Lecture 5 Fiber Optical Communication Lecture 5, Slide 1

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1 Lecture 5 Bit error rate The Q value Receiver sensitivity Sensitivity degradation Extinction ratio RIN Timing jitter Chirp Forward error correction Fiber Optical Communication Lecture 5, Slide 1

2 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 and lower current levels p 1 (I) Probability density functions due to noise The decision threshold I D The dashed area indicates errors p 0 (I) Fiber Optical Communication Lecture 5, Slide

3 Agrawal defines: BER calculation p(1) is the probability to send a one P(0 1) is the probability to detect a sent out one as a zero 1 p(1) p(0) 1/ P(0 1) P(1 0) BER p(1) P(0 1) p(0) P(1 0) Assume that the noise has Gaussian statistics I 1 (I 0 ) is the upper (lower) current level σ 1 (σ 0 ) is the standard deviation of the upper (lower) level I D 1 ( I I 1) 1 I 1 I D P(0 1) exp di erfc P(1 0) ( I I0) exp 0 di I erfc 1 1 D 0 0 x I D erfc( x ) exp( y ) dy I 0 The erfc function Fiber Optical Communication Lecture 5, Slide 3

4 These expressions give us the BER BER calculation BER 1 4 erfc I 1 I 1 D erfc I D 0 I 0 BER using assumptions I 0 = 0, σ 1 = σ 0 BER depends on I D Note: In general σ 1 and σ 0 are not equal Example: Shot noise depends on the current σ 1 > σ 0 since I 1 > I 0 Fiber Optical Communication Lecture 5, Slide 4

5 Optimal decision threshold Minimize the BER using d(ber)/di D = 0 Optimal value is the intersection of the PDF for the one and zero levels Exact expression is given in the book Choosing I D according to expression below is a good approximation ( I I ) / ( I I ) Q D D / 1 I D 0I1 0 1I 1 0 Notice the definition of Q Often used as a measure of signal quality Thermal case: σ 1 = σ 0 and I D = (I 1 + I 0 )/ When shot noise cannot be neglected, I D shifts towards the zero level Fiber Optical Communication Lecture 5, Slide 5

6 The Q value The Q value is a measure of the eye opening since I1 I0 Q The optimum BER is related to the Q value as BER 1 erfc If currents and noise levels are known, the BER can be found from Q 1 0 Q exp( Q / ) Q Q is often defined in db scale as Q ( in db) 0log10Q Example: BER = 10-9 corresponds to Q = 6 or 15.6 db Fiber Optical Communication Lecture 5, Slide 6

7 Minimum average received power (4.6.) 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 Q where the shot noise is and the thermal noise is The receiver sensitivity is then I I1 R P R P P R d P d rec 1 rec 1/ 1 0 ( s T ) T s 1 d rec ( P1 P0 ) / P1 qr d (P ) f rec (4k T / R ) F f B L T n / P rec Q R d qqf T Fiber Optical Communication Lecture 5, Slide 7

8 Minimum average received power When thermal noise dominates in a p i n receiver, we have ( Prec ) pin Q / R T d f This corresponds to SNR / Example: Q = 6, R d = 1 A/W, σ T = 0.1 μa P rec = 0.6 μw, SNR = 144 = 1.6 db I Q When shot noise dominates in a p i n receiver, we have ( P ) ( qf / Rd Q f rec ideal ) This corresponds to SNR I / 1 Example: Q = 6 SNR = 36 = 15.6 db 1 Q Fiber Optical Communication Lecture 5, Slide 8

9 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 15 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 receiver under test PRBS detector transmitted sequence decided sequence XOR gate error counter Fiber Optical Communication Lecture 5, Slide 9

10 Sensitivity degradation 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 Fiber Optical Communication Lecture 5, Slide 10

11 Extinction ratio (4.7.1) The extinction ratio (ER) is defined as r ex = P 0 /P 1 P 0 (P 1 ) is the emitted power in the off (on) state Ideally, r ex = 0 Different for direct and external modulation We use that The average received power is P rec = (P 1 + P 0 )/ The definition of the Q-parameter is Q = (I 1 I 0 )/(σ 1 + σ 0 ) We find the sensitivity degradation to be 1 r Q 1 r ex ex Rd Prec 1 0 Fiber Optical Communication Lecture 5, Slide 11

12 Extinction ratio (ER), power penalty If thermal noise dominates, then σ 1 = σ 0 = σ T, and the sensitivity is The power penalty is (in db) Prec ( rex ) ex log10 Prec (0) Laser biased below threshold r ex < 0.05 ( 13 db) δ ex < 0.4 db For a laser biased above threshold r ex > 0. δ ex > 1.5 db rec ( r The penalty is independent of Q and BER The penalty for APD receivers is larger than for p i n receivers P ex 1 r ) 1 r ex ex TQ Rd 10log r 1 r ex ex Fiber Optical Communication Lecture 5, Slide 1

13 Intensity noise (RIN) (4.7.) Intensity noise in LEDs and semiconductor lasers add to the thermal and shot noise Approximately, this is included by writing s T I where 1/ I Rd Pin Rd Pinr r 1 I RIN( I )d (The RIN spectrum was discussed earlier) The parameter r I is the inverse SNR of the transmitter Assuming zero extinction ratio and using that 1/ s ( 4qR d Prec f ) I ri Rd P we can now write the Q-value as Q R P d rec 1/ ( s T I ) T rec Fiber Optical Communication Lecture 5, Slide 13

14 Intensity noise (RIN), power penalty (4.7.3) The receiver sensitivity is found to be The power penalty is P rec Q T Q qf ( ri ) R (1 r Q ) d I I 10log P ( r ) / P (0) 10log (1 r ) 10 rec I rec 10 I Q BER Note that δ I when r I 1/Q The receiver cannot operate at the specified BER A BER floor BER Floors P rec Fiber Optical Communication Lecture 5, Slide 14

15 Real sensitivities are Receiver performance (4.8) 0 db above the quantum limit for APDs 5 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 Fiber Optical Communication Lecture 5, Slide 15

16 Loss-limited lightwave systems (5..1) The maximum (unamplified) propagation distance is 10 P Lkm log f db/km P P rec is receiver sensitivity rec P tr is transmitter average power α f is the net loss of the fiber, splices, and connectors P rec and L are bit rate dependent Table shows wavelengths with corresponding quantum limits and typical losses tr Loss-limited transmission Transmitted power = 1 mw λ = 850 nm, L max = km λ = 1.55 µm, L max = km Fiber Optical Communication Lecture 5, Slide 16

17 Dispersion-limited lightwave systems (5..) 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 BL c n 1 10(Mbit/s) km λ = 850 nm, multimode GI-fiber Modal dispersion dominates Disp.-limited for B > 100 Mbit/s BL c n (Gbit/s) km 1 Fiber Optical Communication Lecture 5, Slide 17

18 Dispersion-limited lightwave systems λ = 1.3 µm, SM-fiber, MM-laser Material dispersion dominates Disp.-limited for B > 1 Gbit/s Using D σ λ = ps/nm 4 D 15(Gbit/s) km BL 1 λ = 1.55 µm, SM-fiber, SM-laser B Material dispersion dominates Using D = 16 ps/(nm km) Disp.-limited for B > 5 Gbit/s L Gbit/s km λ = 1.55 µm, DS-fiber, SM-laser Material dispersion dominates Using D = 1.6 ps/(nm km) Disp.-limited for B > 15 Gbit/s B L Gbit/s km 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 Fiber Optical Communication Lecture 5, Slide 18

19 System design (5..3) 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 (P tr ) and the average power required at the receiver (P rec ) are often specified P [dbm] tr P [dbm] rec [db] [db] C L M s C [db] L [db/km] f L [db] con [db] splice C L is the total channel loss (sum of fiber, connector, and splice losses) M s is the system margin (allowing penalties and degradation over time) Typically M s = 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 Fiber Optical Communication Lecture 5, Slide 19

20 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 Fiber Optical Communication Lecture 5, Slide 0

21 VPItransmissionMaker Output will contain eye diagrams, spectra, BER etc. Fiber Optical Communication Lecture 5, Slide 1

22 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 Fiber Optical Communication Lecture 5, Slide

23 Power penalties in multi-mode fiber Modal 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 BLDσ λ < 0.1 Fiber Optical Communication Lecture 5, Slide 3

24 Power penalty due to pulse broadening (5.4.4) 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 0 10log A d 10 10log10 0 A L Assuming β 3 C 0 and a large source spectral width, we have 0 1 LD 0 d 5log 1 LD 10 / 0 Fiber Optical Communication Lecture 5, Slide 4

25 Power penalty due to pulse broadening Assuming β 3 C 0 and a small source spectral width, we have d 5log 10 L 1 0 Agrawal introduces the duty cycle A measure of the pulse width Defined as d c = 4 σ 0 /T B The penalty depends on Dispersion parameter Fiber length Bit rate Pulse width (duty cycle) Fiber Optical Communication Lecture 5, Slide 5

26 Eye-closure penalty (5.4.6) The eye is often used to monitor the signal quality The eye-closure penalty is eyeopening after transmission eye 10log10 eyeopening before transmission This definition is ambiguous since eye opening is not well defined NRZ CSRZ NRZ-DPSK RZ-DPSK 0 km eye opening 63 km Fiber Optical Communication Lecture 5, Slide 6

27 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(55, 39) is often used (gives 7% overhead) Coding gain is hereg c Q c is Q value when using FEC 0log10( Q / Q) Coding gain of 5 6 db is obtained with modest redundancy c Fiber Optical Communication Lecture 5, Slide 7

28 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, 5 channels, 40 Gbit/s per channel FEC increases system reach considerably Fiber Optical Communication Lecture 5, Slide 8

29 Lecture Multichannel systems Wavelength division multiplexing WDM components Linear crosstalk Nonlinear crosstalk Spectral efficiency Time division multiplexing Fiber Optical Communication Lecture 5, Slide 9

30 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 Fiber Optical Communication Lecture 5, Slide 30

31 Multichannel approaches Frequency 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 Fiber Optical Communication Lecture 5, Slide 31

32 WDM systems (6.1) WDM system = a single fiber + N transmitters + N receivers + mux/demux WDM systems are commercial since 1995 Spectral efficiency η s = B/Δν ch, today typically η s < 0.5 (bit/s)/hz Standard D(dense)WDM grid spacing (Δν ch ) are 00, 100, 50 and 5 GHz System limitations include Amplifier gain uniformity and laser wavelength stability Fiber nonlinearities and other interchannel crosstalk Residual dispersion Fiber Optical Communication Lecture 5, Slide 3

33 WDM components (6.) 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 Fiber Optical Communication Lecture 5, Slide 33

34 Tunable optical filters (6..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 Fiber Optical Communication Lecture 5, Slide 34

35 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 Fiber Optical Communication Lecture 5, Slide 35

36 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, n g the group index Signal bandwidth must be smaller than Δν L The finesse, F, is defined as L c /( ng L) F L / FP The filter bandwidth is denoted by Δν FP The center wavelength is typically adjusted with a piezoelectric actuator Fiber Optical Communication Lecture 5, Slide 36

37 Multiplexers and demultiplexers (6..) 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 figure in two different implementation alternatives A filter-based (de)multiplexer typically uses 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 Fiber Optical Communication Lecture 5, Slide 37

38 Add-drop multiplexers and filters (6..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 launch into 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 A replacement channel can be input in port 3 Output WDM channel appears in port 4 Fiber Optical Communication Lecture 5, Slide 38

39 WDM components ( ) 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 arms A WDM transmitter can be integrated Figure shows a 10 channel system OPM = optical power monitor EAM = electroabsorption modulators VOA = variable optical attenuator Fiber Optical Communication Lecture 5, Slide 39

40 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 Fiber Optical Communication Lecture 5, Slide 40

41 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 T mn is the filter transmission of channel n when channel m is selected The corresponding photocurrent is I x is the crosstalk contribution I x has different values depending on the data in the interfering channels Worst case appears when all interfering channels transmit one simultaneously I R m P m N nm R T n mn P P n P I m ch N nm I T mn P filter transfer function x n Fiber Optical Communication Lecture 5, Slide 41

42 Heterowavelength linear crosstalk The power penalty can be estimated from the eye closure caused by I x To maintain the eye opening, the signal must be increased by I x The power penalty is In db units we get X X I I ch ch I X Ich I X I X 1 I X 0 Ich Ich 10log1 N nm RnTmnP R P m m n P n and P m 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 X N 10log1 T 10log(1 X ) nm mn Only depends on the filter Fiber Optical Communication Lecture 5, Slide 4

43 Homowavelength linear crosstalk (6.3.) 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 reconfiguration is possible etc An optical cross connect is reconfigurable Fiber Optical Communication Lecture 5, Slide 43

44 Homowavelength linear crosstalk In an (N + 1) (N + 1) router there are N interfering terms (A n ) 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 = P n /P m E m N ( t) Em En exp( imt) N nm nm I( t) RP ( t) R P ( t) P ( t) cos ( t) ( t) m m X 10log10(1 r X Q n ) r X P / P0 X ( N 1) m n Fiber Optical Communication Lecture 5, Slide 44

45 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 η s = B/Δν ch Done using multi-level modulation formats and polarization multiplexing But how large can η s 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 C f (1 log SNR) Provided that the SNR is high, η s can be >> 1 (bit/s)/hz Example: SNR = 40 db, Δf = 10 GHz C = 133 Gbit/s with Δν ch = 50 GHz, η s =.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 Fiber Optical Communication Lecture 5, Slide 45

46 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) Fiber Optical Communication Lecture 5, Slide 46

47 OTDM channel multiplexing (6.4.) Several different approaches All requires a clock signal at sub-channel bit rate Figures show possible implementations: Cascaded LiNbO 3 modulators V 0 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 Fiber Optical Communication Lecture 5, Slide 47

48 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 Fiber Optical Communication Lecture 5, Slide 48