Optical Communications. and Optical Networks

Transcription

1 Optical Communications 128 Gbit/s DP-QPSK (Coherent) Balanced Receiver by Fujitsu ( nm) and Optical Networks Demodulation and Detection Professor Syvridis Dimitris 10 Gbit/s PIN-TIA Fiber Coupled Receiver by WTD, for NRZ applications ( nm)

2 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 2

3 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 3

4 Introduction Modulation/Demodulation in Optical Communications Description of the process of modulation of digital/pulsed signals demodulation of digital/pulsed signals Modulation: the process of converting an electrical signal into the optical domain in order to be transmitted through the optical fiber Most common and simple modulation format: On Off Keying (OOK) A bit 1 is encoded by the presence of a light pulse in the bit interval or by turning a light source (laser or LED) on A bit 0 is encoded (ideally) by the absence of a light pulse in the bit interval or by turning a light source off Demodulation: the process of converting an optical signal into the electrical domain and extracting the data that were transmitted Due to the several types of noise added to the signal along propagation and reception, the decision about the transmitted bits are subject to errors Bit Error Rate (BER) formulas will be extracted taking into account all the noise distortions 4

5 Modulation Types of Modulation, Pulse Forms for OOK (1/2) An optical source can be modulated either directly switching on and off the source or externally using a modulator in front of the source External modulation: less chirp (transient, adiabatic), preferred for increased rates and larger distances Can be used pulsed signals and analog-type waveforms (e.g OFDM) Common forms of pulses for OOK Non-Return-to-Zero (NRZ): the pulse for bit 1 occupies the entire bit interval, no pulse appears during bit 0 Return-to-Zero (RZ): the most significant part of the pulse duration for bit 1 occupies only a fraction of the bit interval, no pulse appears during bit 0 Binary Data NRZ pulses RZ pulses t t 5

6 Modulation Types of Modulation, Pulse Forms for OOK (2/2) OOK with NRZ pulses Usually found in telecommunication systems with rates up to 10 Gbit/s Narrower optical bandwidth than OOK with RZ pulses A long stream of successive 1 or 0 makes bit clock acquisition difficult due to absence of transitions OOK with RZ pulses Variations: 33%, 50%, 67% of the bit duration occupied by the pulse with power over the half of its maximum Usually found in telecommunication systems with very high bit rates Minimization of the impact of chromatic dispersion compared to NRZ pulses A long stream of aces (but not zeros) keeps producing transitions Higher peak power required to maintain the same energy per bit than NRZ p[ulses Binary Data NRZ pulses RZ pulses t t 6

7 Demodulation (1/3) The modulated signals propagate through the optical fiber and are subject to the attenuation and the impact of dispersion are subject to the impact of non-linear effects noise is added by the optical amplifiers along transmission At the receiver, an acceptable BER value is required for optical communications systems at high data rates Between 10 9 and 10 15, for uncoded signals Between 10 4 and 10 3 before decoding when coding is applied, depending on the coding scheme that is used, after decoding BER 10 9 is achieved The extraction of data at the receiver include some steps The optical signal is converted into an electrical current by the photodetector The electrical current is weak and is amplified in the electrical domain The filtering follows Clock Recovery or Timing Recovery is required to sample the signal at proper instants Finally, the decision circuit defines if a bit 0 or 1 was transmitted 7

8 Demodulation (2/3) Block diagram with the different functionalities included in a optical receiver Photodetector Front-End Amplifier Receive Filter Sampler The amplified electrical current is filtered in order to minimize the noise outside the bandwidth occupied by the signal Clock/Timing Recovery The filter is also designed to suitably shape the received pulses to minimize BER Decision Circuit It can include additional functionality, like the minimization of the Inter-Symbol Interference (ISI) due to pulse broadening. Such a filter is called equalizer and it equalizes/cancels the distortion the signal has suffered 8

9 Demodulation (3/3) Block diagram with the different functionalities included in a optical receiver Photodetector Front-End Amplifier Receive Filter Sampler The signal must be sampled at the proper instants, in order to decide if the transmitted bit was either 1 or 0 Clock/Timing Recovery The bit boundaries at the receiver must be recovered in order the signal to be sampled at the proper instants Decision Circuit A waveform that is periodic with period equal to the bit interval is called a clock. This function is termed clock recovery, or timing recovery 9

10 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 10

11 A Practical Direct Detection Receiver (1/10) The optical signal is initially converted into an electrical current Noise components that are additive noise electrical currents distort the signal Thermal Noise Current. It appears due to the random motion of electrons at the input resistance of every electrical amplifying circuit that follows the photodetector. Always present in finite temperature values Shot Noise Current. It appears due to the random distribution of electrons that are generated during detection even when the input intensity is constant. Contrary to the thermal noise, shot noise current is not added on the produced signal photocurrent. It is inherent in the signal itself and is a convenient representation of the variance of the produced photocurrent as a separate noise component. It appears due to the appearance of the signal itself Dark Noise Current. It appears in the photodiode and is induced by thermal effects Electrical Amplifier Noise Current. It appears in the internal of the amplifying unit that follows the photodetector Amplified Spontaneous Emission. It appears due to the optical amplifier(s) that may be used along the link Crosstalk from adjacent channels in WDM transmission 11

12 A Practical Direct Detection Receiver (2/10) Case: we consider a PIN photodiode followed by an electrical amplifier In the cases of our interest, the noise waveforms can be considered statistically independent and Gaussian distributed with zero mean values Due to independency and zero mean values, the electrical power levels can be added Shot noise: two components must be discriminated, quantum and shot noise Quantum noise. It appears when the light signal becomes extremely weak so as its quantum nature becomes apparent, where discrete photons arrive to the receiver. For higher signal levels, the photon arrivals become so frequent that the variations are smoothed/mitigated. The quantum noise can be simulated by a random stream of equal amplitude incoming pulses Shot noise. It is the waveform of the quantum noise as formed after the optical receiver with finite bandwidth The two terms are usually used erroneously without any discrimination which is wrong. The term shot noise expresses the inherent quantum noise of the optical signal itself, after its smoothing due to passing through the devices of finite bandwidth, like the photodetector and the circuitry (of the electrical amplifier) that follows For low signal's power, the shot noise has not significant impact, when the signal s power starts increasing, the impact of this noise component starts becoming significant 12

13 A Practical Direct Detection Receiver Thermal Noise (3/10) The thermal noise current on a resistance R at temperature T (in Kelvin values) can be modeled as a Gaussian random process with zero mean value and autocorrelation function (4k B T/R) δ(τ), where δ(τ) is the delta function (Dirac pulse) The term k B is the Boltzmann constant with value J/K From the Fourier transform of the auto-correlation function, it is clear that the noise is white, and in a bandwidth B e, the thermal noise variance is 2 2 4kBT 1 Ithermal σthermal B e, with Be R 2πRC The electrical bandwidth of the receiver, B e, usually lies between 1/(2Τ bit ) και 1/Τ bit, whereτ bit is the bit duration for OOK signals is limited by the RC value of the input circuit of the amplifier C includes both the parasitic capacity of the device (photodiode s capacitance and other parasitic capacitances) and the amplifier input capacitance The desire is the minimization of C, the photodetector and the frontal part of the amplifier must be as close as possible, even in the same package From the noise variance and B e, the requirements of R are contradictory 13

14 A Practical Direct Detection Receiver Shot Noise (4/10) The photons arrivals can be modeled with accuracy by a Poisson random process The photocurrent can be modeled as a flow of electrical charge impulses, and each impulse is generated when a photon arrives at the receiver For the power levels usually encountered in optical communication systems, the instant value of the photocurrent can be modeled as I I i s Ī is a constant current, Ī = P, where = ηq/(hf c ) is the responsivity of the detector, P is the optical power level that is converted into the current Ī by the photodetector q is the elementary charge ( Cb), h = J sec is the Planck constant, η is the quantum efficiency of the photodetector i s is a Gaussian random process with mean zero value and auto-correlation function 2qĪδ(t) for PIN photodiodes The shot noise current is white noise and in an electrical bandwidth B e its variance is i I σ 2qIB s shot shot e 14

15 A Practical Direct Detection Receiver Shot Noise (5/10) Depiction of the shot noise Impulses of Poisson statistics Time Time Time Smoothed impulses due to the limited response of the photodiode and the electrical amplifier s circuit combination Resultant noise waveform (from the smoothed impulses) Mean value (useful signal) It can be proved that as the power level of the filtered Poisson process increases, the confusion between the pulses converts the initial Poisson process of the impulses into a Gaussian process 15

16 A Practical Direct Detection Receiver Combined Impact of The Thermal and the Shot Noise (6/10) If the load resistance of the photodetector is R L, the entire electrical current on this resistance can be written as i t will have zero mean and variance k T i I σ B The thermal and shot noise currents are considered to be independent, and for the bandwidth of the receiver, B e, the entire current that concerns the noise exclusively can be modeled as Gaussian random process with zero mean value and variance I I i i B t thermal thermal e RL σ σ σ shot thermal Both the shot and thermal noise variances are proportional to the bandwidth B e, a tradeoff appears between the bandwidth of a receiver and its noise performance s t i s will have zero mean and variance i I σ 2qIB s shot shot e 16

17 A Practical Direct Detection Receiver (7/10) For the power levels encountered in optical communications, the thermal and shot noise components are usually sufficient to describe the impact of the additive noise in the receiver But, in general, in the direct detection receiver with PIN photodiode 4 noise components appear the thermal noise current (i t ) the shot noise current (i s ) the dark noise current (i dk ) the noise generated in the transistor of the electrical amplifier (i ampl ) P Photodetector i dk Ī i s Elec. Amplifier Α i ampl i t Optical signal and electrical currents at the receiver Electrical equivalent at the input of a noiseless electrical amplifier Ī i s i dk + i t Α iampl 17

18 A Practical Direct Detection Receiver Electrical Amplifier Noise (8/10) The amplifier noise component is generated in the electrical amplifier It is treated like a noise component that is the input of a noiseless amplifier At the input of the noiseless amplifier an equivalent theoretic source of Gaussian noise is considered, so as at the output of the noiseless amplifier the noise is equal to that of the real amplifier The manufacturers usually give either the current i ampl or directly the variance (σ αmpl ) 2 i σ 2qi B 2 2 ampl ampl ampl e According to another approach, the impact of the electrical amplifier noise is incorporated in the thermal noise Components within the amplifier, like the transistor, contribute to the thermal noise This contribution is indicated by the amplifier s Noise Figure (F n ) F n is the ratio of the electrical SNR at the input of the amplifier (SNR i ) to the electrical SNR at the output of the amplifier (SNR o ), F n = SNR i /SNR o Typical values of F n,db lie between 3 and 5 db When F n is provided by the manufacturer, there is no need to calculate (σ αmpl ) 2 18

19 A Practical Direct Detection Receiver Electrical Amplifier Noise, Dark Noise (9/10) When F n is provided, the thermal noise includes the components contributed by the photodiode, its load resistance and the electrical amplifier The modified thermal noise current will have zero current and variance σ k T F B 2 4 B thermal n e RL A useful manipulation of the thermal noise variance is the following (F n = 1 when the electrical amplifier s noise is omitted) 4k T 1 σ F B, B σ 8πk TCF B 2 B 2 2 thermal n e e thermal B n e RL 2πRLC Dark noise variance Dark noise is a photocurrent that is present under the absence of optical signal The photodiode manufacturers give i dk in the datasheet i σ 2qi B 2 2 dk dark dk e 19

20 A Practical Direct Detection Receiver Electrical SNR (10/10) Suppose that the mean current level for bit 0 is I 0 and the standard deviation of noise isσ 0, whereas the mean current level for bit 1 is I 1 and the standard deviation of noise isσ 1 The electrical Signal-to-Noise Ratio (SNR el. ) of the electrical power levels at the input of the amplifier can be estimated if at the numerator the square of the mean current is set with I mean = ( I 1 + I 0 )/2 = (ηq/(hf c )) P mean at the denominator the summation of all the noise component variances is set In the shot noise component, I mean will be used SN R el. I 2 mean shot thermal σdark σampl σ σ BE CAREFUL!!! The optical SNR will be estimated as a ratio, where the numerator corresponds to the mean optical power the denominator corresponds to the optical noise power The ratio concerns normalized power levels with reference to 1Ω, i.e. the values are in Α 2 20

21 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 21

22 Dominant Noise Component the Thermal Noise Treatment Usually, the dominant noise component at the receiver is the thermal noise in the input of the electrical amplifier The dark current is considered insignificant The noise of the electrical amplifier is considered insignificant There are three ways to overcome the confinements imposed by the thermal noise and are based on the amplification of the signal before it leaves the photodetector and enters the electrical circuits that follow Usage of APD photodiode Usage of an optical amplifier before the photodetector (Optical Preamplifier) Application of Coherent Detection with a high-power (compared to the signal s power) local oscillator which is a laser, so as the thermal noise to become much less powerful than the useful mixing result of the product of the local oscillator and the incoming optical signal Usually, the coherent systems are not combined with APD photodiodes 22

23 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 23

24 Noise in an APD Photodiode (1/3) The process of the avalanche gain in an APDs has the effect of increasing the noise current at its output This increased noise contribution arises from the random nature of the avalanche multiplicative gain G m (t) This noise contribution is modeled as an increase in the shot noise component at the output of the photodetector (against the thermal noise) Defining the responsivity of the APD as APD the average avalanche multiplication gain by G m The average photocurrent becomes APD m I P G P The shot noise current at the APD output has variance i σ 2qG F G PB sh shot m A m e The quantity F A (G m ) is called the Excess Noise Factor of the APD and is an increasing function of the gain G m 24

25 Noise in an APD Photodiode (2/3) The quantity F A (G m ) is called the Excess Noise Factor of the APD and is an increasing function of the gain G m by F G k G 1 k 21 G A m A m A m The quantity k A is called Ionization Coefficient Ratio and is a property of the semiconductor material used to make up the APD Its values lies between 0 and 1 F A (G m ) is an increasing function of k A (for large values of G m ) It is desirable to keep k A small k A for silicon (which is used at 0.8 μm) is much smaller than 1 k A for InGaAs (which is used at 1.3 and 1.55 μm wavelength) it is 0.7 For G m = 1, F A (1) = 1 which results in the variance of the shot noise of a receiver with a PIN photodiode i σ 2qG F G PB 2qPB sh shot m A m e e 25

26 ATTENTION TO AVOID ANY MISINTERPRETATION!!! The three types of photodiodes made by semiconductors PN photodiode (contact) Photodiode PIN with the addition of an intrinsic semiconductor in the previous structure of the PN contact Avalanche photodiode APD The last two type are the practical photodiode types installed in real optical systems 26

27 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 27

28 Optical Preamplifier (1/6) It has been mentioned that the performance of simple direct detection receivers is limited primarily by thermal noise generated inside the receiver The performance can be improved significantly by using an optical (pre)amplifier before the receiver The amplifier provides gain G to the input signal Consider an optical preamplifier system, used in front of a standard pin direct detection receiver The photodetector produces a current that is proportional to the incident power P: received optical power : photodiode s responsivity P G Optical Amplifier I Photodetector... GP It is noted that now the optical amplifier is included in the receiver, as well, even in the case where a small optical fiber cable may lie between the optical amplifier and the receiver 28

29 Optical Preamplifier (2/6) Unfortunately, the spontaneous emission present in the amplifier appears as noise at its output Amplified Spontaneous (ASE) noise power at the output of the amplifier for each polarization mode n sp : a constant called the spontaneous emission factor B o : the optical bandwidth n sp depends on the level of population inversion within the amplifier With complete inversion n sp = 1, around 2 5 for most amplifiers Two fundamental polarization modes are present in a single-mode fiber. The total noise power at the output of the amplifier is 2 P N Notes The electrical bandwidth (B e ) is in the baseband The optical bandwidth (B o ) concerns a slice of spectrum around a central frequency in the THz range THz or around a central wavelength of thousands of nm (e.g nm) P n hf G1 B N sp c o 29

30 Optical Preamplifier (3/6) The optical power is proportional to the square of the electric field The noise field beats against the signal giving rise to the noise component known as the signal-spontaneous beat noise against itself, giving rise to noise components known as the spontaneous-spontaneous beat noise Shot noise and thermal noise components are also present Simplified approach Before the conversion into the electrical domain, the power of the summation of the field of the amplified optical signal and the noise field will beat on the photodiode It concerns the useful amplified signal (G P) 2 E t n t E t n t E t n t sig ampl sig ampl sig ampl 2 2 E t E t n t E t n t n t sig sig ampl sig ampl ampl It concerns the signal spontaneous beat noise It concerns the spontaneous spontaneous beat noise 30

31 Optical Preamplifier (4/6) Variances of the several noise components at the receiver For the BER values of our interest (10 15 up to 10 9 ), these noise processes can be modeled sufficiently as Gaussian processes Initial target: encounter the thermal noise 2 4kBT σthermal Be For reasonably large RL amplifier gain (> 10 db), 2 which is usually the case, σshot 2q GP hfcnsp G1 Bo Be shot and thermal noise 2 2 become negligible σ 4 GPhf n G1 B sigspont c sp e spontspont c sp o e e σ hf n G B B B Can be made very small by reducing B o by filtering, in the limit B o = 2 B e Can be made the dominant noise component The signal has been amplified in the optical domain before photodetection Indirect increase of SNR at the receiver 31

32 Optical Preamplifier (5/6) The amplifier noise is commonly specified by the noise figure F n (= SNR i /SNR o ) SNR i, SNR o concern electrical SNR values despite the fact that it is about an optical amplifier SNR for a mean optical power level equal to P s at the amplifier input Assumption: only the signal shot noise is present SNR i P 2 2qP B At the amplifier output, it is assumed that the dominant noise term is the signalspontaneous beat noise SNR o s 2 4 GP 1 shfcnsp G Be s s GP e 2 32

33 Optical Preamplifier (6/6) The noise figure of the amplifier is F n SNR hf i cnsp 2 2ηn SNR q o with G G 1,G 1 and sp ηq hf c In the best case scenario, with full population inversion, n sp = 1, F n,db = 3 db F n = 4 7 db for practical amplifiers Assumption: there are no coupling losses between the amplifier and the input and output fibers, otherwise input coupling losses degrade F n 33

34 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 34

35 Bit Error Rate BER (1/13) Application of binary modulation (OOK with NRZ pulses) In each bit interval, the receiver samples the photocurrent and decides which bit was transmitted Due to the noise currents, the receiver may decide erroneously about a bit Case: pin receiver without optical preamplifier The thermal and the shot noise will be taken into account The noise signals are Gaussian distributed For a transmitted bit 1, the mean received optical power is P = P 1 the respective photocurrent is Ī = Ι 1 Ι 1 = P 1 Variance of Ι 1 2 σ 2qI B 4k TB R 1 1 e B e L For a transmitted bit 0, the mean received optical power is P = P 0 the respective photocurrent is Ī = Ι 0 Ι 0 = P 0 Variance of Ι σ 2qI B 4k TB R e B e L For ideal OOK, P 0 and I 0 are zero, not easily achieved in practice 35

36 Bit Error Rate BER (2/13) The photocurrents for bits 0 and 1 are samples of Gaussian random variables with mean values I 0 and I 1 and variance values (σ 0 ) 2 and (σ 1 ) 2 The sampled photocurrent that corresponds to a bit 0 or a bit 1 is represented by a probability density function (pdf) The receiver must look at the sample and decide whether the transmitted bit is 0 or 1 Many possible decision rules exist Receiver s objective: choose the rule that minimizes BER Optimum decision rule (can be proved): given the observed photocurrent I, choose the bit (0 or 1) that was most likely to have been transmitted Implementation: Compare the observed photocurrent to a decision threshold I th If I I th, decide that a bit 1 was transmitted Otherwise, decide that a bit 0 was transmitted 36

37 Bit Error Rate BER (3/13) Probability density functions for the observed photocurrents Probability density Probability density function if a bit 0 was function if a bit 1 was transmitted transmitted Ι 1 Ι Ι 0 Ι 0 Ι th Ι 1 P[0 1] P[1 0] Ι 1 Ι th 37

38 Bit Error Rate BER (4/13) Probability density functions for the observed photocurrents Probability density function if a bit 0 was transmitted Here, I th is the current I for which the two probability density functions cross geometrically Probability density function if a bit 1 was transmitted The value of I th is very close to the optimal value of the threshold for which the minimum bit error probability is achieved Ι 0 Ι th Ι 1 For the case when bits 1 and 0 are equally probable to appear, the threshold photocurrent is given approximately by I th σ I σ I σ σ 0 1 Ι 38

39 Bit Error Rate BER (5/13) Error probability when a bit 1 was transmitted: the probability that the receiver considers that I < I th denoted by P[0 1] (probability to decide erroneously that 0 was received given that 1 was transmitted) Error probability when a bit 0 was transmitted: the probability that the receiver considers that I I th denoted by P[1 0] (probability to decide erroneously that 1 was received given that 0 was transmitted) Q(x) is the probability a Gaussian distributed random variable with zero mean and unit variance to surpass a value x. That is, y 2 2 Q x P X x 1 2π e dy x The probability a Gaussian distributed random variable Y with mean value m and variance σ 2 to surpass a value y is z um σ um 2σ y m y m P Y y e du P X Q y 2πσ dz1σ du σ σ 39

40 Bit Error Rate BER (6/13) Q(x) function 1 y 2 2 Q x P X x e dy x 2π Q(x) =P(X x) = x exp(-y 2 /2)dy, 0 x 4 Q(x) =P(X x) = x exp(-y 2 /2)dy, 4 x Q(x) ~10 3 Q(x) x ~ x 40

41 Bit Error Rate BER (7/13) For the Gaussian distributed random variable I, the probability P[0 1] becomes 0 1 th mi P P I I P I I I I 2I1 Ith I 1 I1 I th Q Q σ σ For the Gaussian distributed random variable I that corresponds to the photocurrent samples for a bit 0, the probability P[1 0] becomes P P I ' I Q th th σ0 I I P[0 1] Ι Ι 0 Ι th Ι 1 2Ι 1 Ι th th P[1 0] σσ 1 1 Ι 1 Ι th P[0 1] 41

42 Bit Error Rate BER (8/13) P(x,y) is the combined probability that x has been transmitted and y has been decided that has been received, with P(x,y) = P(x)P(y x) For equally probable 1 and 0, the BER will be BER P P P P P P 0,1 1, I th I 0 1 I1 I th P 1 0 P 0 1 Q Q σ0 2 σ1 For binary communications, the threshold must be set properly to minimize BER If the pdfs f I (x) and f I (y) are known, it is not required to set the threshold I th at the point the two pdfs intersect the threshold can be set so as the two areas enclosed by the tails of the two pdfs left and right of the threshold are equal! Ι 0 Ι th Ι Ι 1 42

43 Bit Error Rate BER (9/13) For equally probable bits 1 and 0, the threshold is set so as the two areas under the tails of the pdfs to be equal very close to the optimum threshold value I I I I I I I I σ I σ I Q Q I 1 th th 0 1 th th th σ1 σ0 σ1 σ0 σ0σ1 as already mentioned and the BER becomes 1 1 I 1 I 0 BER P 1 0 P 0 1 Q 2 2 σ 0 σ 1 Important: variable threshold in receivers if they must operate in systems with signal-dependent noise, such as optical amplifier noise Many high-speed receivers do incorporate such a feature 43

44 Bit Error Rate BER (10/13) In some cases, we are interested in determining what it takes to achieve a specified BER The notion of receiver sensitivity is introduced The receiver sensitivity P sens is defined as the minimum average optical power necessary to achieve a specified BER, usually or better For 10 Gbit/s, there are commercially available receivers with PIN photodiodes and sensitivity at 18 dbm and receivers with APD photodiodes and sensitivity at 24 dbm Sometimes the receiver sensitivity is also expressed as the number of photons required per 1 bit, M Bit rate R (= 1/T b ), Planck constant h, carrier frequency f c M P P PP 2 2P sens sens b with hf and P0 0 cr hfc T 2 P T : Energy per "1" bit sens hf c b : Energy per photon 44

45 Bit Error Rate BER (11/13) For receivers with optical pre-amplifier, signal spontaneous beat noise is usually the dominant noise component, except cases where optical bandwidth B o is very large, where spontaneous spontaneous beat noise may become significant For P 0 = 0 for bit 0 (P sens = P 1 /2), I = GP (for a power level P) σ 4 GPhf n G 1 B 2 2 sig spont c sp e P0 0 GP1 GP 0 GP 1 BER Q Q 2 2 GP1 GP 2 σ 0 GP sig spont, 0 σ sig spont, 1 σ 1 BER 1 Q sig spont, Q σ sig spont, 0 σ sig spont, 1 σ siggp spont, 1 GP 1 1 Q Q 2 4 GPhf cnsp G1 B hf e cnsp G Be BER Q 1 0 I I σ σ

46 Bit Error Rate BER (12/13) The receiver sensitivity can be measured either in terms of the required power at a particular bit rate or in terms of the required number of photons per bit 1 M = P 1 /(hf c R) Assumptions: B e = R/2, R is the transmission rate, G >>1, n sp = 1 P 1 PT M 2 hf 2 2 hfc 2 c R 1 1 b BER Q Q Q To obtain BER = 10 12, the argument of Q(.) function γ must be 7 receiver sensitivity of M = 98 photons per bit 1 46

47 Bit Error Rate BER (13/13) An optical filter is used between the amplifier and the receiver to limit the optical bandwidth B o and reduce the spontaneous-spontaneous and shot noise components For practical pre-amplified receivers, sensitivities of a few hundred photons per 1 bit are achievable A direct detection pinfet receiver without pre-amplifier has a sensitivity of the order of a few thousand photons per 1 bit In systems with cascades of optical amplifiers, the notion of sensitivity is not very useful, the signal reaching the receiver already has a lot of added amplifier noise. Two parameters that are measured Average received signal power, P rec (P rec = G P in,amp, P in,amp mean optical power at the amplifier input) the received optical noise power, P ASE The Optical Signal-to-Noise Ratio (OSNR) is defined as P rec /P ASE For receiver with optical preamplifier, P ASE = 2 P N = 2hf c n sp (G 1)B o 47

48 Contents Modulation/Demodulation in Optical Communications A Practical Direct Detection Receiver How to encounter the thermal noise confinements Noise in an APD Photodiode Optical Preamplifier BER Estimations Coherent Detection 48

49 Coherent Detection (1/22) Performance degradation due to thermal noise in simple direct detection receivers Improvement of sensitivity appeared when a optical amplifier was used in front of or close to the receiver Another way to improve the sensitivity of the receiver is to apply a technique called coherent detection Concept: gain provision to the signal by the mixing with another optical signal that is close to the receiver The function of the powerful signal close to the receiver is that of local oscillator Simultaneously, the noise component at the receiver that dominates (against the thermal noise) is the shot noise due to local oscillator The sensitivity of the receiver is limited by the shot noise and not the thermal noise 49

50 Coherent Detection (2/22) In a simple coherent detector, the input light is subject to mixing with a local oscillator signal through a 3-dB coupler and the result is incident on the photodetector surface The 3-dB losses due to the separation of the signals by the coupler will be ignored Optical signal Laser Photo-Detector Coupler Assumptions: the phase and the polarization of both signals are the same The respective electric fields that concern the signal and the local oscillator are E t 2aP cos 2πf t and E t 2P cos 2πf t r c LO LO LO where P is the input signal power (at the receiver), P LO is the power of the local oscillator, α = 1 ή 0 depending on the bit that was transmitted, i.e. 1 or 0 (for OOK signals), f c and f LO represent the frequencies of the carrier of the signal and the wave of the local oscillator, respectively 50

51 Coherent Detection (3/22) Following the squaring process, the power that is received at the photo-detector input and will be converted into the current that will be processed by the receiver will be P t ap cos πf t P cos πf t r c LO LO If the electrical current at the receiver (I(t) = P s (t)) is filtered in the electrical domain, the spectral components at 2f c, 2f LO and f c + f LO that appear due to the squaring process can be eliminated and the result becomes 2 2 P t ap P app cos π f f t r LO LO c LO In a homodyne receiver, f c = f LO In a heterodyne receiver, f c f LO = f IF 0. The frequency f IF is called Intermediate Frequency (IF) and conventionally can be a few GHz 51

52 Coherent Detection Receiver types (4/22) Three different types of optical receivers Direct detection receiver Coherent homodyne receiver (f c = f LO ) Coherent heterodyne receiver ( f c f LO = f IF 0) Modulated light (f = f c ) Photo-detector Front-End Amplifier Receive Filter Clock/Timing Recovery Direct detection receiver with a PIN or APD photodiode as the photo-detector Sampler Decision Circuit Before the photo-detector, an optical amplifier can be used 52

53 Coherent Detection Receiver types (5/22) Three different types of optical receivers Direct detection receiver usage of an optical pre-amplifier Coherent homodyne receiver (f c = f LO ) Coherent heterodyne receiver ( f c f LO = f IF 0) G Modulated light (f = f c ) Photo-detector Optical preamplifier Front-End Amplifier Receive Filter Clock/Timing Recovery Direct detection receiver with a PIN as the photo-detector (mainly when combined with an optical amplifier) Sampler Decision Circuit 53

54 Coherent Detection Receiver types (6/22) Three different types of optical receivers Direct detection receiver Coherent homodyne receiver (f c = f LO ) Coherent heterodyne receiver ( f c f LO = f IF 0) Modulated light (f = f c ) Laser (Local Oscillator f LO = f c ) Photo-detector Front-End Amplifier Low Pass Filter Sampler Coherent homodyne receiver Clock/Timing Recovery Decision Circuit 54

55 Coherent Detection Receiver types (7/22) Three different types of optical receivers Direct detection receiver Coherent homodyne receiver (f c = f LO ) Coherent heterodyne receiver ( f c f LO = f IF 0) Modulated light (f = f c ) Laser (Local Oscillator f LO f c ) f c f LO = f IF Photo-detector Electrical Amplifier IF Band-pass Filter Coherent heterodyne receiver Demodulation and Tranfer in Baseband Clock/Timing Recovery Sampler Decision Circuit 55

56 Coherent Detection Improved performance (8/22) Coherent detection performs better (lower) sensitivities. WHY? For the coherent homodyne receiver and OOK modulation format, we showed P t ap P app ap P app For a bit r LO LO LO LO I P P PP LO LO For a bit 0 0 LO 1 2 KEY POINT: ensuring that the power of the local oscillator P LO is sufficiently large, the shot noise can dominate against the rest noise components Noise variances for bits 1 and 0 I P σ 2qI B and σ 2qI B e 0 0 Usually, the power level P LO is around 0 dbm and the level P < 20 dbm (P << P LO ) P can be ignored when the currents I 0, I 1 are calculated P and (PP LO ) 1/2 can be ignored when the variance (σ 1 ) 2 is calculated 2 2 I P 2 PP, I P,σ σ 2qP B 1 LO LO 0 LO 0 1 LO e e 56

57 Coherent Detection Improved performance (9/22) I I 2 PP P 1 0 LO BER Q Q Q σ0 σ1 2 2q P 2qB LOB e e Assuming: B e = R/2, R = 1/T b and= ηq/(hf c ), BER becomes η 1 ηq P BER Q Q M hfc 2q R 2 where Μ = PT b / hf c is the number of photons per bit 1 For BER = Q(M 0.5 ) = 10 12, M 0.5 = 7, sensitivity M = 49 photons per bit 1, significantly better than the sensitivity of a simple direct detection receiver 57

58 Coherent Detection Further Advantages (10/22) In WDM systems, with coherent receivers, in order to select a desired signal Instead of using an optical demultiplexer or filter Usage of electronic filters in the IF domain designed to have very sharp skirts tight channel spacing can be achieved the receiver can be tuned between channels in the IF domain: rapid tunability between channels desirable to support fast packet switching highly wavelength-stable and controllable lasers and components will be required With coherent receivers and higher order two dimensional modulation formats large bit rates can propagate for very large distances Today at least 100 Gbit/s per wavelength can be supported 58

59 Coherent Detection Disadvantages (11/22) Coherent receivers are generally quite complex to implement and must deal with a variety of impairments Orthogonalization must be applied when imperfect devices are used in complex versions of coherent receivers with polarization multiplexing The two currents of the two polarizations must be orthogonal to be recovered Frequency offset must be estimated, due to possible difference between local oscillators frequency and signal s center frequency Due to lasers finite linewidth, phase recovery must be achieved No phase difference was assumed between the signal and the local oscillator so far Coherent receivers are sensitive in phase noise in both signals Assumption made: polarization of both waves is the same THIS MAY NOT BE THE CASE IN REAL SYSTEMS! With perpendicular polarizations, the mixing between the two waves (signal and local oscillator) generates no output Coherent receivers are sensitive in variations of the polarization of the signal and the local oscillator (not a problem in direct detection receivers) 59

60 Coherent Detection Possibility of Perpendicular Polarizations (12/22) If the polarization of the waves that represent the signal and laser of the local oscillator are not the same Possible performance degradation In case of perpendicular polarizations, zero output after mixing the two waves Modifications in the fields representation from now on by the addition of the unitary vectors ur ur 2 2 jφc Er t er ap cos πfct with er e uuur uuur E t e 2P cos 2πf t with e e LO LO LO LO LO Power at the input of the photo-detector that will be transformed into current 2 P t E t E t E t E t E t E t r r LO r LO r LO E t E t Re E t E t r LO r LO jφ LO 60

61 Coherent Detection Possibility of Perpendicular Polarizations (13/22) The current (I(t) = P r (t)) will be filtered in the electrical domain and the spectral components 2f c, 2f LO and f c + f LO will be eliminated jφ 2 cφlo P 2 r t ap PLO Re e applo cos π fc flo t Consider the case of a coherent receiver with f c = f LO the polarization of the two waves are perpendicularφ c φ LO = π/2 P t ap P 2cos φ φ app ap P r LO c LO LO LO Photocurrent for bit 1 I P P Photocurrent for bit 0 1 LO Variances for bits 1 και 0 I P 0 LO σ 2qI B 2q P P B and σ 2qI B 2qP B e LO e 0 0 e LO e 61

62 Coherent Detection Possibility of Perpendicular Polarizations (14/22) P << P LO and P is ignored in I 1 and (σ 1 ) 2 P + P LO P LO, I 1 I 0 I I P P LO LO BER Q Q Q σ0σ1 2qPLO Be 2qPLO B e In case of perpendicular polarizations between the signal and the local oscillator waves the limitation is severe: inability to discriminate if a bit 1 or bit 0 was received. The phenomenon must be controlled States of Polarization (SOPs) will be considered instead of single polarizations In single mode fibers, each polarization of the electric field, E x και E y, is linearly polarized along the axis x and y, respectively, and both components are perpendicularly polarized between each other, giving the fundamental mode When two perpendicular polarizations of the same wave are defined, the SOP of the entire wave is characterized by the relative phase and the amplitudes of the two perpendicular components

63 Coherent Detection Possibility of Perpendicular Polarizations (15/22) The fundamental mode that propagates along the fiber and is received by a coherent receiver can be resolved into two polarizations and the SOP of the received signal is defined The field of the local oscillator laser at the receiver is resolved into two perpendicular polarizations and a SOP is defined for this laser In case of perpendicular SOPs between the signal and local oscillator waves the detection becomes inefficient Perpendicularity of SOPs may occur occasionally, even if we manage to keep the SOP of the laser of the local oscillator fixed The SOP approach is more general than the polarizations approach already given 63

64 Coherent Detection Encounter Perpendicular Polarizations (16/22) Five ways to encounter the problem of the perpendicular polarizations in a coherent receiver Application of polarization diversity in order to ensure the reception of the signal independently of its SOP Spreading the signal comes by many SOP positions that are distant during the bit interval to ensure that the SOP of the signal at the receiver and SOP of the local oscillator laser will not remain perpendicular for the entire bit Installation of polarization maintaining fibers, which impose the reception of constant SOP Polarization Tracking which incorporates the measurement of the received signal s SOP and the subsequent arrangement of the SOPs of the signal and the local oscillator laser in order to coincide Polarization Shift Keying (PolSK). The transmitter sends two orthogonal SOPs, one for bit 1 and one for bit 0. The devices used for the SOP measurement in polarization tracking technique can be used to conclude differentially if a bit 0 or 1 was received 64

65 Coherent Detection Encounter Perpendicular Polarizations (17/22) Receivers without polarization diversity General configuration of a simplified receiver without diversity where a signal with SOP sig arrives, whereas the receivers requires to see SOP rec SOP sig και SOP rec may become perpendicular at specific instants causing performance degradations SOP sig Polarization sensitive device (SOP rec ) Reception with a polarization sensitive device Amplification, Filtering, Synchronization, Sampling Decision Circuit The polarization sensitive devices could be polarization sensitive tunable filters, polarization sensitive direct detection receivers or coherent receivers 65

66 Coherent Detection Encounter Perpendicular Polarizations (18/22) Receivers with polarization diversity The design is based on the diversity principle Two discrete receivers are used Each receiver responds to a perpendicular SOP relative to the other The two outputs are combined after detection before decision circuit A signal will be received whose 1 and 0 can always be discriminated SOP sig Polarization Beam Splitter (PBS) Polarization sensitive device (SOP 1 ) Polarization sensitive device (SOP 2 ) Receivers with polarization diversity Amplification, Filtering, Synchronization, Sampling Amplification, Filtering, Synchronization, Sampling Decision Circuit + 66

67 Coherent Detection Encounter Perpendicular Polarizations (19/22) Receivers with polarization diversity In polarization diversity, the two receivers respond to perpendicular SOPs In phase diversity, the two receivers are configured so as to have 90 o phase difference π/2 LO Mixer Amplification, Filtering, Synchronization, Sampling + SOP sig Coupler Phase shifting Mixer Phase sensitive devices Receiver with Phase Diversity for BPSK Amplification, Filtering, Synchronization, Sampling Decision Circuit 67

68 Coherent Detection Encounter Perpendicular Polarizations (20/22) Receivers with polarization diversity In a coherent receiver, it is possible to successively apply the phase diversity and the polarization diversity Despite the ability to encounter the random variations of polarization after signal propagation, polarization diversity requires double receiver complexity The use of an additional second branch in the entire receiver results in noise doubling compared to the single branch receiver A useful signal from the received SOP with levels that can be discriminated (if a pulsed signal is transmitted) will always be generated after detection, but the combined electrical output at the point before decision will have 3 db additional noise The devices that apply spreading, change irregularly the polarization between the two perpendicular SOPs more than once during the bit interval in order a receiver configured to respond 100% to a specific SOP to be able to always detect even partially the signal For several gigabit/sec bit rates of interest in optical communication networks, devices like lithium niobate phase modulators have the ability (in terms of speed) to apply the spreading at least two times during each bit interval 68

69 Coherent Detection Encounter Perpendicular Polarizations (21/22) Installation of polarization maintaining fibers In a single mode fiber, the only mode that propagates consists of two orthogonal degenerate states which are the two polarizations Even if the single mode is transmitted vertically polarized, both the slight birefringence and the irregularities in the fiber along propagation will cause coupling of a part of the light to the horizontal polarization This coupling is a random function of the distance covered The two polarizations will propagate with slightly different velocities and will appear with a phase difference at the end of the link After a few kilometers, the result will be a received SOP that is very difficult to be predicted The principle of operation of the polarization maintaining fibers is based on the artificial increase of the propagation velocity (i.e. increase of the birefringence) of the two degenerate modes in order the coupling between the two modes to be limited significantly and the conversion from one state into the other to be eliminated 69

70 Coherent Detection Encounter Perpendicular Polarizations (22/22) Polarization Tracking Two stages: SOP measurement of the received light SOP correction From these measurements, control signals are produced that feed the polarization controlling devices which shift the SOP of either the received signal of the local oscillator laser until the SOPs coincide or are adjusted to a satisfactory level PolSK Modulation If the SOP of a wave is changed to its orthogonal SOP, the orhogonality of the two SOPs will survive along propagation and the received states keep being orthogonal This situation can be exploited in order to apply Polarization Shift Keying (PolSK) or Differential PolSK (DPolSK) Binary PolSK: one SOP represents bits 0 and the orthogonal SOP represents bits 1 Each SOP that arrives at the receiver will be in general different from the one emitted by the transmitter, but the two SOPs of 0 and 1, will always be orthogonal at their arrival at the receiver The PolSK and DPolSK modulation formats have not been applied in practical optical communications systems, without being indifferent, though 70