Lecture 8 Fiber Optical Communication Lecture 8, Slide 1

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1 Lecture 8 Bit error rate The Q value Receiver sensitivity Sensitivity degradation Extinction ratio RIN Timing jitter Chirp Forward error correction Fiber Optical Communication Lecture 8, Slide

2 Bit error rate (4.6.) 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 < 0 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 (I) Probability density functions due to noise The decision threshold I D The dashed area indicates errors p 0 (I) Fiber Optical Communication Lecture 8, Slide

3 Agrawal defines: BER calculation p() is the probability to send a one P(0 ) is the probability to detect a sent out one as a zero p() p(0) / P(0 ) P( 0) BER p() P(0 ) p(0) P( 0) Assume that the noise has Gaussian statistics I (I 0 ) is the upper (lower) current level σ (σ 0 ) is the standard deviation of the upper (lower) level I D ( I I ) I I D P(0 ) exp di erfc P( 0) ( I I0) exp 0 di I erfc D 0 0 x I D erfc( x ) exp( y ) dy I 0 The erfc function Fiber Optical Communication Lecture 8, Slide 3

4 These expressions give us the BER BER calculation BER 4 erfc I I D erfc I D 0 I 0 BER using assumptions I 0 = 0, σ = σ 0 BER depends on I D Note: In general σ and σ 0 are not equal Example: Shot noise depends on the current σ > σ 0 since I > I 0 Fiber Optical Communication Lecture 8, 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 0 0 D / I D 0I 0 I 0 Notice the definition of Q Often used as a measure of signal quality Thermal case: σ = σ 0 and I D = (I + I 0 )/ When shot noise cannot be neglected, I D shifts towards the zero level Fiber Optical Communication Lecture 8, Slide 5

6 The Q value The Q value is a measure of the eye opening since I I0 Q The optimum BER is related to the Q value as BER erfc If currents and noise levels are known, the BER can be found from Q 0 Q exp( Q / ) Q Q is often defined in db scale as Q ( in db) 0log0Q Example: BER = 0-9 corresponds to Q = 6 or 5.6 db Fiber Optical Communication Lecture 8, 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 receiver uses an APD, the p i n case is obtained by setting M = F A = The average current for a one is where the average received power is The Q value is Q where the shot noise is I I MR P MR P P rec MR P d rec / 0 ( s T ) s d ( P P0 ) / P qm F R (P ) f A d rec T d rec / and the thermal noise is The receiver sensitivity is then P rec T (4k T / R ) F f Q R d B qf A L Qf n T M Fiber Optical Communication Lecture 8, 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 / 4 Example: Q = 6, R d = A/W, σ T = 0. μa P rec = 0.6 μw, SNR = 44 =.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 / Example: Q = 6 SNR = 36 = 5.6 db Q Fiber Optical Communication Lecture 8, Slide 8

9 Optimum sensitivity in APD receivers In a receiver dominated by thermal noise, an APD will increase the SNR There is an optimum gain, given by The corresponding sensitivity is / / T T k A ka Qqf k Qq f A M opt ( Prec ) APD (qf / Rd ) Q ( kamopt k Note: P rec Δf and not Δf as for thermally limited receivers For InGaAs APDs, the sensitivity is typically improved over a p i n diode receiver by 6 8 db A ) / Fiber Optical Communication Lecture 8, Slide 9

10 Quantum limit of photo detection (4.6.3) At very low power levels, the noise statistics are no longer Gaussian Denote the average number of photons per one bit by N p The probability of generating m electron-hole pairs is then given by the Poisson distribution m P exp( N ) N / m! Assume: No thermal noise, P 0 = 0, threshold is at one detected photon For BER < 0 9, we must have N p > 0 photons per one bit This corresponds to a power in a one of P = N p hνb and an average received power P rec = N p hνb/ Example: B = 0 Gbit/s, N p =0 P rec = 3 nw at λ = 550 nm m p P(0 ) P( 0) p( m 0) 0) exp( ) BER p N p Poisson distribution with N p = 5 Fiber Optical Communication Lecture 8, Slide 0

11 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 5 The BER is measured as a function of received average optical power Sensitivity = average power corresponding to a given BER (often 0 9 ) PRBS generator laser optical attenuator receiver under test PRBS detector transmitted sequence decided sequence XOR gate error counter Fiber Optical Communication Lecture 8, Slide

12 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 8, Slide

13 Extinction ratio (4.7.) The extinction ratio (ER) is defined as r ex = P 0 /P P 0 (P ) 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 + P 0 )/ The definition of the Q-parameter is Q = (I I 0 )/(σ + σ 0 ) We find the sensitivity degradation to be r Q r ex ex Rd Prec 0 Fiber Optical Communication Lecture 8, Slide 3

14 Extinction ratio (ER), power penalty If thermal noise dominates, then σ = σ 0 = σ T, and the sensitivity is The power penalty is (in db) Prec ( rex ) ex log0 Prec (0) Laser biased below threshold r ex < 0.05 ( 3 db) δ ex < 0.4 db For a laser biased above threshold r ex > 0. δ ex >.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 r ) r ex ex TQ Rd 0log 0 0 r r ex ex Fiber Optical Communication Lecture 8, Slide 4

15 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 / I Rd Pin Rd Pinr r 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 / s ( 4qR d Prec f ) I ri Rd P we can now write the Q-value as Q R P d rec / ( s T I ) T rec Fiber Optical Communication Lecture 8, Slide 5

16 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 ( r Q ) d I I 0log P ( r ) / P (0) 0log ( r ) 0 rec I rec 0 I Q BER Note that δ I when r I /Q The receiver cannot operate at the specified BER A BER floor BER Floors P rec Fiber Optical Communication Lecture 8, Slide 6

17 The recovered clock is based on the received, noisy signal The decision time fluctuates and causes timing jitter The data is not sampled at the bit slot center Leads to additional fluctuations of the signal entering the decision circuit In a thermally limited p i n receiver, we have Δi j is the current fluctuation σ j is the corresponding RMS value The penalty depends on the pulse shape, but for a typical case P rec( b) b / j 0log 0 0log0 Prec (0) ( b / ) b Q b = (4π /3 8)(Bτ j ) τ j is the RMS value of Δt Timing jitter Q I i j / ( T j ) / real decision times T 0 time optimal decision times Fiber Optical Communication Lecture 8, Slide 7

18 Timing jitter, power penalty The power penalty depends on Q (BER) The penalty will be higher at a lower BER Rule-of-thumb: The RMS value of the timing jitter should typically be smaller than 5 0% of the bit slot to avoid significant penalty Fiber Optical Communication Lecture 8, Slide 8

19 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 8, Slide 9

20 Loss-limited lightwave systems (5..) The maximum (unamplified) propagation distance is 0 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 = mw λ = 850 nm, L max = 0 30 km λ =.55 µm, L max = km Fiber Optical Communication Lecture 8, Slide 0

21 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 0(Mbit/s) km λ = 850 nm, multimode GI-fiber Modal dispersion dominates Disp.-limited for B > 00 Mbit/s BL c n (Gbit/s) km Fiber Optical Communication Lecture 8, Slide

22 Dispersion-limited lightwave systems λ =.3 µm, SM-fiber, MM-laser Material dispersion dominates Disp.-limited for B > Gbit/s Using D σ λ = ps/nm 4 D 5(Gbit/s) km BL λ =.55 µm, SM-fiber, SM-laser B Material dispersion dominates Using D = 6 ps/(nm km) Disp.-limited for B > 5 Gbit/s L Gbit/s km λ =.55 µm, DS-fiber, SM-laser Material dispersion dominates Using D =.6 ps/(nm km) Disp.-limited for B > 5 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 8, Slide

23 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 8, Slide 3

24 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 8, Slide 4

25 VPItransmissionMaker Output will contain eye diagrams, spectra, BER etc. Fiber Optical Communication Lecture 8, Slide 5

26 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 8, Slide 6

27 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. Fiber Optical Communication Lecture 8, Slide 7

28 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 0log A d 0 0log0 0 A L Assuming β 3 C 0 and a large source spectral width, we have 0 LD 0 d 5log LD 0 / 0 Fiber Optical Communication Lecture 8, Slide 8

29 Power penalty due to pulse broadening Assuming β 3 C 0 and a small source spectral width, we have d 5log 0 L 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 8, Slide 9

30 Power penalty due to chirp (5.4.5) Frequency chirping increases the impact of dispersion Occurs in directly modulated lasers Cannot modulate the amplitude without changing the phase Figure shows driving current, output power and wavelength of a directly modulated laser t c ps = chirp duration Δλ c = spectral shift associated with the chirp Exact impact is complicated Assume pulse is Gaussian with linear chirp Fiber Optical Communication Lecture 8, Slide 30

31 Power penalty due to chirp For chirped Gaussian pulses with β 3 0, we have c C L 0 5log0 L 0 A chirp-free pulse (C = 0) has negligible penalty when β B L < 0.05 Lasers have C = 4 to 8 giving δ c 4 6 db when β B L = 0.05 A negative penalty occurs if β C < 0 due to initial pulse compression Fiber Optical Communication Lecture 8, Slide 3

32 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 0log0 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 8, Slide 3

33 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 0log0( Q / Q) Coding gain of 5 6 db is obtained with modest redundancy c Fiber Optical Communication Lecture 8, Slide 33

34 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 8, Slide 34