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Noises in Optical Communications and Photonic Systems

Le Nguyen Binh

Optical Coherent Reception and Noise Processes

Publication details https://www.routledgehandbooks.com/doi/10.1201/9781315372747-4 Le Nguyen Binh Published online on: 07 Nov 2016

How to cite :- Le Nguyen Binh. 07 Nov 2016, Optical Coherent Reception and Noise Processes from: Noises in Optical Communications and Photonic Systems CRC Press Accessed on: 26 Sep 2021 https://www.routledgehandbooks.com/doi/10.1201/9781315372747-4

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The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 chapter provides the fundamental understanding of (CoD) coherent detection understanding signals, of optical provideschapter fundamental the This (PD) amplification. photodiode electronic the then in power and signal current electronic to receiver conversion optical out by atthe direct of optical carried be can signals of optical Detection * dispersion fiber to tolerance high effects potentially [1–6]. efficiency, provide it spectral can because high highreceiver desired, sensitivity, be will formats and systemsdispersion multilevel (PMD) with communication tolerance, coherent optical modulation dispersion spacing, designsuchas chromatic specifications channel (CD),mode polarization and wavelengthmission per To system complying while current rate with is required. achieve data this trans data of 100 serial rate Gbit/s data requirements, 100 GbE anticipated 10 GbE. on the Based next the considered logical be (100 GbE) to evolution is currently 100 Gigabit Ethernet after step of technology next generation metro/core key networks. the transport become networks will but also access in not only dominate will technology Ethernet It that is expected desired. highly become networks have optical applications, cost-effective driven bywidth multimedia ultrahigh-speed band ultrabroad demand the for dueto especially traffic, data in exponential increase With the 3.1 receiver. end optical of front the atthe integrated be also CoD can in preamplification Optical domain. electronic the in characteristics amplitude and its phase both (LO), preserving signals would product modulated ahigh-power the its result beating in so that laser oscillator the that local of and fields optical ofsignals the optical the of mixing the which requires to recover transmitted signals. These technological advances, especially in the digital processors processors digital the in especially advances, technological signals. These recoverto transmitted phase-locked loop optical (OPLL), an maysignals not require self-coherent hence DSP and and of detection such modulation and and (iv) Turbo coding and and differential algorithms, the that such Viterbi as algorithms (PE), processing of signal availability advanced (iii)estimation the phase or phase the recover to few of tens signals giga-samples/s of processing beating allowingthe reach (DSP) can rate processors signal whose (ii) ofsion advances sampling digital the distance, transmis limit the thus and have spans fiber noises in cascade added significant amplifiers optical motivation systems networks. possibleoptical and The been (i) has fact due that of uses the to the activities dense ultrabitresearch rate for wavelengthdivisionsignificant multiplexing(DWDM) overcome attempt? Recently, have communications this coherent optical attracted in interests fiber at bitrate of 140 Gb/s. However, inventionthe late the in has 1980s amplifiers of fiber optical for of single optical 40 km mode instead 60 km to is pushed spans between sion distance of repeater 1980s were systems the exten considered in when forCoherent transmission the techniques optical tion systems networks improve to and receiver distance. the sensitivity transmission extra thus and dously improve receiver the sensitivity. tremen therefore, and can light, of the information phase retrieve CoD the signal, light of can the of intensity the the only systems (IMDD) detects intensity-modulation/direct-detection that tion in

locking of the local oscillator to that of the carrier. of the that to oscillator local of the locking phase the with association in oscillator local astrong and signals the by mixing implemented is detection Synchronous Coherent optical receivers are important components in long-haul components in fibercommunica optical important receiversCoherent optical are

3 INTRODUCTION and Noise Processesand Reception Coherent Optical * Compared to conventional detec to Compared direct 39 ------Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 matically due to electronic processing and availability of stable narrow linewidth lasers. linewidth of availability stable and narrow processing due electronic to matically systems have reviving communication signals. Coherent optical dra been also original ofthose the reflect signals resultant of the property frequency and phase, the carrier, of the that to or different be identical those frequencyLO can with of a whosemixed are fieldssignals optical the incoming of However, format. recoveryfor decoded then of original are The signals amplifier.electronic when front end a electronic through amplified electronically then are photodetector the in generated trons by aPD (adetected or avalanche diode [APD] photodiode PIN device); or aphoton-counting elec coherent system first the the in generation in ducted 1980s. allow rate, overcomingcon in coherent homodyne reception severalat ultra-sampling difficulties 40 received optical signals before detected by an optical receiver. optical by an before detected signals optical received 3.1FIGURE of equivalent signal such circuits areceiver’ssmall end. However, front at signals of phase the the 3.2 end. Figure front shows atthe receiver mixer detection optical the but an with direct the to keying or multiple levels, so on. and shape, or exponential on-off Gaussian pulse or digital, analog modulation in is dependent on the it systems. particular, (BER) In rate bit-error transmission the the receiver ofand thence the and plays detection shaping also role phase the the in acritical frequency. and phase, Furthermore, of form amplitude, the in be can carrier optical modulation of the The transmitter. the through ted transmit thus and signals of receiver modulation format design the optical on the of depends The an 3.2 development coherentimportant detection. optical for modern Section 3.4 and OPLL of which is the gives avery techniques, details homodyne, or intradyne heterodyne, ent under receivers, coherent of principles detection optical Section the 3.3 outlines chapter. this in treated OPLL is thus signals. An of the carrier and LO of alocking the would require cases signal. Both electronic of baseband the the is in detection the thus and difference is no frequency there homodyne detection, in hand, other region. passband the On this end must front in be atthe ing process electronic the all Thus, domain. electronic region the apassband in in is fallen signal beating the thus and frequency the in is adifference there detection, Foror homodyne detection. heterodyne heterodyne as termed be LO, CoD of can the the that and signals optical of the lightwavethe carrier elements between of receiver. acoherent difference optical frequency on the fundamental Depending devices the photodetection as act and mixing optical the both receivers Thus, following mixing. this by optoelectronic the detected thence and domain optical the in LO of the that and signals of optical As is well known, a typical arrangement of an optical receiver is that the optical signals are are signals optical receiver optical the of is that an arrangement is wellAs a typical known, Figure 3.1Figure receiver, coherent optical of adigital shows which is schematic similar diagram the follows: as is chapter organized This Section 3.2 components gives of of account the coher an design analysis of and mixing coherent the with receivers the OPLL with and deals chapter This

COHERENT RECEIVER COMPONENTS

Schematic diagram of a digital optical coherent receiver with an additional LO mixing with the the with mixing LO additional an receiver with coherent optical of a digital diagram Schematic optical signal Received narrow linewidth) (high powerlaser, Local oscillator detector Reverse Photo- bias Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises Electronic pre-amp data output Recovered amp Electronic main + AGC Decision Electronic circuit recovery Clock filter ------Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 the electrical signals. electrical the (ii) and signals demodulation of refers recovery from of signals the that the to baseband than larger average an lightwaves with aLO other much energy the and one is information-bearing carriers, following with association in twolightwavesbetween definitions: mixing (i) the or CoDoptical is by “demodulation” the techniques communications scheme distinguished in be CoD can Optical 3.3 respectively. or homodyne technique, a heterodyne as is termed technique detection the and passband, or the baseband the in be can signals electronic the the detector, from derived these fieldsbetween resulting the signals or electronic of null finite is additivedifference offrequency the fieldthe the beating PD. in the on whether Depending mize lightwaves maxi to these between orientation critical is very signals. Polarization optical of the that fieldsand optical LO the the endof sums front mixing optical recovery The section. data the and control and automatic gain (AGC) amplifier if necessary, main of the channel linear the end section, processes. amplification cal with opti dealing chapter this in treated be receiver front an endoptical the will of at amplification frontimprove endto amplifier receiversensitivity. receiving optical optical its an with optical This by a then sampled clockdecisionwithandby a recoverysynchronization circuitry. circuit filtered be the signal voltageelectronic is followedan automatic controlregulate to to with amplifier by amain preamplifier sequence. optoelectronic Therefore, received the and digital recovery transmitted of the sequence; avoltage-level and timing the waveform decision for the circuit sampling for final the voltageamplification; a for further regenerating recoverycircuitry amplifier clockfor form; a main for followed extension, bandwidth voltage current in electronic usually equalizer electronic by an amplification the generated of further for preamplifier electronic an currents; electronic into energy following end for consisting front of processing aphotodetector optical converting lightwave the signals. modulated of the amplitude and phase the both preserving current electronic the into photodetector, of range is converted the absorption the within lower which falls term, frequency lightwaves. of frequencies the of the difference the the Only and frequencies of the summation the with aproduct to other each with envelope the beating be so that can signals optical of the fields the signals the optical the optical wavesand combining of mixer laser optical the local of an front end is voltages An and optical preamplifier. output electronic of atthe current the electronic generated the in would remain domain electrical the in signals detected of or passband base the signals. optical the and oscillator local of the beating the due to photodetector the in generated current the electronic represents source current The end. front the at amplifier electronic 3.2 FIGURE Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical The structure of the receiver is thus consisted of four parts: the optical mixing front, the front front the front, mixing optical receiver of the the of consisted is thus four parts: structure The an tofront the photodetector form in of incorporated be can amplifier fiber optical inline An is connected detection, direct of the that receiver as optical much same very end, front an the Thus,

C o D

inside thephotodetector Schematic diagram of an electronic preamplifier in an optical receiver of a transimpedance transimpedance receiver of a an optical in preamplifier electronic of an diagram Schematic via thesquarelaw,(i.e., Beating signalscurrent summation offields signal andLOthen squaring) i d RC d impedance Feedback − A Z f C d

= photodiode capacitance. photodiode 41 - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 maintaining coupler and then detected by receiver. a coherent optical detected coupler then and Most previous of the CoDmaintaining apolarization via mixed are signal transmitted the and LO The carrier. information-bearing the of that with its match to polarization would controller used be also source; apolarization matic approximately equivalent and amonochro to tuned be whose can frequency source is alaser signals. ALO of the carrier of the that and LO of frequencies the or not the between difference is a there whether depending homodyne techniques and heterodyne with distinguished further be which can of communications, coherent optical feature CoD is aprincipal The types. or EA is fed a microwave via LiNbO optic modulator, used commonly integrated an powerto amplifier Information transmitter. optical the is usually modulator external an with isolatoroptical cascaded an components 3.1, is shown and Figure in medium incorporating laser band which anarrow in 42 modulation coherent optical systemsmodulation coherent optical for today’s so far. is missing rates data networks and However, BER investigation performance. practical theoretical and of multilevel amore detailed the calculating and receiver and structures possible the 1990s, early describing transmitter the in field optical of the proposed were four quadratures modulation of on all the based lation formats Several modu different domain. electrical the to optical the from complexity the and is transferred avoided be systems—can detection direct in used be to has detection—which interferometric with This waycomplex field domain. demodulationtion optical of optical the is the electrical in available informa- the all because beneficial, too, also coherent systems For are this, modulation is required. efficiency. of spectral limits efficiencies,use the ultimate multilevel ofthe higher spectral reach To convergence the use of CoDpermits only to Furthermore, filtering. electrical steep via separation sation of CD. systems, allow channel WDM to With coherent and regard receivers offer tunability CoD of enables phase the for new temporal of methods adaptivepreservation the compen electronic several CoD provides. and advantages that rates The data athigh relaxed receiver requirements of focus availability DSP due low-priced the of the to and interest, become partly components, the without difficulty. gain Nowadays,offer up 20 dB to however,coherent systemshave again once that the late in advent 1990s the with amplifiers of optical was interrupted research their but then detection. heterodyne or self- process reception autocorrelation as which is classically termed may utilized, reception be detection. heterodyne as to is referred IF of LO an an and signals the of mixing The domain. electrical the in frequency atlower PLL recovered using electrical carrier be then can signals electronic The passband. 3 dB of the that times tor which is about two three to oscilla (IF) frequency intermediate an with mixed first are signals optical the general, In required. no OPLL is and signals receiving of the that as same is approximately LO of the the frequency the receivers, For homodyne reception. asynchronous as is termed technique so this baseband, the and signals bandpass of the mixing tive LO. receivers of synchronous the that to allow Thus, direct rela signals of absolute the frequency the and phase measure to so as signal of the that to LO the received of lock to the frequency signals and recovers phase OPLL that the an requires detection for exemplarily Square-16-QAM clarified and modulation. expressions general deriving applicable modulation format every to M-ary-QAM M-ary-PSK and multilevel optical of is shown the by modulation signals. This properties different to lead driving the andelectrical configuration transmitter optical the in Differences analyzed. theoretically and shown are transmitters modulation (M-ary-QAM) amplitude quadrature M-ary and (M-ary-PSK) keying multilevel phase-shift cal M-ary of modulation signals. Several optical possible structures possibilities for multilevel optical investigates section generation of modulation. the This opti to enhanced leading detection, field optical of the during information the of preservation all the electronic/microwave and of photonic domain domain. amixture implemented in schemes are A typical schematic diagram of a coherent optical communications employing wave of communications acoherent optical guided schematic diagram A typical Coherent communications have been an important technique in the 1980s and the early 1990s, early 1980s the the in and technique have important Coherent an communications been or self-homodyne differential then signals, optical digital for the nois used LO demodulating If Synchronous asynchronous. and synchronous between Coherent distinguished receivers are advantage is significant focus One the of research. become has transmission Coherent optical Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises ------3

Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical and feedback circuitry, optical, or electrical, which may be complicated; and (iii) for differential (iii) which for may and complicated; be feedback differential or electrical, circuitry, optical, and would control for PLL that need heterodyne electrical OPLL and receivers require (ii) homodyne end receiver; of front the atthe tracking polarization sensitive requires polarization that are ers ease. bechanged with can filtering the the DSPin in which conduct to users filtering DSP rate allows sampling cut-off Presently, the to band. passband of of the availability ultrahigh the roll with sharp filters by using electrical domain electrical the in separated be DWDM can channels or exact signals. (ii) PE optical of Using the receivers, equalization heterodyne exact electrical receivers, detection allows direct the to contrast in This, domain. optical the in that to portional which is pro domain, electrical the (i) The in received receivers coherent of signals optical the are Quantum. Elect Quantum. PC device,coupled fiber maintaining tion PM coupler polariza is carrier. optical signal the to locking phase any without LO an as diode laser linewidth 3.3 FIGURE lower thanthatofthecarrier, allowing ismixed carrier thus withthe information-bearing down- or nel carrierisdifferent withthatofthelocaloscillator. behigheror The LO,whosefrequency can shows alsomoredetailsofaheterodynereceptionsub-systeminwhichthefrequency ofthechan A typicalschematicofacoherentopticalreceptionsub-systemisshown inFigure3.3.3.4 3.3.1 diversity technique. polarization implemented best by be the can this practice, In must signals aligned. be the and LO tions of the signal. of baseband the the within falls difference frequency when the (iii) intradyne, and is nil; signal; (ii) baseband of bandwidth the homodyne, difference when 3 dB the the than isence higher classifiedas be can follows: types LO. ofdiffer (i) the the that Three when heterodyne, and channel chapter. this in described keying (FSK) modulation are shift frequency and recovered. binary-levelthen Both multilevel and schemes modulations employing phase, amplitude, and detected envelop. signal are signals the and domain down-converted carrier The electrical the in range chapter, IF is coherently detection the converted to the this In 2. Chapter mentioned in as is manipulated carrier of the frequency or phase, the the amplitude, on the whether depend signals lightwave of optics, modulation formats planar The of technology circuits. integrated advanced the systems, of use photonic components the is extensivelytransmission exploited advantage of take to nature. receiving differentiation due compensation may complicated the to be the detection July 1986. permission.) With Currently, coherent reception has attracted significant interests due to the dueinterests to following significant reasons: Currently, attracted has coherent reception It is noted that to maximize the beating signals at the output polariza photodetector, of atthe the the signals beating the maximize to It that is noted optical of the frequency central the between by difference the distinguished be CoD can Thus, for amplified presented optically are when chapter alater modulation formats some advanced In However, coherent receivers that disadvantages would are suffer: (i) there coherent receiv

O High power and narrow Local Oscillator(LO) ptical linewidth source

Typical arrangement of coherent optical communications systems. LD/LC is a very narrow narrow avery is LD/LC systems. communications optical of coherent Typical arrangement ., QE-17, 1981; 946–959, W. al., et Stallard A. Laser H (narrow linewidth) eter Laser diode O dyne

d etecti frequency translator Tunable = O modulator polarization controller. (Adapted from R. C. Alferness. Alferness. C. R. (Adapted from controller. polarization Optical n controller (PC) Polarization

IEEE J. Lightwave Technol J. Lightwave IEEE Optical transmission line Optical receiver

., LT-4(7), 852–857, processor Signal IEEE J. 43 ------Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 the quantum efficiency, quantum the response, frequency by photodetector (the the term sum) frequency higher is eliminated where the for bitdifferent the “1” bit and “0.” is continuous, we phase of(DQPSK), the have variation when is the and of variation rate FSK the if PSK PSK (DPSK), quadrature PSK, be it differential phase, can For or differential discrete term. phase time-dependent of the or continuous variation power discrete the with or frequency or phase keying—ASK) off (amplitude switching on and the with optical shift of amplitude the be tion can including any phase noise of the signal and the LO, the and including noise and any phase signal of the 44 where expressed as be can LO the and field The electric the optical detection. signals of fieldsthe ofoptimum these for critical is alignment ing processorenvelop detectiontorecover thesignals. the mixingofthesecarrierswould resultintoanIFcarrierinthe electrical domainpriortothemix controlling thestabilityoffrequency spacingbetweenthesignalcarrierandLO. This means is notedthatthedetectionconductedatIFrangeinelectricaldomain,hencethereaneedof converted carrierisrecovered andthenmixed withIFsignals,thenthisissynchronousdetection.It detector, theprocessis asynchronous,hencethenametermasynchronousdetection.Ifdown- ics ofthenonlineardetection photodetection process,thesquare-law detection. With anenvelope demodulated by a demodulator. A low pass filter (LPF) is also used to remove higher order harmon into electroniccurrentsignals,whicharethenfilteredbyanelectricalbandpassfilter(BPF)and signal envelop isreceived bythephotodetector. This combinedlightwave isconverted bythePD upconversion oftheinformationsignalstoIFrange. The down-converted electricalcarrierand LPF receiver structures. 3.4 FIGURE respectively, respectively, Under an ideal alignment of the two fields, the photodetection current can be expressed by can two of fields, the current the photodetection alignment Under ideal an The CoD thus relies on the electric field component of the signal and the LO. The polarization fieldLO.polarization the The electric and CoD relies on the component thus The the signal of P (b) Signal input Signal input (a) s s s ( ( () t t ) ) t and and

Laser Laser (LO) (LO) ω Schematic diagram of optical heterodyne detection: (a) asynchronous and (b) synchronous, (a) (b) and detection: synchronous, heterodyne asynchronous of optical diagram Schematic s () t P i LO () and and t are the instantaneous signal power signal average and power instantaneous LO, the and signals of are the =+ PM optical PM optical = coupler coupler q η h ω low filter, pass BPF is the electronic charge, electronic is the υ q LO   are the signal and LO angular frequencies, frequencies, angular LO and signal the are PP ss E ss LO () E tP LO +− =+ 2 Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises =+ Asynchronous Detection 2 PP = 2c bandpass filter, PD bandpass Pt () LO tt L (electrical) (electrical) co co os BPF BPF h s( is Plank’s and constant, s( Synchronous delection {} {} {} ωφ ωφ ωω LO ss ss recovery ψ Carrier () t LO LO + is the modulation phase. The modula modulation phase. The is the )( Demodulator ϕ = tt +−

photodiode. t Mixer ) φφ

LO + φ υ s is the optical frequency. optical is the ϕ and and )   φ

LO LPF LPF are the phase phase the are (3.2) (3.3) (3.1) η is is - - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4

given be thus as can avariance and mean azero with pendent of other each inde follow to are assumed and be noise distribution can power probability The a Gaussian terms 3.3.1.1.1

is the square root of the product of the power signal. of product of root the the the and LO of square the is the and amplitude PD, the to inside the signal the which and is proportional LO the between beating the level, from signal signal-to-noise is (SNR). resulted ratio the term hence enhancing oscillating The Processes Noise and Reception Coherent Optical noise values power orthogonal expected variables. of random the the components, which are are IF The envelope demodulated expressed as be amplitude then can signal. The component beating of frequency of the the tracking the to according carrier the that to is tuned frequency LO. LO the The and carrier of frequencies the the between alocking require would detection synchronous the a clock with is established While recovery circuit. instant pling demodulator)the followed asam and is by obtained, eye adecision is, the circuitry. That diagram Under ASK the 3.4 of modulation scheme, demodulator Figure envelope the is an (in of lieu detector 3.3.1.1 where (OSNR) as written be can where the photodetection process. Under this quantum limit, the OSNR the limit, quantum Under process. photodetection this the in noise inherent by quantum the sensitivity the coherent of receiverSNR, limited the only be can the over increasing shot noise the equivalent dominates time so that the noise, same atthe increased powerthe fierreceiver.the if of that LO is equation, the significantly observe of we can this From The electronic signal power signal electronic The the boosts time shot-noise same the power atthe the and Thus, dominates process LO of the B N

ω is the 3 dB bandwidth of the electronic receiver. electronic of bandwidth signal-to-noise the ratio optical the Thus, 3 dB is the

eq IF ASK Coherent System Coherent ASK is the difference between the frequencies of the LO and the signal carrier, and and carrier, signal the and LO of frequencies the the between difference is the is the total electronic noise electronic equivalent power preampli total electronic is the input the to atthe Envelop Detection rt () =ℜ [] 2 r ωω () IF tP PP sx =− =ℜ LO 2 s ++ S and shot noise and nn ω OSNR sx LO Pt pn 22 LO (, N ℜ= SP xy ss cos( y = n =ℜ =ℜ OSNR cos( 2 2 2 η ) h ωω qP qP ν = q IF ℜ+ ωΦ 2 2 = )c () () IF N πσ QL s 1 responsivity ++ P 2 tt s s LO can be expressed as be can ℜ += + nt = 2 2 e PB PB ℜ PP −+ qB LO LO )t s os () P nn xy 22 s LO with () σ

; the probability density function (PDF) (PDF) density function probability ; the IF + / 2

N σ Φ 2 eq

nt QL

y is given is by an sin( − 1 ω 2 IF ℜ+ ) PP

sx n LO y n

n x and and (3.5) (3.6) (3.8) (3.4) (3.7) (3.9) 45 n - - - y

Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 “1s” the between “0s”: and of error probability equal an assuming obtained be BER the can and of error probability the then where The PDF of the amplitude can be obtained by integrating the phase amplitude PDF over amplitude phase the range by the integrating obtained be can PDF amplitude ofThe the [3] as written be can equation this amplitude, and phase the to With respect 46 lent noise current of the electronic preamplifier as seen from its input port. input from its seen as preamplifier electronic of the lent noise current 3.5 FIGURE value decision as ofapproximate level the obtained be can or keying DQPSK (CPFSK) or continuous-phase frequency-shift converting amplitudes. to and signals of DPSK difference receiver phase (B2B) the to-back for of of abalanced detecting photodetectors pair or aback- aphotodetector from scheme, output detection of that the the derived from and general be can is noiseshown in equivalentcurrent and the Figure 3.5, preamplification in signal electronic which of the shot noise quantum due the to noise current the and current physicalThe detected of representation the power, becomes SNR this equivalent the noise and current signal of power the that the is much LO ofWhen than larger the of 2 0 to where where The BER is optimum when setting its differentiation with respect to the decision level the to respect with its differentiation when BER setting is optimum The I Q 0

π is the Magnum function and and function Magnum is the is the modified Bessel function. If a decisionthe If a function. Bessel level “1” modified is the level,“0” and setdetermine is to and given and as

Equivalent current model at the input of the optical receiver, average signal current and equiva and receiver, average current optical of signal the input the at model current Equivalent < i BE 2 s

> Re d =+ ρ= AP opt δ 1 2 i p 2 sq =ℜ (, pI == PP ≅+ ρ () 2 ee 10 ρ 2 [( AP φ 2 δ σ 2 ) 2 ℜ+ is given is by Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises = 2 1 2 = σ s ρ δ 2 2 () Pt 2 2 πσ tP ss ρ ⇒≅ e qP =− δ= i −+ 2 Neq ℜ+ 2 )( LO () 1 2 ρσ Pn BE e 22 () LO   −+ ℜ 2 12 qB (c A sN ρρ Re ℜ P 22 s AS Qd 2

AA 2 PB K LO s − () 2 − P 22 Noiseless amplifier tn e LO )] 0    22 δ os + σ A + , 1 2 φ ρ 2 )/ i 2 y    − σ eq () +

() 2 δ t

/4

−

() Output voltage d v 2 / o 2 ( t   )

δ , and an an , and (3.15) (3.16) (3.12) (3.10) (3.13) (3.14) (3.11) - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical 3.3.1.1.2 3.6 FIGURE * is bit recovered the atthe represent to adifference “1”and coding adifferential or “0.” requires This 3.7, next of Figure of the in that bit, with one bit is compared carrier IF of phase the which the in as shown modified be can process detection The detection. differential the secutive is called bit; this next of the of that to con one-bit period bysignal carrier aself-homodyne the by process beating It is possible overall which receiver complicates using the the aPLL, mented detect to structure. imple usually is required, recovery circuitry acarrier detection, synchronous the in observed As 3.3.1.3 received of the probability “1” total BER the as the “0”: and We “1” of the that equal. be to obtain and can assumed “0” of the probability are the Furthermore, received of of the probability signal a “1” the assumption, Under statistical Gaussian the is given by as simplified be can signal received the electrical then carrier, signal ofthose the term phase time-dependent the in is contained information The received is given signal signal. The bydetected of phase the (see the detection BPF, track to 3.6) is used the Figure mixer but after electrical an 3.4 of Figure that to for heterodyne is similar Under detection PSK the the modulation format, 3.3.1.2 detection using synchronous detected ASK be can

locking of the local oscillator to that of the carrier. of the that to oscillator local of the locking phase the with association in oscillator local astrong and signals the by mixing implemented is detection Synchronous When the phase and frequency of the voltage-controlled oscillator (VCO) voltage-controlled of oscillator frequency the with and matched phase the are When Signal input

PSK Coherent System Coherent PSK Differential Detection Differential Laser (LO) Synchronous Detection

Schematic diagram of optical heterodyne detection for PSK format. detection heterodyne of optical diagram Schematic rt () PM optical coupler =ℜ 2 PP sx LO cos[ a pr rt n () () () BE t BE () ωϕ =± =ℜ = R IF R 2 AS (electrical) 1 PSK tt 2 K ++ 1 πσ − BPF S PP = ≅ () sn 2 * 2 1 and the BER is the given and by e 2 1 LO ]c erfc −− erfc (( at ru nt () () δ )) 22 δ / os + /2 2

σ

() n ωω x recovery

Carrier

Mixer IF φ ( t ). + nt y sin( IF )

LPF (3.20) (3.17) (3.21) (3.19) (3.18) 47 - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 given by BER signal. baseband is the of the limit ultimate the and signal, baseband transmitter and an additional phase comparator for the recovery process. In later chapters on DPSK, chapters later for In recovery process. the comparator phase additional an and transmitter 3.7 FIGURE 48 There are a number of formats related to FSK depending on whether the change of the frequencies change frequencies of on the FSK to whether the related of a number depending formats are There bits “1” the “0.” determine of and components two that FSK frequency on the is based nature The 3.3.1.4 detection. erodyne het of double-sideband due the the to nature of its counterpart is half detection ofbandwidth the the and heterodyne, of the that than better sensitivity is atleast 3 dB The homodyne of process the is given and of detection asynchronous by that as BER same is the The (power) SNR Hence, the is given by where expressed as be delay BERoptical can The line. delay of the the time for section tuning athermal with delay (MZDI) MZ ofform interferometer an in comparator aphotonic via phase photonic domain is implemented in decoding differential the by approximated be can current this function, over transfer of bandwidth the dB integrating the filter. ofthe powerthe signal, amatched that As and than LO is the much of preamp larger tronic where Signal input The noise is dominated by the quantum shot noise of the LO, with its square noise current shot noise noise LO, current of its the with by quantum square the noise is dominated The s H

( t (j ) is the modulating waveform modulating ) is the and PM FC FSK Coherent System Coherent FSK ω

) is the transfer function of the receiver system, normally a transimpedance of the elec of the receiver of atransimpedance the function system, transfer normally ) is the Schematic diagram of optical heterodyne and differential detection for PSK format. detection differential and heterodyne of optical diagram Schematic Optical delay s ( line t − T PM FC

) Laser (LO) PM FC i Ns 2 − r sh () tP =ℜ BE =ℜ Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises 2( BE qP R 2 S i N 2 NR homodyne − A Re sh k DPSK represents the bit the “1” represents or “0.” is equivalent the to This  ≡ sk + (electrical) PA 2 δ LO PH − qP ≅  e BPF LO ℜ ≅ cos[ 1 2 2 )( ℜ qB ∫ LO ∞ 1 2 0 erfc P B π s −

δ

jd st δ ωω ()

) 2 ]

recovery Carrier

Mixer LPF (3.26) (3.25) (3.27) (3.24) (3.22) (3.23) - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical FIGURE 3.8 FIGURE pass filter, PLL pass 3.9FIGURE may also be used. This modulator is excited by the output signal of a VCO whose frequency is VCO a of frequency whose is excited modulator signal output by This the used. be may also modulator. However,optical is preferred. Asingle-sideband modulator optical adouble sideband sideband use of component the it modulated via the the to by signals of shifting the frequency rier of development arecent ture [4] 3.10. is shown Figure in car is locked the frequency into LO The whose OPLL, struc Implementation an of such asystem9 photons/bit. require would normally of would detection give type sensitivity, LO. of high avery the that This and principle, of in carrier signal of the frequency of the matching phase the requires homodyne detection Optical 3.3.2.1 is thereforeandformed. decision a circuitry filtered is then signal electrical resultant The aPLL. via waves carrier signal of locked the that with are LO, phase the whose and with frequency is mixed receiver optical A schematic of 3.9. is the shown Figure in signals fieldoptical incoming The the of signal. phase LO of the that to phases signal transmitted the matches homodyne detection Optical 3.3.2 states. these is continuous between phase keying spacing, the modulation frequency scheme. At this minimum-shift the as termed be can preamp. optical an as used may which be amplifiers, or optical by contribution LO phase the the it wouldbecause eliminate structures receiving balanced the with compared as preferred is indeed discrimination frequency receiver The for used. balanced be PSK and can detection discriminator frequency the CPFSK, both the signals. For to used are extract filters 3.8, shownnation band as Figure which two in in narrow discrimi frequency of dual by astructure performed isnoncontinuous usually detection FSK, the bits is the continuous or noncontinuous, FSKrepresenting the or CPFSK For modulation formats. When the frequency difference between the “1” and “0” equals a quarter of the bit FSK of the the rate, “1” aquarter the between difference equals frequency “0” the and When

Signal input s O ( t Detection and OPLL and Detection ) Signal input ptical

Laser (LO) Schematic diagram of optical homodyne detection of FSK format. detection homodyne of optical diagram Schematic General structure of an optical homodyne detection system. FC detection homodyne optical of an structure General = phase lock loop. phase H O oscillator (LO) FSK detection m PM optical O coupler dyne Local

d etecti FC PD O n PLL − ve (electrical (electrical Elect. pre- BPF BPF amp f f 2 1 LPF ) ) Envelop Envelop Det. Det. sampling Decision/ = fiber coupler, LPF fiber → DSP LPF LPF = low low 49 - - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 close of confusion the the sideband loop ease suppression. locking. This 50 where of driven signals with voltage the and point level transmission output VCO of atthe the minimum the is adjusted to Aclose at loop carrier. is biased modulator intensity would the to astable the locking. ensure If would exhibit lightwave. LO two the sidebands and components would of locked be One these then modulator of the lightwaves the modulating modulator intensity LO. output of spectrum an the The voltageThis level fed a VCO to is then a sinusoidalgenerate to wave modulate to used is then that carriers. two optical the between range extend it locking so can that the is important modulator optical of bandwidth ing. the The stage voltage offinal lockthe levelreached the has OPLL thus and output filter of atthe the is there nozero, is difference frequency the filter.When electronic of passband the the within falls carrier signal the to respect with difference frequency region the the such to that tuned voltage level is normally LO of modulator. of frequency the the electrode The the for driving by voltage the level determined BPF electronic output of of required the an condition the meet to OPLL. an solid)(continuous using and 3.10FIGURE be can where system. baseband of the that as same is the rate error the Under a perfect phase matching, the received is given the signal matching, phase Under by aperfect Any frequency offset between the LO and the carrier is detected, and noise is filtered by the LPF. noisethe and isby filtered is detected, carrier the and LO offset the Any frequency between The shot-noiseThe power signal expressed power as be the and can by LO induced the a H k takes the value the takes () j ω

Signal input s ( is the transfer function of the receiver of the function whose transfer expression, is the filtering, amatched under if t Schematic diagram of optical homodyne detection—electrical line (dashed) and optical line line optical (dashed) and line detection—electrical homodyne of optical diagram Schematic ) modulator translator sideband (MZIM) Laser Opt. (LO) π ± 2 1, and phase shift with each other, we each with then would suppression shift have phase and carrier Optical PLL PM optical coupler s ( i i t NS 2 ss ) is the modulating waveform. thus modulating and signal, ) is the is a baseband This () tp =ℜ H =ℜ 2 () Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises qp j 2 Locking signalcarrierand ω frequency shiftandLO () 2 = s + PD controlled    oscillator Ps Voltage PH LO sin( LO ω co ω ∫ T ∞ 0 s( T / {} 2 /) πα 2 () j ωω k    2

t d ) LPF

Electronic amp and decision (3.30) (3.28) (3.29) 2 V π -

Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 of current signal normalized would or counter-phase LO, homodyne it detection such in-phase the the give with that acts lated a modu is perfectly signal phase the that signal. Assuming locked phase the to be to is assumed and frequency and amplitude, field signal polarization, in incoming way the matches special very that a in is used LO the case, achieved. this be In can limit For a super quantum homodyne detection, 3.3.2.2 the PDF is related to this linewidth conditioned on the deviation conditioned on the linewidth PDF this to the is related and deviatesIF dueto a phase fluctuation, the is significant, light sources of the linewidth the When 3.3.2.3.1 3.3.2.3 symbol. 3.3.2.3.2.1 3.3.2.3.2 nals, then the current can be replaced with 4 with replaced be can current the then nals, is SNR the Thus, where sity and sity and where [5] as written deviation be afrequency can under PDF IF ofThe the that further Assuming

Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical ing signals in the PD between the incoming signals and the LO would LO electronic the give and signals beating the incoming PD the between the in signals ing beat the then domain, electrical the in If domain. electrical the or in domain optical the either in BER the is and p s , the total probability of error is given of error probability as total the T Dυ

is the bit period. Then the noise power the Then bit is becomes the period. T

is full linewidth at the full width half maximum (FWHM) of the power spectral den power of the spectral (FWHM) maximum half width full atthe linewidth is full Quantum Limit Detection Limit Quantum Linewidth Influences Linewidth is the bit is the period.

Heterodyne Phase Detection Differential Phase with Detection LO DPSK Systems nn p i NS 2 = i sC P =ℜ

E LO =+ qp =→ The DPSK detection requires an MZDI and a balanced receiver abalanced and MZDI an DPSKThe requires detection , the number of number photon the for for LO sig the generation of detected 2 1 2 1 T () p erfc P IF   ss S EC  () + NR ∂= =∂ () P ω 22 −∞ ∫ LO ∞ SN nn = Pp p T qP 1 RB 22 (, ℜ ℜ ∆ n  s p pP υ 1 LO for the detection of for detection a“1” the for a“0” nothing and qP ss BT ℜ ωω LO / LO T T )( ER e   LO p 2 −∂ IF = () = when ωπ ∂∂ fo 2 erfc / pT q 4 r ) ∆ υ ω ()

B 0

δ pP SN ≤≤ ω tT of the IF. of the For power asignal of R

LO

(3.36) (3.35) (3.34) (3.32) (3.33) (3.31) 51 - - - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 given be noise phase [8] can as quantum the phase noise due to shot noise of the generated current and the third and fourth terms are the quan the are terms fourth and third the and noisephase due shot to current noise generated of the the 0 value or takes and data the the phase of is term first The phase The [6] expressed as be can current signal dyne up. hetero is The delay split. which branch summed is then One then by and one-bitcurrent, period 52 0 to 2 MHz. 0 to for from DPSK linewidth laser of at140 Mbps the modulation format variation the bit and rate (orrate bit the relative rate) and the linewidth laser of 3.11 bandwidth is shown the Figure in receiver the sensitivity, bit against is plotted the of and error linewidth of product the the and received of the power. afunction as gives of equation error probability probability the This The 3.39, Equation into we obtain 3.40 Substituting 3.41 Equations linewidth. and FWHM LO the and transmitter of sum the is the where [7]. LO the and transmitter the noise from generated where is given of error probability by signals. The the shot noise and LO duetum the to

where The probability of error can be written as written be can of error probability The Γ D p () n is the phase diffusion constant, and the standard deviation from the central frequency central deviation the from standard the and constant, diffusion phase is the . () . is the gamma function and is the modified Bessel function of the first kind. The kind. PDF of first the function Besselof modified is the and function gamma is the φ φϕ is the PDF noise shot is phase the of due noise the to the and s ss () () t tt is expressed by =+ i ss () () tP P E =ℜ a pa =+ m Nm {} 2 ϕϕ ()  22 1 φφ NN 12        () −= tt 2 ρρ LO m −+ e − P − 1 pt En ρ ΓΓ ∑ =−    n cos( () 2 ∞ = m Γ 1 0 −− π π ∫∫ p ∆ π 2 [] / + 21 Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises / () q 2 m +− 2 υυ ωω Tt − () n 1 φ ρ IF 1 + =+    + 1 ∞ ∞ e π 12 n ∆∆ −− − ++ = pp ρ    e {} φ m −+ ∑ ϕϕ () 2 RL m sx () φφ ∞ () 21 = 2 pS 12 tn + nT 1 πτ 1 () 1 )( D    υ 2 πυ co    ∆ II e = mm s( φ q pS −+ 1 tt () ()    2 2 12 / )c D φφ m 2 /( () II π D 11 tT nn os ρρ τ −+

+ φφ

∂∂ 12 12 /( + 22 IF π φ . The second term represents the the represents term second . The + −− )

− 12 {} )/ nt p ϕϕ q y pL 12 () (. 2 )/ ) ()    is for the quantum phase phase is for quantum the tt si        ρ 2 n

   ω 2

IF pL t (

+ T )

(3.37) (3.40) (3.38) (3.39) (3.42) (3.43) (3.41) - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 and bit period—bit rate bit period—bit and 930–932, March 2004. With permission.) With 2004. March 930–932, S. T. Savory from and Hadjifotiou, Bit 10 Gb/s (Extracted rate channel. per linewidth. fit zero for linear the is line dashed BER. The double to the required that and linewidth of zero cases 3.12FIGURE penalty. is a0.1-dB impact the if neglect to being doubleto linewidth bound tighter SNR BER the with the a10 in source is a laser GSymbols/s impact the if is system. neglect to loose bound linewidth The 3.12 shown as Figure in of error probability the [8]. 3.13 Figure of linewidth shows maximum the would laser influence not significantly transmitter of the of up linewidth 3 MHz to shown the that self-coherent which It been detection. No means has is used, LO studied. DQPSK been also has for detection Recently, for DQPSK requirement differential linewidth modulation and laser the 3.3.2.3.3 BER at receiver sensitivity of optical (b) Degradation 3.11FIGURE Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical With permission.) With (a) BER 1e–12 1e–9 1e–6 1e–3

− 70 Differential Under Phase Self-Coherence Detection

Analytical approximation (solid line) and numerical evaluation (triangles) evaluation BER for (solid of the the numerical line) approximation and Analytical (a) Probability of error versus receiver sensitivity with linewidth as a parameter in MHz. MHz. in aparameter as linewidth with versus receiver sensitivity (a) of error Probability Rec. sensitivity(dBm)

− log10 (BER) − − − − − − − − − 0 10 1 0 3 2 1 9 8 7 6 5 4 = 140 Mb/s. (Extracted from Nicholson, G., from (Extracted 140 Mb/s. − 2 60 3 4 Δ 1 M v 2 M = 51 0.5M − 50 01 = (b) 52 10

γ ΔP (dBm) b R – 0 2 4 6 9 for DPSK systems as a function of the linewidth linewidth of the for DPSK afunction as systems 0 σ σ σ σ σ 02 ψ ψ ψ ψ ψ =1/γ =1/γ = = = 0 (Linearfit) 0 (Analytical) 0 (Numerical) b b Elect. Lett. Elect. (Analytical) (Numerical) 53 IEEE Photonic Technol. Photonic IEEE Lett 0.005 , 20/24, 1005–1007,, 20/24, 1984. 0 Δν .T 0.01 ., 16,

Asymptotic limit 53 Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 54 Technol T., Masumoto, and K. Iwashita, from (Extracted detection. of FSK differential relationship 3.14FIGURE domain. electrical backsignals the to 3.14b.relationship Figure in is employed, detection heterodyne the If aBPF then bring to is used is shownin Figure 3.14a, configuration ferential detector conversionthe and frequencyto of voltage noise deviation, phase [10]. frequency detector, and the differential 3.8, dif Figure to the Similar consideration delay into of the the line of derived CPFSK ofby be error probability taking can The 3.3.2.3.4 Electron 0.1 dB Y. penalty. from Bit SNR 10 GSymbols/s. T. rate Yamamoto and (Extracted Kimura, a is impact the if linewidth neglect to being bound tighter the BER double with to is the impact the if linewidth 3.13FIGURE ., LT-5/4, 1987, 452–462, 1. permission.) Figure With ., QE-17, 919–934, 1981. permission.) With

Differential Phase Coherent of Continuous Detection Phase FSK Modulation Format

(a) Configuration of a CPFSK differential detection and (b)to and voltageconversionfrequency detection (a)CPFSKdifferential of a Configuration Criteria for neglecting linewidth in a 10 GSymbols/s system. The loose bound is to neglect neglect to is a 10 bound in loose GSymbols/s system. The linewidth for neglecting Criteria (a) (b) Photodetected Maximum linewidth for a 10 Gbaud system (MHz) 20 10 12 14 16 18 current 0 2 4 6 8 − 9

Baseband output voltage − 8 BPF Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises − ω SNR penaltyislessthan0.1dBcriterion Phase noisedoublestheBERcriterion 7 c =( ω m 2 Δω log =π/τ n + Delay 1 10 − )π/ (BER) 6 2 τ τ − 5 IF frequency − LP 4 F − 3 IEEE J. Lightwave J. Lightwave IEEE IEEE J. Quantum J. Quantum IEEE - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 obtain of case DPSK the to system, 3.40 3.41 substituting Equations and Similar 3.45, Equation into we for “1” the carrier symbol, the or “0”

where at aBERat of 10 f2). and f1 (b) between Receiver power spacing penalty frequency maximum and deviation frequency between as of error pulse period or bit period. The modulation index parameter modulation index parameter The or bit period. period pulse data symbol. data values the of shot noise takes and quantum LO the and noise transmitter due the to where FIGURE 3.15FIGURE modulation index the and degradation of the power penalty to achieve the same BER as a function of the linewidth factor power linewidth of of achieve BER to the the afunction degradation as same penalty the deviation. 3.15 frequency Figure deviation maximum frequency the to shows of dependence the 452–462, 1987,452–462, 4. permission.) With 3and Figures T., Masumoto, and K. Iwashita, from noise. (Extracted phase LD ing Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical The detected signal phase at the shot-noise limit at the output of the LPF can be expressed as be shot-noise output LPF can of atthe atthe the phase signal limit detected The Thus, by integrating the detected phase from from phase detected the byThus, integrating τ ω is the differential detection delay detection time, differential is the P m α is the deviation of the angular frequency with with frequency deviation is the angular of the E = =

(a) – 1 22 πβ 9 (a) aBER at of of 10 receiver power penalty Dependence as a function of the product of the beat bandwidth and the bit delay time—effects exclud bit delay the time—effects and bandwidth beat of the product of the afunction as () ρρ Power penalty (dB) 1 0 1 2 3 4 5 2 e 1.0 − − ρ ∑ n ∞ = 0 an Modulation index 21 () β − n d . 1 = n β P e En == −+ φ with () =− () 21 ∆ ω tt n π ω −− m − =+ ∆ 2 φ ∫∫ 2 ∆ ω πυ 2 ω ω ( ∆ ωπ τ β t τ / 2 cn ) is the phase noise shot phase due noise, the ) is to the 2 cc τ πτ    == −∞ ∞ II at 22 / nn T −+ pp 0.5 12 0 fn ∆ /( () 2

ω φφ ∆ 22 − (b) 12 τϕ ω + ∆∆ Power penalty (dB) () 22 ++ 10 is the deviation of the angular frequency of frequency deviation is the angular of the ω 0 5 0 τπ + () 12 1 q )/ () φφ m − 2 π → ρ 11 ϕ τ the modulation index, and modulation index, and the b ∂∂    n β⋅ is defined as the ratio of the actual actual the ratio the of as is defined 2 () 0.7 t e IEEE J. Lightwave Technol. J. Lightwave IEEE −+ Δυτ

φ () 1 21

n ω (10 – 5 9 τ on modulation index index onmodulation 2 , πυ − we obtain the probability probability the we obtain ∆ 3 β⋅ ) τ 1 co s( {} 21 n n 10 + ( ± t ) is the phase phase ) is the 1, the binary 1, binary the ) α T

, LT-5/4, 0 β is the is the (3.46) (3.44) (3.45) (ratio (ratio ∆υ 55 τ -

Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 56 CD, PMD, fiber nonlinearities. and including of presence fiber-degrading effects systems the in transmission of the performance the improvealsoto systems and overcome to communication coherent optical of difficulties OPLL, the tion of systems. DSP-based communication coherent optical carrier. signal of the that and LO of OPLL the frequency for of the an availability stable locking and LO above would described improvementCoherent offer techniques significant but setback a the face dueto 3.4 next the few in (see sections 3.21).described Figure also diversity is detection This photodetectors. by abalanced detected are signals mixed the then and a with mixing received and the channels and LO of the polarization the oversequences lines. fiber noncompensating long very transmission cycles the slips in are advantage when of would there an ing bits due walk-off to gain pulse of the decod differential the reception, DSP-based in For used coherent reception. be differential-based can format or nondifferential simpler differential electronics. Either require reception intradyne of range of devices, operation frequency a electronic large homodyne and whereas would require domain digital [12].the ferencein without much difficulty Obviously,detection the heterodyne system coherent reception dif would DSP modern able the in be this extract to Furthermore, CoD is more realistic. intradyne Thus, by of afew is KHz. varied frequency hundreds central the and hence mirror, reflection is locked the frequency stably laser by the oscillating time, of the Most source. of the due exact, jittering to be sometimes cannot LO the and carrier oflocking the 3.16 Figure in illustrated as signal baseband ofbandwidth the [11]. Naturally, control and the signal the within lies is and nonzero, carrier central offset)frequency the and LO the between IF, the LOFO ((LO) difference, or the frequency the detection, intradyne In paths. phase and polarization due is considered different to as path receivers, optical optical the In one path. than over transmission the more describes that links diversity transmission is well radio in known term The required. locking phase no with optical reception heterodyne and bandwidth processing signal diversity phase receivers advantagesOptical minimum homodyne of with combine the the 3.3.3 3.16 FIGURE DSP play have and key widely communications wireless implementa been roles in the used in achieved be by can using a polarization diversity and The phase in

SELF-COHERENT DETECTION AND ELECTRONIC DSP O ptical

Spectrum of CoD (a) (c) and (b)Spectrum homodyne, intradyne, heterodyne.

i ntradyne

d etecti − f IF f IF

O

− Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises n B f IF f

IF +

B DSP techniques haveDSP to applied techniques been π /2 hybrid/2 coupler splits that π /2 optical phase shift, shift, phase optical /2 - - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 can show the can that it thus is computations, more feasible and systems. of processing Intuitively real forlinear online one CD, PMD, and nonlinearities for both single channel and DWDM for and single systems. channel both CD, PMD, nonlinearities and includingeffects, presence the of in fiber-degrading systemstransmission the significant for be can PSK improvement QAM The and formats. systems M-ary using by different DSP receiver atthe end In addition, nonlinear phase noises phase always exist long-haul nonlinear addition, in In systems Gordon–Mollenauer due the to scheme. of processing the for real-time potential further would operations limit system. Such nonlinear the taking as conjunction receiver. acoherent with optical such operations, However, nonlinear scheme requires this [13,18]in PSK the to signals received the M-ary raise to OPLL for using an demodulation. Conventional than rather block attractive increasingly becoming converters (ADCs) are DSP baseband units high-speed to-digital and receiversmaller [19]. bandwidth coherent receivers hand, employing analog- other the On high-speed a sensitivity requires offers homodyne and detection better above. detection, heterodyne to Compared receiver detection mentioned as aheterodyne in signal electrical IF an to signal optical converting the down-loop delay after [18]. phase large is too carrier the track to PLL option is electrical use to Another and linewidth product the of laser implementedbecause be to may quite difficult feedback be lasers uted However,homodyne detection. wavelengths atoptical OPLL operating combination an distrib with in in carrier LO the to respect with phase ent receiver, carrier the option initially, track OPLL to is an an scheme. for As coher this the coherent in receiver [17]. necessary is also encoding differential Further, conversion adigital to analog-to-digital higher compared resolution as more DSP and power required are improve to however, PSK system the is introduced performance; M-ary differential ofdetection optical receiver cause apower the to which sensitivity. will lasers, penalty result from Aself-coherent multisymbol noise Phase information. phase receivedcan modulated retrieve to the signals with the beat to LO an PMD. and CD to ance systemMoreover, have the can toler is reduced, symbol ahigher rate the bit for because same rate, the in [22]in show such that effect [20], system optical [21]. of aphase-modulated which severely performance the affect results The and even QAM with CoD, which can increase the spectral efficiency evenand by a spectral QAM factor the of CoD, with log increase which can efficiency of spectral up the to Nyquistthe limit), multilevel with modulation formats (which is called to 1 bit/s/Hz/polarization limited is modulation efficiencyformats of binary spectral by coherent receiver. using the the multilevel introduced be can While modulation formats phase system improve [13]. receiver IMDD can the the with sensitivity compared and (3) detection roll-off characteristics; of phase ability the having filters sharp electrical with rated sitivity achieved be asufficient with power; can LO (2)sepa be can closelyWDM channels spaced Processes Noise and Reception Coherent Optical the photodetector responsivity. photodetector the Underthe that CoD, noisesof be must amplifier much than the less on derived based be can OSNR therefore the and SNR optimum so that signals ofdetection optical receiver stage an optical of preamplification as a plays amplifier a electronic major the The in role 3.5.1 3.5 of of noise. phase algorithm The receiver the improving nonlinear cantly sensitivity the to tolerance and signifi thus noise phase is dominant, nonlinear when the especially detection, ventional differential mate the ideal synchronous CoD in optical PSK optical CoD systems. synchronous in ideal The the mate ML However, noise phase when one major of using CoD the challenges is overcome to in carrier the The maximum-likelihood ( maximum-likelihood The Coherent optical receiversCoherent optical have following the advantages: (1) shot-noise-limited receiver the sen

i phase estimator is expected to improve the performance of coherent optical communication of communication coherent optical improve to is expected performance the estimator phase ELECTRONIC AMPLIFIERS: RESPONSES AND NOISES ntr M O ducti th power,th resolving and the ML O estimation receiver outperforms the the receiver estimation outperforms M n th power noise. may phase th not effectively PE techniques nonlinear with deal ML N bits/s/Hz/polarization. Recent research has focused on M-ary PSK focused on has M-ary Recent research bits/s/Hz/polarization. ) carrier phase estimator derived in [23] derived in approxi to estimator used phase be can ) carrier ± 2 π / M phase ambiguity, which incurs a large latency to the ambiguity, phase latency alarge the to which incurs N M bits of information per symbol can achieve symbol can per bits of information th power to estimate the phase reference in reference phase power in the th estimate to M th powerth con and block estimator phase ML M th powerth PE scheme is proposed phase estimator requires only only requires estimator phase

In addition, any kind of any kind addition, In 2 M [14–16]. M 57 ------

Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 verted to electronic current in the photodetection device, the photodetector of device, either photodetector p-i-n photodetection or the APD, the in in current electronic to verted con be must signals domain the optical sequence. So, and shapes atfirst, original of the properties equivalentelectronic followed signals, recoverto andprocessing and sampling by amplification circuit. amplifierdesign the allowablethe electronic and hence of stage by preamplification the density noise electronic spectral maximum the responsivity we determine photodetector of can the power optical receiver available signal assumed the optical of of front the and the the with atthe then for modulation any specific format, receiver atthe is determined required OSNR the if hand, the other On inputreceiver, the the the OSNR. optical stage at then of the and SNR without difficulty average the with and is known, power, signal current this we obtain When can receiver is determined. found be overall when of equivalent input bandwidth can the the atthe density total is found, the current density this is derived. Once current is which found, the from source equivalentan current thus and amplifier the of inputvoltageport the to referred are sources) elements of amplifier of all the density, (current noise equivalent and sources the input noise total is, spectral all the that stage as as as well lowamplifier wideand noisebandwidth. preamplifier the the noise of define We electronic Section 3.7suppression in feedback the in technique for design achieving stability strategy the with design of a single input single detailed output noise the with but address input TIAs, differential (TIAs). amplifiers low-noise on and concentrate We high-gain, transimpedance ultrahigh-speed, to above average signal of the that power. breakdown levelbreakdown of the reverse-biasing Similarly, worksgeneration the APD with of level an current. close reverse the to either to sides in resulting diode, of the attracted holes and electrons are thus and diode, biasing the region this fieldreversein by electric Ahigh established is occurs. signal of optical absorption the a with is structured detector p-i-n law” “square The detection. power name the to hence the signals, optical of the proportional positive- the to negative-biased and respectively. electrodes, isattracted current generated the Thus, holes active are and power electrons generated the optical which region in both the and is absorbed quantum shot noises contributed by the high power shot by high noises the contributed levelquantum of the 58 as “a long-tail pair” instead of a single transistor stage for the former type TIA. of stage for type former asingle transistor instead the “aas long-tail pair” termed pair transistor using designed adifferential is normally type later The two-port. differential inputor a provide the a port single at amplifiers by the whether distinguished are They input TIA. differential and single input TIA by term the distinguished and Two described are of TIAs types 3.5.2 remarkable. The design is scalable to ultra-wide-band reception subsystems. design is reception scalable ultra-wide-band to The remarkable. is bandwidth this transistors, of the frequency transition limited with only of afew MHz, hundreds is frequency corner noise feedback including the mentation, control reduction. and the Although stability [24–26]. feedback would the that ease input reasonable hence impedance input high and at the pair tail transimpedance gain ( gain transimpedance offers much higher input TIA differential The port. acomplementary with differential be can output single ports output. and The inputs two single differential and inputthe single output port two noise types, level the though are there type, higher. be might With TIAs, impedance high as it than muchpreferred wideis wideroffers band, type amplification transimpedance signals, band and wide amplifier, type. ahigh-speed For main by a gain voltage amplified further then and and must sufficientlyhighgenerates low be a that noisesufficient so be obtained can voltage signal avalancheabsorbed. are flow the in signals the optical when Thus, this section gives an introduction of electronic amplifiers applicable widefor of givessignals amplifiers section band electronic introduction an this Thus, The principal function of an optoelectronic receiver optoelectronic of is convert to into an received function signals the optical principal The In Section 3.3, design imple to In the from study of receiver a case coherent optical is described This photogenerated current is then fed into an electronic amplifier whose transimpedance transimpedance whose amplifier electronic fed an into is then photogenerated current This

W ide B and

tia Z pn T ) and wider bandwidth as well. This is contributed to the use of use along- the to is contributed well. as wider bandwidth ) and This s junction (no intrinsic layer) so that electronic carriers can be multiplied be junction can (no layer) intrinsic carriers electronic so that p + and and n + Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises :doped regions sandwiched by the intrinsic layer:doped regions which by intrinsic sandwiched in the L O, which is normally about 10 dB which is normally - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical differential group delay may be serious and must be compensated in the digital processing domain. processing digital the in delay group must compensated be and may serious differential be DSP. and ADC with interconnected The (RF) frequency radio then and integrated be can APD p-i-n or high-speed then DSP. and InP implemented ADC in if and detector hand, other the On Ge-APD ahigh-speed with integrated be can advantage circuit of SiGe The the is that material. and the resistance of electronic element occur. This type of noise depends on the ion temperature. of ion noise on the temperature. of depends element electronic type resistance the occur. This and is well at which above movement no random absolute temperature the ating temperature of electrons noises result oper when the Thermal detection. optoelectronic in shot noises, especially quantum and noises, systems, shot any electronic several noises, which in include noise are sources thermal There 3.5.3 transimpedance high the locus network offers of thus the pole. stability of the This limit up the to increased be can resistance feedback stable. be the output stage Thus, can the feedback from the thus and input impedance high avery has pair This operation. mode different maximum rejection mode and common minimum is employed pair input stage. at the or differential Two the ensure to used are transistors matched 3.17, is shown Figure in input TIA example differential ofAn circuit the pair which along in tail 3.5.2.2 reasonably and low noise. transimpedance large with treated is low-noise and TIA inputa wide band differential the the nextIn amplifier.section, of demonstration experimental the We adesign as example section describe and this prefer treat to 3.5.2.1 FIGURE 3.17FIGURE from H. Tran, et al., al., et Tran, from H. image of the ofimage the (see bandwidth 3.19), Figure 3 dB 30 GHz with 3.18 shown as Figures in 3.19. and chip the Also a

Out

To LAstage Single Input, Single Output Single Input, Single Differential Inputs, Single/Differential Output Single/Differential Inputs, Differential mplifier 2 T

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T 200 pH

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dB(ZT28rx) dB(ZT32rx) 50 60 10 20 30 40 0

05 Differential amplifier: frequency response and differential group delay. group differential and response frequency amplifier: Differential Differential amplifiers: (a) chip level image and (b) referred input noise equivalent spectral amplifiers: equivalent spectral (a)input(b) noise and level chip referred image Differential 10 15 Freq (GHz) 20 25 30

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51

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dsp DSP SYSTEMS AND COHERENT OPTICAL RECEPTION S current referredtotheinput NR

- Total equivalentnoise a Equivalent noise spectral density current sources. current density noisespectral Equivalent = ssisted current square_of_current_generate current Signal Signal

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d etecti square_of_current_generate O n d ++t otal_equivalent_noise_current_power amplifier Noiseless amplifier Noisy d

(3.47) 61 - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 demultiplexing of polarized modes in the optical waveguides. optical the diversity in phase modes demultiplexing The using a90 of polarized the facilitate inputs LO and signal atthe splitters beam diversity polarization the with section 3.21b–d. shown diversity Figure in the polarization are hybrid The coupler domain optical in DSP with of such 3.21a. systemsshown reception Figure incorporating in structures the Further, diversity phase and employed. receivers are polarization schematics of such The receiver are available time must for effective be processing. algorithm processing due limited to real-time the that is processing offline and real-time between difference main implementation. The aDSP. in processed are signals intensively DSP are for Currently, real-time practical researched digitalized the then and ADC by sampled ahigh-speed received analog are signals the signals, conversion optoelectronic the that the fieldof and LO the total of after of the DSP is incorporated 62 noise suppression is given Section 3.7 techniques in 3.23). (Figure receiver and circuit electronic balanced optical of an design, measurements implementation, and receiver. balanced study of the A case effects the in unbalancing and mixing polarization imperfect due receiver. of to bandwidth its the degradation receiver and objective the penalty Our is obtain to to the extend equalized further and type transimpedance using a is amplified current electronic the then and B2B connected two into then photodetectors launched output fields are The 2. 1and ports coupled are via a coupler fieldsLO andfiber optical the Consider two the with signals output of that givessection analysis of the receiver systems.transmission for fiber coherent optical synchronous This techniques. transmission heterodyne PSK homodyne and the scheme both under especially system, for transmission sensitivity the The heterodyne. of coherentand receiver important is also self-coherent, or homodyne direct, be can detection The line. transmission fiber alongserves the lightwave of phase the the thus, con modulated; must externally bit laser be the rate, At ultrahigh 3.6.2.1 3.6.2 for clock for function, example recovery can within algorithms which the within limit a to certain carrier signal of the that and LO offrequencies the lock to the 5, Chapter it in is necessary described as locking phase optical of processing soft the the DSP-based the coherent in receiver.of DSP possible the Besides incorporated in phases processing 3.22 Figure shows algorithms. processing of these aschematic aspects fundamental the detail in describe 6will so on. Chapter and sequence clock data the of for the and rate phase resampling rier recover to car and the medium, guided optical the propagation signal effects due through optical to distortion nonlinear and employed be for stage compensate to can linear this cessing in algorithms of anumber pro Thus, conducted. be “soft can domain” the fetched in DSP into processing and then are signals digitalized These domain. digital converted to signals analog the and conducted be right can the level that sampling to these so ADC signals boost to the is used of amplifier gain avoltage- avoltage output. Further, so derived that atthe be PDs can is fed signal aTIA into nected B2B the con from generated current asingle to PD The detection. compared as betterment 3 dB 3.21b. Figure in achieved, be a hence Two can operation B2B push–pull so that connected PDs are receiver optoelectronic shown as coupled abalanced into are Q- I- of and negative the and parts by hybrid coupler, the separated positive the components are Q-optical I- and the and polarization schematic of coherent receiver synchronous The on DSP based 3.22. is shown the Figure Once in 3.6.1.1 multiplexedpolarization channels. modulation scheme or dual QAM for the modulators using single I-Q polarization described has sensitivity. the in gain Section 2.7 B2B a3 dB hence and 2 of Chapter connected pair detector nents of QAM Using channels. a2 (Q-) (I-) inphase of compo quadrature phase the allows separation and the shifter phase optical When polarization division multiplexed (PDM) QAM channels are transmitted and received, and division multiplexed polarization transmitted When QAM are (PDM) channels c

DSP-Based Reception Systems Reception DSP-Based Sensitivity OH erent

r ecepti O n

a nalysis × 2 coupler also enables the balanced reception using photo reception coupler enables 2 balanced also the Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises ± 2G Hz . ° ------

Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 Communications Conference (OECC) TuA-4, ’08, Paper Conference pp. 1–2, Sydney, JulyCommunications 2008.) Australia, and OptoElectronics DQPSK system. In optical coherent in estimation phase likelihood maximum aided Adaptive al., et decision- S. Zhang 2008; December Singapore, C3-4A-03, ’08, Global Paper Photonics In PSK system. optical coherent in estimation of phase A comparison al., et S. Zhang from (Adapted estimation. Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical TE mode. FS mode. TE TM mode, polarized (H) horizontal (c). in of structure TE_V, ports eight output and TE_H ports (c) 90 hybrid diversity coupler, phase polarization one only receiver using optical (a)cations. (b) scheme, detailed Generic 3.21 FIGURE ° (d) (b) (c) (a) coupler for polarization and phase diversity, phase and (d) view two of input coupler ahybrid with coupler for typical polarization

= Side viewofpolarized Optical signal phase shifter; PBS shifter; phase Scheme of a synchronous coherent receiver using DSP for PE for coherent optical communi DSP receiver using for coherent PE optical for coherent ofScheme asynchronous maintaining fiber Laser streams LO Inputs from90 hybrid coupler Local oscillator Data signals

LO Signal E s ( E t L )

coupler hybrid 90 ° ° = Q = I polarization beam splitter; and MLSE and splitter; beam polarization transverse magnetic mode with polarization orthogonal to that of the of the that to orthogonal polarization with mode magnetic transverse PBS PBS Balanced Balanced Rx Rx π /2 optical LiNb0 delay 3 Side view I-Qmodulator Top view FC 70 mm qu FC ORx – O-comp ORx – I comp LPF LPF Balanced Balanced 90 90 = ° ° Im Re FS transverse electric mode with vertical (V) or or (V) vertical with mode electric transverse FS ( ( E E A/D A/D L L ∗ ∗ Fibers ( ( t t ) ) E E S S ( ( t t )) )) = (template M Q Q Q Q maximum-likelihood phase maximum-likelihood I I I I DSP Digital algorithms Processing − + − + algorithm − + − + previous

( ( ( ( events)

MLSE TM_V TM_V TE_H TE_H ( ( ( ( DSP TM_V TM_V TE_H TE_H TIA preamp Electronic I-Q ports I-Q ports channel channel ) ) H–pol. V–pol. ) ) ) ) ) ) 63 - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 izer. FC equal and port input from its seen as preamplifier electronic of the noisecurrent equivalent and current, signal 3.23 FIGURE control. feedback 3.22 FIGURE 64 = fiber coupler. fiber E

s E ( Flow of functionalities of DSP processing in a QAM-coherent optical receiver with possible receiver with optical aQAM-coherent in of DSP processing Flow of functionalities t Equivalent current model at the input of the optical balanced receiver under CoD, receiver under average balanced optical of the input the at model current Equivalent L ) E E s s ( ( t t FC ) )

+ + Optical phase locking E E < < of local oscillator and L L i i s s 2 2 carrier frequency > > i i 2 2 sN sN polarization diversitymixingLOandchannels Symbol recovery,decodingandevaluationof Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises Optical processingfrontend/phaseand Baseband signalsinelectricaldomain Equalization oflinearandnonlinear Mixing LOandreceivedchannels i 2 Neq Optoelectronic conversion Sampling andanalogto Timing/clock recovery Transmitted/received Multiplexed (PDM) Polarized Division digital conversion distortion effects optical channels performance Noiseless amplifier → Equalizer H E ( ω ) Output voltage v o ( t ) - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 given 2are as 1and powerstotal atports derived the by be combining 2can and with Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical as matrix respectively. where fieldas components polarized separate their with written couplerbe can directional via field a LO and combined The the signal of

K LY it s P E E analysis: in used commonly are followingThe parameters Thus, the output fields at ports 1 and 2 of the FC in the in andFC the 2 of 1 output fields the ports Thus, at St Z H Ne 2 it it ( NS are the intensity fraction coefficients in the coefficientsin fraction intensity the are T s L s s NS 2 2 t E , q ) α () () () P () () ω () ω defined as the intensitycoupler.the ratio coupling the of as 1 the Thus,field defined ports at components φ L mt

() represents the phase modulation, modulation, phase the represents    E E    φ with P P RY RY Mean squarenoisecurrent(power) producedbythetotalopticalintensityonphotodetector The modulatedpulse Optical power ofsignalandlocaloscillatorattheinputphotodetector Amplitude oflocaloscillatoropticalfield Amplitude ofsignalopticalfieldatthereceiver Voltage transfercharacteristicoftheelectronicequalizer followed theelectronicpreamplifier Transfer impedanceoftheelectronicpreamplifier Equivalent noisecurrentoftheelectronicpreamplifieratitsinput Shot noisespectraldensityof Mean squarecurrentproducedbythephotodetector E E p Rs Rs 1 2 1 2 RX RX = 1 2    =− =+ ta = PP P    n     = () α − 12 1        Kt KK αα PPP sY Kt K ps K Ls () () sX = ++ 1 sY 12 s K XXL −− −+ () α KK 1 sX Ls αω φ EK EK EK EK αα −− si αω mt XL KK sY sX Xs LY LX () nn( αω K cos( sin( sX +− =− =− =+ = ωα = X cos( sm X tK π 2 +++ LY PP it and and −− s 2 ssm Ks sm KK () tK sY sX sin( YL LY φ LX PK −− m sY Lp K Lp sm Et Et αα andlocaloscillatorpower () Et E φ Y φ tL () Ss Ss () δδ K t LL () YL L components from Equations 3.49 Equations components from 3.50; and the thus, )( 1 cos( cos( 1 LY () () Ls φ cos( tL ccos( tL m cos( −+ −+ − )( is the modulation depth, and and modulation depth, is the )s () X αω tL ωδ ω 2 and and )s ωδ ω δδ Kt ) L KK t ) sin( sin( sX φ φ X Y mt mt Kt YL s directions of the signal and LO fields, LO and signal of the directions -plane can be obtained using the transfer transfer using the obtained be -plane can () () L ) ω s ) LX 1    ( Kt ) XL YL + t IF IF ) αω KK 1 XL t s sY αω ) )c in αω φφ

φφ () mt os )c mt in LY () () () () os cos( ωδ +− +− + () t δ pc pe δδ L + t Ls φ φ     − L )    +     K E E    π ) L s sX E E )    ,

L s

K   

sY , K LX (3.50) (3.48) (3.49) (3.51) , and , and 65 Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 V decision is given circuit the to input signal or the by equalizer tronic the outputthe at elec of The signal preamplifier. electronic followedbandwidth equalized by an amplitude amplitude given. as would detected be two of product terms the only the and wavelength of the frequency of sum the the would with LO and detected signal not of be term the the Thus, sensitive of range the the current. would electronic photodetector the ofwithin produce the that power.frequencyfalls the fieldwith and term conjugate the to its obtain vector Only taken is tion reference error. phase is given by equalizer of the the output and at inputpreamplifier the the at of equivalent noise preamplifier electronic total of the the and LO noise the shot voltage noise and by signal total generated the quantum of a sum the as we detection, haveFor heterodyne homodyne and where 66 For a perfectly balanced receiver, balanced For aperfectly 3.52 Equation given in are line by quencies of the LO and the carrier of the signals. of the carrier the quencies and LO of the D () Now assuming a binary PSK (BPSK) modulation scheme, the pulse has a square shape with with PSK shape (BPSK) asquare has modulation scheme, pulse abinary Now the assuming the product the of then and 3.51, Equation added are In LO the fieldand the total signal of the f is the transfer function of the matched filter for equalization, and filter equalization, matched forof the function transfer is the ω IF is the intermediate angular frequency, which is equal to the difference between the fre the between frequency, difference the to which angular is equal intermediate is the + →= vt KKK  1 or D HH () vt  == D − () 11 =− 1, the PD is a p-i-n type, and the PD bandwidth is wider than the signal 3 dB 3dB signal the PD is wider than bandwidth the 1, and PD is ap-i-n the type, for 21 KK 21 homodyne Hp o KK vt vt r N N 2 2 Hp −∞ −∞ ∫ ∫ ∞ ∞ () () vt N 2 st Hf PP () () sL = = E PP () d [( [ ;/ αα sL =ℜ tT K KS K () = B BB d αα B α α f 2 q () = SK == Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises λ B ′ ′ IS IS − 2 P T T and and KH L 1 +− +− B B pE 2 () [( KT KK 2 2 −∞ KS ∫∫ ∞ fo IS 2 pm α= BI rh α si KS  B φ nc B e eterodyne () Hf ′ 0.5 is the phase offset, and offset, and phase is the SB )]    fd SS K +− EB π 2 Ix Ix ; otherwise ; otherwise () IS 2 ft + + 2 −∞ ∞ SH    IE IE () KS si ] os −∞ ∫ ∞ dt n( ) () cT φφ si Ix pe π nc 4 +] K − ()    B S ff π 2 IE f = K 2 ) 1

d . The integrals of the first first of the integrals . The m T   

φφ B is the bit period. The The bit is the period. oos pe − () φφ pe is the demodula the is −

(3.54) (3.55) (3.52) (3.53) - - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical densities spectral where the by receiver the sensitivity penalty is characterized and shot-noise-limited sensitivity the from receiver condition,Under the anonideal sensitivity departs 3.6.2.3 shot-noise-limited receiver 3.24. shown as Figure plotted sensitivityThis in be can scale) receiver the sensitivity is givenequalizer, (in linear as the and noise preamplifier electronic of the power when the case the the dominates LO ofIn the 3.6.2.2 as scale 3.52, using Equations Thus, 3.55, power 3.58 receiver and the linear sensitivity we the in obtain with

where tion is given by receiver the sensitivityThus, for BPSK density Gaussian distribu equiprobable and and detection δ given by given η

is the LO excess LO is the noise factor. Shot Noise-Limited ReceiverShot Noise-Limited Sensitivity Receiver Sensitivity under Nonideal Conditions Nonideal under Receiver Sensitivity P ss == Pt P D () T S = IX ′ 10 −− − P , 4 10 10 e S Lo λ ℜ+ = IE ′ TK Lo Lo q g are given are by BH 1 2 δ 10 g g[ 2 erfc P 10 10 P     2 D ss KS [[]    P ηα K T ==    e BB ηφ KK α B = = ][ () δ pB S S P 1 10 2 () KK 2 1 IE IX ′ ′ ′ 1 IS L    [( pm erfc − Lo +− α KS = = ]s () BB gd in S with S S 2 S K α 4    IE α IS ′ IX IS ′ 22 λ ℜδ B P P    α TK ′

IS δ KS sL s q 2 P π 2 BH 2 δ D si    2 =

T n 2 2 B as 2 Ix 222

−+

      + co v KS  π 2 S D v s( K N IE 2 )] mp     Ix

   pe co − S s( φ IE ) φφ   

− e )

(3.56) (3.57) (3.60) (3.58) (3.59) (3.62) (3.61) 67 - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 FIGURE 3.25 FIGURE 573–587, 1987, permission.) With 2. 1and Figures excess LO. of noiseof the the afunction as level over shot-noise-limited wavelength. the bandwidth the (b) from receiver sensitivity of Power the penalty 3.24 FIGURE 68 the summation of the two fields are squared and the product term is decomposed into the difference difference the into decomposed is term product the and two ofsquared fields are the summation the is, law that photodetectors, square the in occurs beating The carrier. channel signal identical the to frequency LO laser whosethe be approximatelywouldwith beating fields are signal optical the Obviously, conversion form. and digital to sampling state the analog DSP from system after is placed DSP and coherent system of reception the 3.25, is shown Figure in which the A generic in structure 3.6.3 polarization angle. polarization power optical of same the a function atthe ratio as and modulation parameter of the function a as [31], vary can frequency center heterodyne receiver normalized the the power and penalty found [30]. be in in can that LO of the Furthermore, polarization of rotation of the the function density, equivalent electronic noise a as spectral total of and the afunction as deduced be can excess the noiseagainst factor LO, of 3.24b. shown the as Figure in Receiver power penalty power receiver of the the 3.24a, and shown sensitivity penalty as Figure detection, in erodyne The receiver ratio The sensitivity the against is plotted d (a) (dBm) − − − − 80 70 60 50 igital

(a) Receiver sensitivity of coherent homodyne and heterodyne detection, signal power signal versus detection, (a) heterodyne and homodyne Receiver of coherent sensitivity Coherent reception and the DSP system. the and reception Coherent Local laser

p r

Integrated chorent O

reception front end cessing 10 QAM signals 4 pipe lines Heterodyne f

B s / ystems λ 10 2 Homodyne Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises

4xADC I., Hodgkinson, from (Extracted 10 3 MHz μ m Digital signal processors (b) PDx (dB) 10 20 f B / λ for the case of het for case homodyne and the IEEE J. Lightwave Technol., J. Lightwave IEEE • • estimation • estimation) • • • • Processing algorithms Filters MLSE for each pipe Carrier phase LOFO (freq. offset Adaptive equalizer Resampling I/Q imbalance compo 0.5 α ηχ = = = = = 10 40 100 1 4 s 1.0 5, 5, - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 TABLE 3.1 TABLE Milestones of Progresses of Resolution Linewidth of Progresses Milestones 1 1.5 3 10 Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical is also used as a quality measure for other blocks such as sample-and-hold amplifiers. This forThis way blocks other measure such sample-and-hold as amplifiers. aquality as used is also above signal digitized the noisethe the floor.of in ENOBtion.number bitsOften, ENOB specifies lower informa useful only system represent signal bits do noise not contain digitized of and the of converter noise.amount is able the levels signal represent If to below system the noise floor,the are built into the hardware processors or memory and loaded to processing subsystems. processing to loaded and or memory processors hardware the into built are algorithms so on. These and sation of estimation, propagation phase dispersion effects using ML for compen adaptive PE phases, signal for ofequalization the estimation carrier the resampling, for timing and recovery clock of the the rate transmitter, atthe components created quadrature the and the inphase between imbalance such the as impairments combatto of anumber transmission algorithms contain the processors The or offline. time real in processed are parts imaginary and real the of signals both digitized The channel. mode polarization other the comes from pair Another type. transimpedance differential whichbalanced preamplifier, the isa electronic by amplified region baseband and back is the fallen into term difference only the thus, term; summation and in principle, 2 giving in ofanalog aDAC the value, the represent of to number bitsby used specified is commonly or ADC Effective resolution of number bitssignal. The (ENOBs) of adigitized quality of the is ameasure 3.6.3.1.1 3.6.3.1 development speed the of Fujitsu DAC. and ADC clock applied the sinusoidal waveformor ADC, 3.27 is Figure only 2 GHz. shows in progresses the For operation. example, speed high form a to very for Fujitsu lines DAC digital 64 GSa/s digitized the of all summation the taking delaying and registers, of outputs by the of extracted paralleling, converter (DAC), digital-to-analog and ADC clock is increased the high-speed speed the Regarding CMOS device SiGe electronic dously; of in would the speed several of reach the at5 mm, tens GHz. tremen would increase speed electronic exponentially. the reduced is reduced, width gate the When resolution the that is meaning is obtained, line 3.26, shown as a log-linear Figure scale a linear in in such SU-80, as which resolution would So, 2020. we line 5 nm in allow if reach to the plot trend the X-ray photoresist and UV, such appropriate with the as beam, lithographic optical electronic the wavelength atshort using optical techniques lithographic the in successes due the to made could be shown tremendously as Table exponential over in trend gressed an in year the 3.1. progresses These 3.37. Figure in depicted as of 56 rate 64 GSa/s, G to a sampling with requirement this Fujitsu reached has ADC high is rate for25 G very this to Although 32 GSy/s satisfied. Nyquist are criteria channels, optical µ µ µ m—1985 m—1975 µ If the signals are complex, then there are the real and imaginary components that form apair. form components that imaginary and real the complex, are are there signals then the If The linewidth resolution linewidth forThe processing of pro semiconductor the device been fabrication has the that ensure to bandwidth signal of the that twice be must rate normally sampling The m—1971 m—1982

Effective Number of Bits Number Effective Definition Semiconductor ManufacturingProcesses andSpatialResolution(Gate Width) N 130 nm (0.13 180 nm (0.18 250 nm (0.25 350 nm (0.35 600 nm (0.60 800 nm (0.80 signal levels signal for an UV lithography µ µ µ µ µ µ m)—2000 m)—1999 m)—1998 m)—1995 m)—1994 m)—1989: N -bit signal. However, all real signals contain a certain -bit signal. However, acertain contain signals real all 22 nm—2012 32 nm—2010 45 nm—2008 65 nm—2006 90 nm—2002: electron lithography 5 nm—approx. 2020: 7 nm—approx. 2018: 10 nm—approx. 2016: 14 nm—approx. 2014: X-ray lithography X-ray lithography X-ray lithography X-ray lithography 69 - - - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 FIGURE 3.26 FIGURE FIGURE 3.27 FIGURE 70 * converts decibels (a log divisor the in 6.02 signal; term the wanted noise the to and including signal distortion total of the (SINAD) ratio distortion signal-to-noise and given the ratio values and dB, is the are in where all of blocks below is usually ENOB worst of the the block. ENOB of achain total the as calculations easily included be signal-chain to also blocksanalog can quantization error in an ideal ADC ideal an in error quantization

http://en.wikipedia.org/wiki/ENOB - cite_note-3 http://en.wikipedia.org/wiki/ENOB Thus, we can represent the ENOB of a digitalized system by ENOB of we the represent Thus, adigitalized can

μ Line resolution ( m) 5 × 10

10 10 Linewidth resolution (nm) 10 60 40 30 20 10 43 − − − Evolution of ADC and DAC operating speed with corresponding linewidth resolution. linewidth corresponding with Evolution DAC and speed of ADC operating Semiconductor manufacturing with resolution of line resolution. resolution of with line manufacturing Semiconductor 1970 1 1 2 3 56 GSa/sADC 10 2009 65 nm representation) bits to (a log 1980 2010 55–65 GSa/s * . 40 nm ADC E NOB Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises (access date: Sept. 2011). Sept. date: (access 2011 55–65 GSa/s 1990 = 28 nm DAC SI NAD 2012 60 2 110–130 GSa/s ADC andDAC representation); 1.76 the and comes from term . 2 − 2000 20 nm 17 . 6 2013

2014 2010 2015 2020 Year (3.63) Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 less than 1(i.e.,less than it is always positive dB). when in quoted never can be reading a receiver the SINAD sensitivity.SNR, unlike definition, this with Note that alongside is quoted receiver and the dB expressed sensitivity, in give to aquantitative evaluation of where as device, defined often acommunications from a signal or DAC SINAD the ADC of SINAD the the Indeed with tested. being each with with each output 2 into is divided the (DNL): ADC, ideal For an nonlinearity Differential of calculation ENOB the for ADC. in is used an SINAD definition, it is nowWith this possible definitionused when is than This be to less 1. for SINAD audio is removed. signal modulating original the after powersis, noise-plus-distortion remaining (b) to audio residual power, the carrier frequency radio that amodulated is, from audio that signal, power. is modeled above. by equation the This (ii) of ratio (a) The power modulating the of original following: (i) of ratio (a) The received power, total (b) to signal is, the noise-plus-distortion that the as the one afewof collected is calculated definitions. has use, different SINAD widespread SINAD Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical times, this is the number present on ADC datasheets. present on ADC number is the this times, intuitively, Quite many ADC. reason, the this For best-fit the results INL. yields for better method ADC. of curve the transfer actual the to tion approxima first-order nearest depicts here the drawn curve transfer ideal The origin. the through not best-fitdoes go considered the forINL curve transfer calculating 3.29 ideal Figure the in that see or (ii) end method. point using either (i) measured line) is popularly best-fit (best method straight INL characteristics. transfer ADC by the plotting is measured reality, In INL point. up that to cumulative of errors sum DNL the by step ateach using calculating DNL estimated be can curve. INL transfer ideal the from ADC the function of transfer LSBdeviationthe actual in the as of defined be can response. INL of its DAC. due mismatching to mid-range the near may caused be error DNL tion-register ADC, For example,successive-approxima an in its architecture. comes from error DNL ADC, practical of (lower number counts in sidebands).is measured is 0 LSB.and DNL a the In ADC, ideal For an − 2.93, 3.91, 4.96, 5.93, 7) LSB. This allows INL the and DNL calculated: to be INL and gain offset the error,Correcting we obtain following the list (0, of measurements: 1.03, 2.00, This definition compares the SINAD of an ideal ADC or ADC an DACideal the of SINAD with a compares definition ENOBword of length bitsThis The gainThe is error in error this is case offset The (V) output Analog input Digital DACunipolar reference voltage with of a3-bit following the measurements Consider Example: it exclude to is common distortion, the components. of DC Because calculating the the When The intercept and slope of this ideal curve can lend us the values of the offset and gain error of error values lend gain offset of usthe can and the curve ideal slope and of intercept this The error.can One gain considers Best-fitbest-fitmeasurement andoffset INL The INL: of method of how is a measure (INL) closely its output matches ideal ADC the nonlinearity Integral 0.09, 0.09, P is the averageis the power components. is usually SINAD noise, signal, distortion of the and − ∆ 0.04, 0.04,

width as shown in Figure 3.28. Any deviation from the ideal step width is called DNL DNL 3.28. shown is called width step as Figure width ideal in deviation Any the from − 0.07, 0) LSB, and DNL () 7.08 += − 0.01 0.01 000 − 0.01 V or (/ 71 S INAD 1.03 001 ), 1 = − (0.03, 0.09 = 0.01 LSB 1 V as V PP ref 2.02 sig 010 LSB

PP − = ++ noise 0.03, 0.03, 8 V: where LSB stands for the least significant for least the stands LSB where bits. noise + − 2.96 distorio 011 .7 0.07, P = distorio 1 LSB (lower sideband) in this example. n − 0.02, 0.05, n

3.95 100

is a measure of the quality of quality of the is ameasure 5.02 − 101 0.03, 0.07, 0) LSB. = (0, 0.03, 0, N 6.00 uniform steps, steps, uniform 110 − .7 0.07, 7.08 111 (3.64) 71 - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 72 surements and control (Figure 3.30). control (Figure and surements must considered for be applications involving parameter budget This calculation. precision mea useful forerror typically be number would INL using fit best This DC applications.measured for one the to compared as number it this use to is more useful provides worst-casemethod the INL, 3.6). (Figure this As ADC of output code the maximum and origin the through line straight the of end-point INL. instead So, this use to one has datasheets. provided in estimation. provide numbers abetter end-point INL To numbers. budget, error INL the calculate than numbers it is always distortion the use to better would number be tions. This 3.29 FIGURE 3.28 FIGURE End-point INL: End-point applica signal time-variant in distortion predict to is best-fit of use number the INL only real The Output code

Best-fit INL. Best-fit Representation of DNL in a transfer curve of an ADC. of an curve atransfer in of DNL Representation 000 001 010 011 100 101 110 111 The end-point method provides the worst-case INL. This measurement passes passes measurement This provides worst-case end-point method the INL. The 0 1.25 LSB 0.5 V 1234567

equivalent to the maximum deviation for AC an equivalent maximum application. the to However, Output 1.75 V 1 LSB Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises 0.5 2.75 V 1 LSB 1 LSB Each Input

Also, this is the specification that is generally that is generally specification is the this Also, 0.75 INL 1.75 LSB 8 V in (V ) - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 0.09 V.

where: Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical The ENOB relative accuracy is calculated using the largest relative ENOB using the relativeThe is deviation calculated (INL) accuracy largest absolute using the deviation is calculated racy 3.30 FIGURE as by ADC the noise introduced RMS the we estimate can PDF; Gaussian following thus, varies anormalized normally ADC level an in quantization of the decision The clipped. are signals region, the then unity, saturated amplitude/power the surpasses signal normalized region. the If nonsaturated linear the in is operating ADC the as ENOB far as AGC tive an amplifier [31]. and noise sources levelsequivalentthus are to a specific The quantized for. ofnumber ENOB equivalent accounted is proposed. be bits term can Hence, the such bydue components in noises to aconvertor. electronic contributed effective only an Thus, equivalent of by number digital levels the by modulo-2 the represented levels, reduced which are convert its can to signal analog of number an bits the is that considered as ENOB ADC ofThe an 3.6.3.1.2 is you ANOB, because converter, the always ideal of an than which error have quantization the add to However, never ENOB inaccurate. LSBs can the larger result of that are be the argue also one can some of number of bits that the (ANOBs). means ANOB, this the than ENOB is the smaller When actual the than or smaller larger be ENOB can of the ENOB that note calculation, kind For this ± σ similarly, similarly, x ENOB absolute the case, accu this absolute In now relativeThe and can calculated. be accuracy As shown in Figure 3.31b, shownAs Figure addi in and of ADCs two acascade modeled ideal as be can ADC areal 0.5 LSB. designers mayENOB! definitions Different of different use is the variable related to the integration of decision integration voltage the to related variable is the is the variance is the

RMS High-Speed ADC and DAC Evaluation Incorporating Statistical Property

y for inside one LSB integration End-point INL. End-point _ noise = − LS LS ∫∫ 2 Output 2 B B d − ∞ D ∞ =→ =→ x 2 2 V 2 ENOB V re ENOB re f 2 f 1 πσ 2 ENOB ex LS ENOB p B Input     − re () D l xy = , in this case, 0.08 V: case, this , in 2 = − 66 σ 64 . 2 . 4 2 7 bits INL     bits d x

ddL

y =+ SB 22 / 12 σ d , in this case, case, this , in

(3.66) (3.65) (3.67) 73 - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 saturated in the high level. high the in received signal The saturated (clipping)regionand linear saturated the the to in level.high respect is significantly gain The input-sampled which the power in signal with level characteristic gain is normalized nonlinear AGC a The has line. transmission conditions optical onof the the depending receiverthe vary at evaluation fieldsarrived optical of We is essential. the amplitudes the performance that note noisy dispersive different under and conditions; equivalentoperating an model thus, of ENOB for resolution receiver of different the the transmission of ADC of the signals? indicates the band This device,quency ENOB what sampling of device is of response the the when the excited broad with excitation the to respect with frequency, 5.5. 5to from varies range the fre in Having the known excitationthe DSA of the by sinusoidal waves ENOB the observed, As of frequencies. different (DSA) analyzer sampling of 3.31a, is response shown ENOB Figure frequency digital of in the with where 74 Given the known quantity Given quantity known the signals. of broadband of (a) response frequency spectrum and experimental onthe ENOB based of model variable ADC of(b) 50 GSa/s. rate Deduced sampling and width 3.31 FIGURE levels the to ing of noise Gaussian as noise ENOB We Gaussian distribution. values the the via deduce correspond thus can determined to to R _X A out (b) (a) is the RMS amplitude derived from the noise power. the derived from amplitude ENOB RMS model, is the the to the According X X = Q I R_

(a) Measured ENOB frequency response of a commercial real-time DSA of 20 GHz band DSA of 20 GHz real-time of acommercial response (a) ENOB frequency Measured XP Noiseless front end in

ENOB (bit) 6.0 3.5 4.0 4.5 5.0 5.5 in_a of frontenddevice 05 Effective noise vR /P L E SB ef NOB , where the signal-averaged where the power 2 / 12 ADC withvariableENOB ENOB 1 by the introduction of the ideal quantization error, error, quantization ideal of by the introduction the =− ADC 1 Ideal N Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises R_X Frequency (GHz) lo in 10 g 2      P R Ref AGC _X LS 15 in LS B is scaled with a gain coefficient according coefficientaccording again with is scaled 2 / R_X B 12 Additive noise / out + 12 () 2 A ENOB 2 02 σ ADC 2 Ideal 2 P in_a     

v is estimated and the gain gain the and is estimated

5 DSP σ 2 can be be can (3.68) - - - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 contours ofcontours 2 3.33, of contours Figure the BER using ENOBs processing same the to the obtain prior to produce employedsets, achieved. be data We can offline effectivethus, the that note equalization PE and AGC; of the gain nonlinear the via lesswith higher resolution noise be to allowingthe ADC of the 3.33d (Figure e), and lower compensation link are non-CD dispersive amplitudes the sampled pulse of case the in hand, other is achieved. the On performance the in AGC moderate hence freedom and ineffectiveness resolution the to ADC contribute of the effects further nonlinear the compensated, powerthe launch with fibers ofand the 5 dBm,regimes CD respectively.of 4 fully is link the When nonlinear launch power and links) both (0 dBm in linear the in compensation operating non-CD AGC ENOBsthe and compensation and of for CD cases 1500 km long-haul the of full transmission adjusted of reference plots contour the variation of the power the BERwith aparameter, as level of but identical ENOBs, with 3.33a, shown as Figure in for 3.33b–e shows, B2B Figure the experiment. levels of quantization different for ADC the examined clipping be effect the can Thus, introduced. of adjusted byclipping AGC, degrees effect the different would nonlinearly be gain and controlled, of amplitudes, different are ADC the to presented signals sampled ENOBof the our model. When ENOB of DSA 3.1a. shown Figure in effectiveness Several the were more tests ensure to conducted with data of case offline in of BER parameter variation versus ENOBs variation with OSNR, the as (Gaussian noise is due distribution the difference or uniform). 3.32b The eters. Figure depicts the resolution param ADC as ENOBs with full output 8-bit of and samples atthe ADC the simulated 3.32a Figure using B2B the under OSNR transmission shows the to respect with BER variation the 3.6.3.1.3 ENOB signal-dependent is now ENOBs.averaging as denoted This process. by signals, of an the spectrum frequency the across evaluated noise with be ENOB distributed can energy, DSPsignal the (see from feedback control path 3.31b). the via Figure new Thus, values of to obtain the output sampled value output sampled the obtain to relativeis scaled reference the to power level of real ADC and AGC in coherent QAM transmission system. In system. In QAM transmission AGC coherent in and ADC of real receiver. Mao, B. coherent effect clipping N. (From et al., ENOB and digital Investigation on the experimental (b) and (8-bit ADC) 3.32 FIGURE Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical B2B. for However, ENOBs requirement for the for is higher cases, the both scenario for nonlinear even and of for transmission case compensated the CD for for full is higher than noncompensating model of range AGC. the the It dynamic model, is obvious especially 3.33a–e the Figure that from ENOBs of range the dynamic the BER of indicates the contours distance opening The is used. (a) BER 10 10 10 10 10 − − − − − 13.0 5 4 3 2 1

13.5 ADC ADC ADC ENOB ENOB ENOB Impact of ENOB on Transmission Performance

× = = = (a) B2B performance with different ENOBs values of the ADC model with simulated data data simulated with model ADC ENOBs of values the different (a) with B2B performance 14.0 10 5bits 4bits 3bits = = = 5bits 4bits 3bits

– OSNR versus BER under different simulated ENOBs of offline data obtained from an from obtained data ENOBs of offline simulated different versus BER under OSNR 3 for all cases. Hence, a fair comparison can be made when the ENOBs when the made be model can comparison Hence, cases. for afair all 14.5 OSNR (dB) 15.0 15.5 R 16.0 _X out 16.5 . The gain of the AGC is also adjusted according to the the to AGC of adjusted the according is also gain . The 17.0 P Re (b) f BER factor is used scaling AGC; of the alinear then 10 10 10 − − − 3 2 4 14 Back-to-back offlinedata(scopeENOB Proceedings of ECOC of Proceedings ENOB ENOB ENOB ENOB 15 = = = = 5bits 4bits 3bits 2bits OSNR (dB) 16 , Geneva, 2011.) Geneva, , 17 18 = 5bits) 75 19 - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 76 required for the in-phase and quadrature phase components of QAM-modulated polarized channels; components of phase QAM-modulated polarized quadrature and for in-phase the required aloweris derived from sinusoidal wave DAC. frequency the into externally injected are Four units would four DACs be which DAC IC, each in an in is clocked section aclock with which sequence DAC of 3.34 the shown 3.35, Figures and in are structures ADC and The respectively. Normally, there 3.6.3.2 more hence noise.adjacent and channels, 3.33cdispersive (Figure e). channel and modulation effects of cross-phase may due the to be This 3.33 FIGURE nonlinear region with launch power launch of with region 5 dBm. nonlinear (d) (e) and power; (d) launch linear, compensation and non-CD 4 dBm (c) with regions (b) linear, nonlinear (CDC) and compensation CD (a) under full with B2B, operation transmission (b) DWDM linear experimental (d) (b) (a) Inverse Pref (a.u) Inverse Pref (a.u) 1 2 3 4 5 6 1 2 3 4 5 6 Offline data(DWDMwithoutCDC,pin

234 2 Offline data(DWDMwithCDC,pin Digital Processors Digital 0.02

2.5 2.5 0.01 Comprehensive effects ofComprehensive AGC (inverse effects clipping of P 0.02 3 0.01 ENOB (bits) ENOB (bits) 0.005 0.005 3.5 3.5 Inverse Pref (a.u) 1 2 3 4 5 6 0.002 2 0.003 45 Offline data(B2B,OSNR 2.5 = Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises 4.5 4.5 0.01 0dBm) = 0.02 0dBm) 345 0.005 ENOB (bits) 5 3.5 (e) (c) Inverse Pref (a.u) Inverse Pref (a.u) 0.002 5 6 1 2 3 4 1 2 3 4 5 6 Offline data(DWDMwithoutCDC,pin Offline data(DWDMwithoutCDC,pin 2345 234 = 15.7dBm) 2.5 2.5 0.02 4.5 Ref 0.01 0.02 ) and ENOBs of the coherent receiver, ENOBs coherent of) and the 0.01 ENOB (bits) ENOB (bits) 0.005 3.5 3.5 0.005 0.003 4.5 4.5 0.002 = = 4dBm) 5dBm) 5 Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical (b) processing function. FIGURE 3.34

Fijitsu DAC structures for four channel PDM_QPSK signals: (a) schematic diagram and (a) (b) HQDAT[1023:0] VQDAT[1023:0] DAC HIDAT[1023:0] VIDAT[1023:0] SPI_OUT SPI_CLK SPI_IN V CLKO XRST RDY EN XSS FIFO VI I DAC

VID

WADDR RADOR AVDRF

FIFO VQ

Q DA

AVD

÷ AVD18 VQD CQ

DAC DIGITAL 4 DAC DIGITAL

AVDNEG AVDDAC PLL DAC IFACED

CLKO 511.0MH

DSP core Q DAC 18G PLL AVDDAC18 Q DAC I DAC I DAC Customer

logic AVDNEGDAC

VDD VSS zH FIFO HI DAC CAPAAC CAPLF VQON VQOP VION VIOP RREF BGAP REFCLKN REFCLKP HQON HQOP HION HIOP WADDR RADOR ID FIFO HQ I DAC HOD H 77 Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 is available 3.37. is chip shown Figure commercially. in IC ADC of image the An of 64 GSa/s rate sampling maximum QPSK or QAM under current signals. modulated The ADC and Interleaved mode Sampler using (CHAIS). aCHArged mented or alternatively, is 1/(128 interval sampling the cycle clock clock slowed 500 MHz to the for been Thus, has 8-bit ADC. down by afactor of 128, For example, 3.35, shown as Figure in corresponding achieved 1024 at samplesa periodicity are is sufficiently islarge samples. sufficientlythat number to achieveall the long,sampling that so end of at the simultaneously a clockclock bits sampling period waveform, appear the digitalized the DSP for the subsystem. in Qlanes offour processing groups Iand interleaving of Because of the of PDM-QAM would by sampled into form be afour-phase digital converted to then sampler and tice it is expected that in network and system management the tuning of the LO is to be done is be to LO of the network system in tuning and it management that the tice is expected FIGURE 3.35 FIGURE 78 offset between the LO and the carrier must be within the limit of limit the must within be carrier the and LO offset the between for that DSP-Telecommunication coherent receiver based requires frequency the Union standard for effective CoD, important very sensitivity of the not International degradation of if results. The chapters. the chapter, in but lines a separate between not in DSP. of the functions described, be noise considerationsmain will and DSP algorithms The with techniques associated of principles and coherent reception the described has chapter This 3.7 of notations I the thus channels. modulation 3.36 FIGURE Figure 3.36 DSP-basedFigure optical of employing shows transceiver an DAC both ageneric diagram Furthermore, the matching of the LO laser and that of the carrier of the transmitted channel is channel transmitted of the carrier of the that and laser LO of the matching the Furthermore,

CONCLUDING REMARKS 10G/40G/100G Input

ADC principles of operations (CHAIS). of operations principles ADC Schematic of a typical structure of ADC and ADC transceiver subsystems for subsystems PDM-QPSK transceiver ADC and of ADC structure of atypical Schematic OTU-4 framer DAC and Q and

Calibration ADC pair

One per sampling

LO 4-phase DAC

are shown in the diagram. Similarly, received optical signals the diagram. shown the in are Tx Rx

Noises in Optical Communications and Photonic Systems Photonic and Communications in Optical Noises DEMUX 1-4 encoding decoding QPSK QPSK DSP × 500 MHz) ADC bank (D) ADC bank (A) ADC bank (C) ADC bank (B) DAC 4 DAC 3 DAC 2 DAC 1 ADC 4 ADC 3 ADC 2 ADC 1 = 1/64 GHz. The sampling is imple sampling The 1/64 GHz. ± 25

.G (hybrid-coupler Digital (I-Q modulator) balanced Rx) Hz converter converter . Furthermore, in prac in . Furthermore, O/E E/O 1024 bits @ OUTPUT 500 MHz + - - Downloaded By: 10.3.98.104 At: 20:11 26 Sep 2021; For: 9781315372747, chapter3, 10.1201/9781315372747-4 REFERENCES subsystem. coherent reception for intradyne an LO source the phase locking the optical frequency. action brieflydescribes initial this LO Thus, the knowledge some with remotely prior LO of automatic region locking the and frequency set of to the 3.37 FIGURE Optical Coherent Reception and Noise Processes Noise and Reception Coherent Optical

1. 2. 5. 4. 3. 6. 7. 8.

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