiber, MM-laser

– Material dispersion dominates

– Disp.-limited for B > 1 Gbit/s

– Using |D| σλ = 2 ps/nm

• λ = 1.55 µm, SM-fiber, SM-laser


– Using |D| = 16 ps/(nm×km)


• λ = 1.55 µm, DS-fiber, SM-laser


– Using |D| = 1.6 ps/(nm×km)


kmGbit/s)(12541 DBL

kmGbit/s04001612

2

2 LB

kmGbit/s400001612

2

2 LB


• Part of the system design is to make sure the BER demand can be met

– The power budget is a very useful tool

– The transmitter average power (Ptr) and the average power required at the receiver (Prec) are often specified

– CL is the total channel loss (sum of fiber, connector, and splice losses)

– Ms is the system margin (allowing penalties and degradation over time)

• Typically Ms = 6–8 dB

• A complete system is very complex and some of the parameters that must be considered are

– Modulation format, detection scheme, operating wavelength

– Transmitter and receiver implementation, type of fiber

– The trade-off between cost and performance

– The system reliability

System design (5.2.3)

[dB][dB][dBm]

rec

[dBm]

tr sL MCPP [dB]

splice

[dB]

con

[dB/km][dB] LC fL


Computer design tools• To evaluate a complete system design, simulations are used

– VPItransmissionMaker™ is a commercial code for doing this

• Accurate modeling for many components but closed source = black box


VPItransmissionMaker™• Output will contain eye diagrams, spectra, BER etc.


Further sources of power penalty (5.4)• The above mentioned power penalties were all due to the transmitter

and the receiver

• Several more sources of power penalty appear during propagation

– Modal noise (in multi-mode fibers)

– Mode-partition noise (in multi-mode lasers)

– Intersymbol interference (ISI) due to pulse broadening

– Frequency chirp

– Reflection feedback

• All these involve dispersion


Power penalties in multi-mode fiberModal noise

• Different modes interfere over the fiber cross-section

– Forms a time-varying ”speckle” intensity pattern

– The received power will fluctuate

• Problem occurs with highly coherent sources

• To avoid this

– Use a single-mode fiber

– Reduce coherence

• Use a LED

Mode-partition noise

• The power in each longitudinal mode of a multimode laser varies with time

– Output power is constant

• Different modes propagate at different velocities in a fiber

– Additional signal fluctuation is caused and the SNR is degraded

• Negligible penalty if BLDσλ < 0.1


• Broadening affects the receiver in two ways

– Energy spreads beyond the bit slot ⇒ ISI

– Pulse peak power is reduced for a given average received power

• Reduces the SNR

• Power penalty for Gaussian pulses assuming no ISI is

• Assuming β3 ≈ C ≈ 0 and a large source spectral width, we have

Power penalty due to pulse broadening (5.4.4)

010

2

10 log100

log10

LA

Ad

2

00

1

LD 2

010 /1log5 LDd


Power penalty due to pulse broadening• Assuming β3 ≈ C ≈ 0 and a small source spectral width, we have

• Agrawal introduces the duty cycle

– A measure of the pulse width

– Defined as dc = 4 σ0/TB

• The penalty depends on

– Dispersion parameter

– Fiber length

– Bit rate

– Pulse width (duty cycle)

2

2

0

210

21log5

Ld


Eye-closure penalty (5.4.6)• The eye is often used to monitor the signal quality

• The eye-closure penalty is

– This definition is ambiguous since ”eye opening” is not well defined

ion transmissbefore opening eye

smissionafter tran opening eyelog10 10eye

NRZ CSRZ NRZ-DPSK RZ-DPSK

0 km

263 km

eye opening


Forward error correction (FEC) (5.5)• FEC can correct errors and reduce the BER

• Redundant data is introduced

– Decreases the effective bit rate...

• With given throughput, the bit rate increases

– ...but BER is typically decreased by this operation

• Increases system complexity since encoders/decoders are needed

• Optical systems use simple FEC

– Symbol rate is very high, real-time processing is very difficult

– Reed-Solomon, RS(255, 239) is often used (gives 7% overhead)

• Coding gain is here

– Qc is Q value when using FEC

– Coding gain of 5–6 dB is obtained with modest redundancy

)/(log20 10 QQG cc


Optimum FEC• The coding gain saturates with increasing redundancy

– There is an optimal redundancy depending on system parameters

• Figure shows simulated Q values before and after FEC decoding

– WDM system, 25 channels, 40 Gbit/s per channel

– FEC increases system reach considerably


Lecture

• Multichannel systems

– Wavelength division multiplexing

• WDM components

• Linear crosstalk

• Nonlinear crosstalk

– Spectral efficiency

– Time division multiplexing


Fiber bandwidth• The bandwidth of fibers is

huge

– Potential bit rate is >> 1 Tbit/s

• In practice, electronics, dispersion, etc. is a bottle neck

– Limits the OOK bit rate to 40 Gbit/s

Simultaneous transmission of many channels offers the simplest way to make better use of the available bandwidth


Multichannel approachesFrequency Division Multiplexing (FDM)

• Optical FDM [Wavelength DM (WDM)]

– Multiple optical carriers are modulated with independent bit streams

– The optical data is combined optically into the same fiber

– 100’s of channels can be transmitted this way

• Electrical FDM [subcarrier multiplexing (SCM)]

– Modulating different microwave sub-carriers which are combined to modulate a single optical carrier

Time Division Multiplexing (TDM)

• Optical TDM (OTDM)

– Several signals with identical bit-rate are combined on the same carrier

– Only for RZ formats, not yet commercial

• Electrical TDM (ETDM)

– Channels are combined before modulating a single optical carrier


WDM systems (6.1)• WDM system = a single fiber + N transmitters + N receivers + mux/demux

• WDM systems are commercial since 1995

• Spectral efficiency ηs = B/Δνch, today typically ηs < 0.5 (bit/s)/Hz

– Standard D(dense)WDM grid spacing (Δνch) are 200, 100, 50 and 25 GHz

• System limitations include

– Amplifier gain uniformity and laser wavelength stability

– Fiber nonlinearities and other interchannel crosstalk

– Residual dispersion


WDM components (6.2)• Implementing a WDM system requires several optical components

– Multiplexers

• Combine the individual WDM channels

– Demultiplexers

• Separate the WDM channels

– Star couplers

• Combine signals from multiple origins and sends to multiple destinations

– Tunable optical filters

• Used to filter out a specific channel

– Wavelength-tunable transmitters

– Add-drop multiplexers/optical routers

• Used in the transmission path to switch channels to correct destinations

• Often the term reconfigurable optical add-drop multiplexer (ROADM) is seen


Tunable optical filters (6.2.1)• A tunable optical filter is used to select one WDM channel while blocking

all other channels

– Is a band-pass filter, typically with transmission in multiple bands

– Has adjustable center wavelength

– Is based on diffraction or interference

• Desirable properties include

– A wide tuning range, allowing processing of many WDM channels

– Negligible crosstalk, close to zero out-of-band transmission

– Fast tuning speed, allowing quick system re-configuration

– Small insertion loss, avoiding need for extra amplification

– Polarization insensitivity, since the signal polarization varies

– Robustness against disturbances like vibrations

– Low price


Types of tunable optical filters• There are several types of filters

– A Fabry-Perot filter (a) is a cavity between mirrors

• Length is adjustable

• Transmission at longitudinal modes

– A Mach-Zehnder filter (b) is an interferometer

• Uses cascaded Mach-Zehnder interferometers

• Phase shift is wavelength-dependent

– A grating-based Filter (c) uses Bragg gratings

• Reflection is wavelength-dependent

• Often uses an optical circulator

– An acousto-optic filter (d) forms the grating from acoustic waves

• Photoelastic effect ⇒ refractive index is changed

• Set up dynamically


The Fabry-Perot filter • Typically, several wavelengths can pass an optical band-pass filter

• The Fabry-Perot filter is a good example

– Transmission of all longitudinal modes of the cavity

– The frequency spacing is known as the free spectral range, given by

• L is cavity length, ng the group index

• Signal bandwidth must be smaller than ΔνL

– The finesse, F, is defined as

• The filter bandwidth is denoted by ΔνFP

• The center wavelength is typically adjusted with a piezoelectric actuator

)2/( Lnc gL

FP/ LF


Multiplexers and demultiplexers (6.2.2)• A multiplexer with reversed propagation direction is a demultiplexer

• (De)multiplexing can be done in several different ways

– A grating-based (de)multiplexer is shown in figurein two different implementation alternatives

– A filter-based (de)multiplexer typicallyuses MZ filters

– Fiber Bragg gratings can be used to make a all-fiber (de)multiplexer

– An arrayed waveguide grating (de)multiplexer is seen in lower figure

• Waveguides have different lengths

• Phase shifts are wavelength dependent

• Different channels focus to different outputs

– In a coherent receiver, the channel is selected by tuning the local oscillator frequency


Add-drop multiplexers and filters (6.2.3)• During transmission it may be necessary to modify the data content

• An add-drop multiplexer (a) will in principle

– Demultiplex the incoming signal

– Modify individual channels by passing through, dropping, or adding

– Multiplex individual channels and launchinto transmission fiber

• The principle for an add-drop filter is explained by (b)

– WDM signal is input in port 1

– The channel in the grating stop band is reflected and output in port 2

– A replacement channel can be input in port 3

– Output WDM channel appears in port 4


WDM components (6.2.4–6.2.6)• A star-coupler combines input signals and divides among the outputs

– Are not wavelength-selective

– Can be used for broadcasting

• Example: Distribution of television to multiple areas

• A wavelength router will redistribute the channels of multiple incoming WDM signals to multiple output fibers

– Different wavelength ⇒ different receiver

– A common design is the waveguide-grating router (WGR)

• Like a MZI, but with more than 2 arms

• A WDM transmitter can be integrated

– Figure shows a 10 channel system

– OPM = optical power monitor

– EAM = electroabsorption modulators

– VOA = variable optical attenuator


Crosstalk in WDM systems

• WDM channels should not interfere with each other during transmission

– The most important design issue is interchannel crosstalk

– Loosely speaking this means power transfer between channels

• Crosstalk occurs due to

– Non-ideal demultiplexing/filtering/routing components (linear crosstalk)

– Nonlinear effects in optical fibers or devices (nonlinear crosstalk)

• Any crosstalk degrades the BER and causes crosstalk-induced penalty

• Linear crosstalk is classified as either out-of-band or in-band crosstalk

– Out-of-band crosstalk means that power ”leaks” from neighboring channels

– In-band crosstalk means that the crosstalk is at the same wavelength

• Occurs in routing/networks

• Adds coherently to the signal


Heterowavelength linear crosstalk (6.3.1)• Assume we use

– Direct detection using a photodetector

– An optical bandpass filter for channel selection

• The optical power entering channel m (of a total N) is

– Tmn is the filter transmission of channel n when channel m is selected

• The corresponding photocurrent is

– Ix is the crosstalk contribution

– Ix has different values depending on the data in the interfering channels

– Worst case appears when all interfering channels transmit “one” simultaneously

filter transfer function

N

mn

nmnm PTPP

xch

N

mn

nmnnmm IIPTRPRI


Heterowavelength linear crosstalk• The power penalty can be estimated from the eye closure caused by Ix

– To maintain the eye opening, the signal must be increased by Ix

• The power penalty is

• In dB units we get

– Pn and Pm correspond to values for ’one’ bits representing worst case

• If all channels have the same power and if the responsivity is constant within the wavelength range we have

• Only depends on the filter

chch

ch

ch

ch 10 I

I

I

II

II

II XX

X

XX

N

mn mm

nmnnX

PR

PTR1log10

)1log(101log10 XTN

mn

mnX


Homowavelength linear crosstalk (6.3.2)• Crosstalk is within the bandwidth of the channel

• Caused by non-ideal WDM components used to route/switch signals for example wavelength routers or optical cross connects

– A wavelength router is static and no reconfigurationis possible

– An optical cross connectis reconfigurable

etc


Homowavelength linear crosstalk• In an (N + 1)×(N + 1) router there are N interfering terms (An)

– The field entering the receiver is

• We have signal-crosstalk beating interference

– Compare with ASE beat noise from EDFAs

• All phases are random ⇒ Acts as intensity noise

• The penalty is

– with X = Pn/Pm

)exp()( tiEEtE m

N

mn

nmm

N

mn

nmnmm tttPtPRtRPtI )()(cos)()(2)()(

)1(log10 22

10 QrXX )1(/ 2

0

22 NXPPrX


Spectral efficiency and the capacity• The throughput is the number of successfully transmitted bits/second

– This is often called “capacity” in the fiber-optic world

• Currently, throughput is increased by increasing the spectral efficiency

– Remember: For a WDM system, the spectral efficiency is ηs = B/Δνch

– Done using multi-level modulation formats and polarization multiplexing

– But how large can ηs be? Larger than 1 (bit/s)/Hz?

• The channel capacity is given by Shannon’s famous formula

– Δf is the bandwidth

– C is the capacity

• Provided that the SNR is high, ηs can be >> 1 (bit/s)/Hz

– Example: SNR = 40 dB, Δf = 10 GHz ⇒ C = 133 Gbit/swith Δνch = 50 GHz, ηs = 2.7 (bit/s)/Hz

• Wireless systems can have spectral efficiencies as high as 10 (bit/s)/Hz

– In optical communication this is not easily achieved

)SNR1(log2 fC


OTDM channel multiplexing (6.4.1)• OTDM means optical time-division multiplexing

– OTDM is a technique to eliminate the ”electronic bottleneck”

• ”Sub-channels with lower bit rate are interleaved in time

• Enables higher bit rates > 40 Gbit/s

• Total bit rate per channel is B × N

• Can be combined with WDM

• Characteristics:

– Only ”low-speed” electronics required in each “sub-channel”

– Needs RZ format

– Needs precise delay control

– Pulse source requirements:

• Short pulses

• Small timing jitter

• High extinction ratio (> 30 dB)


OTDM channel multiplexing (6.4.2)• Several different approaches

– All requires a clock signal at ”sub-channel” bit rate

• Figures show possible implementations:

– Cascaded LiNbO3 modulators

• V0 is required for π phase shift

• Modulators reject other ”sub-channels”

– Nonlinear optical loop mirror

• Normally reflects, based on XPM

• Made transparent by clock signal

– FWM in nonlinear medium

• Often uses highly nonlinear fiber (HNLF)

• Signal is shifted in frequency

• ”Sub-channel” is filtered out


Subcarrier multiplexing (6.5)• Subcarrier multiplexing (SCM) = electrical microwave signals encoded

with data are combined to modulate a single optical carrier

– Possible to combine SCM and WDM

– Figure shows 4 WDM channels, each with 5 SCM channels

• The modulation can be analog or digital (or a combination)

– Analog format is often used for video distribution

a definition of fiber optics - ttu.ee 5 - 2016.pdf · fiber optical communication lecture 5, slide...

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