Extending the Reach of Short-Reach Optical Interconnects with DSP-Free Direct-Detection

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1 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of Exending he Reach of Shor-Reach Opical Inerconnecs wih DSP-Free Direc-Deecion Enrico Foresieri, Member, IEEE, Marco Secondini, Member, IEEE, Francesco Fresi, Gianluca Meloni, Luca Poì, Member, IEEE, and Fabio Cavaliere Absrac Coheren deecion is he usual soluion o achieve high bi rae ransmission over long disance. However, i requires a local oscillaor and energy consuming digial signal processing ha make i no suiable for cos and energy sensiive inerconnecions and shor haul links. In hese applicaions, direc deecion is he preferred soluion and he main impairmen is he chromaic dispersion of opical fibers. In heory, combined ampliude-phase shif (CAPS) codes are able o defea any amoun of chromaic dispersion. However, while hey can be deeced wih a very simple direc deecion receiver, heir generaion is no rivial. heir complexiy grows wih he order of he code which, in urn, increases wih he chromaic dispersion. In his paper, he IQ-duobinary modulaion scheme, a novel echnique for approximaing an order- CAPS code, is presened. Such a modulaion scheme allows o bridge up o km a a bi-rae of Gb/s over a sandard single mode fiber using a simple direc-deecion receiver wihou he need of any digial signal processing echnique. Index erms Opical fiber communicaion, opical inerconnecions, modulaion formas, opical ransmiers. I. INRODUCION Shor-reach opical inerconnecs are acively invesigaed in several applicaion areas such as daa cener, baseband cenralizaion in radio access neworks (RANs), ec. In daa ceners, he need for increasing processing speed and capaciy represens a major challenge for convenional soluions based on elecrical swiching, because of he ineviable increase in energy consumpion and number of inerconnecions ha follow []. Opical echnologies based on dense wavelengh division muliplexing (DWDM) could overcome boh hese limiaions, hanks o he large bandwidh capaciy of he opical fiber and o he low power consumpion rae in opical swiching. herefore, a significan amoun of research is being carried ou o develop opical inerconnecs, neworking echnologies, and suiable modulaion schemes for such applicaions [] []. oday, cenralized RANs (CRANs) mainly rely on dedicaed fiber connecions beween remoe radio uni (RRU) nodes and baseband processing node. DWDM echnologies can help o evolve he fronhaul nework o face: a) he concurren increase his work was suppored in par by Ericsson. Enrico Foresieri, Marco Secondini and Francesco Fresi are wih ecip Insiue, Scuola Superiore San Anna, Pisa, Ialy, and wih Naional Laboraory of Phoonic Neworks, CNI, Pisa, Ialy. Gianluca Meloni and Luca Poì are wih Naional Laboraory of Phoonic Neworks, CNI, Pisa, Ialy. Fabio Cavaliere is wih Ericsson, Pisa, Ialy. Copyrigh (c) IEEE. Personal use of his maerial is permied. However, permission o use his maerial for any oher purposes mus be obained from he IEEE by sending a reques o pubs-permissions@ieee.org. of bi rae and number of RRUs per area uni (respecively, imes o imes higher ypical user daa rae and imes higher mobile daa volume per geographical area, according o he G-PPP key performance indicaors); and b) he consolidaion of he number of baseband nodes in a fewer daa cener sies o save operaional coss. he firs aspec leads o an increase of he bi rae, up o Gbi/s, he second aspec leads o an increase of he link disance. aking ino accoun he maximum fiber propagaion delay ha mos common fronhaul proocols can olerae, ypical disances ha can be covered wihou opical amplificaion are up o km. Nonlinear effecs and polarizaion mode dispersion do no represen an issue for such shor disances. Indeed, he major limiing ransmission impairmen is he chromaic dispersion, whose effecs scale linearly wih he disance and quadraically wih he symbol rae, which should be in he order of or Gb/s o mee he capaciy increase in he G ranspor nework. In long-haul sysems, his issue was radiionally addressed by deploying dispersion compensaing fibers and, more recenly, coheren deecion and digial signal processing (DSP) [] []. However, as cos and power consumpion a he receiver are imporan facors in shor haul fronhaul and inerconnecion applicaions, coheren deecion and DSP should be avoided, hus reducing he choice on he modulaion forma ha can be used. Ideally, he adoped forma should: i) allow for direc deecion a he receiver, o decrease he opics cos by avoiding he local oscillaor; ii) require minimal elecronic processing a ransmier and receiver o save energy and cos; iii) allow for a low sensiiviy receiver o achieve sufficien link budge wih (or possibly wihou) opical amplificaion; iv) no require dispersion compensaion up o km. he simple on-off keying (OOK) forma wih direc deecion is ruled ou by he fourh menioned consrain because i could only achieve a few kilomeers a he considered bi raes wihou dispersion compensaion. On he oher hand, he use of muli-carrier modulaion formas such as orhogonal frequency-division muliplexing (OFDM) or is discree muli-one (DM) varian o reduce he impac of chromaic dispersion is beer avoided because hese echniques enail a significan increase of complexiy, laency, and energy consumpion [9]. Given he consrains lised above, he only way o comba chromaic dispersion seems o be using higher-order modulaion formas, as hey allow for a reduced symbol rae while mainaining he desired bi rae []. Indeed, unipolar fourand eigh-level pulse ampliude modulaion (PAM) formas - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.

2 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of OOK DBPSK A A p A p. OPICAL SIGNAL P o = A P o = A A A A ELECRICAL SIGNAL P e = A P e = A Fig. : OOK and DBPSK (lowpass equivalen) opical and elecrical signals. he DBPSK elecrical signal is polar because i is demodulaed by an opical differenial inerferomeer and deeced by a balanced receiver. (referred o as PAM- and PAM-, respecively) have been proposed as candidae formas enabling a significan increase of he ransmission disance compared o OOK [9], []. However, using unipolar higher-order formas may require more power compared o polar formas of same order o mainain he same spacing beween levels. So, for example, PAM- should require more power compared o differenial quadraure phase-shif keying (DQPSK), which also allows for direc deecion hrough a differenial inerferomeer ha convers he phase modulaion ino ampliude modulaion jus prior phoodeecion []. Moreover, in he absence of opical amplifiers, noise is no involved in he phase-o-ampliude conversion process, such ha here is no signal-noise beaing and, a leas when hermal noise dominaes, DQPSK should have a clear advanage compared o PAM-. Such a comparison was performed in [] and i urns ou ha PAM- acually has an elecrical power penaly of abou db compared o DQPSK bu almos no opical power penaly. ha is o say, given he same opical power, he achieved bi error rae (BER) is he same in boh cases bu he generaed elecrical power is much less for DQPSK. his is beer undersood by comparing OOK and differenial binary phase-shif keying (DBPSK). he corresponding (lowpass equivalen) opical and elecrical signals are shown in Fig. under he hypohesis of uni phoodeecors responsiviy. As can be seen, given he same average opical power P o, he elecrical power P e generaed by DBPSK is half of he one generaed by OOK bu he BER is he same because he disance beween signal levels is he same. In his case, as i is noiselessly demodulaed in he opical domain, DBPSK has a db elecrical power advanage over OOK bu no opical power advanage. Even aking ino accoun ha he capaciive coupling beween he phoodeecor and he following circuiry blocks he direc-curren (DC) bias, in he elecrical domain DQPSK would have an advanage of abou db over PAM- and would no require a digial-o-analog converer (DAC) a he ransmier and an analog-o-digial converer (ADC) a he In opics, when using direc-deecion, PAM-M also refers o mulilevel inensiy modulaion, where he informaion is insead associaed o M differen equispaced inensiies of a supporing pulse. receiver. Neverheless, is receiver is possibly sill oo complex for shor-reach inerconnecs applicaions. As shown in [], line coding (e.g., duobinary) does no allow o exend he reach when using mulilevel formas. Indeed, signal specrum compression is no, per se, he key facor o defea chromaic dispersion. Raher, i is he combinaion of coding and proper pulse shaping ha allows o increase he signal robusness, as demonsraed by he phase-shaped binary ransmission (PSB) echnique and he combined ampliudephase shif (CAPS) codes [], []. I has been shown ha an order- CAPS code has he same resilience o chromaic dispersion as DQPSK [], while requiring (given a db opical power budge penaly) less opical power han DQPSK o bridge he same disance wih a comparable specral efficiency []. Moreover, CAPS codes of any order can be deeced wih he same receiver used for OOK []. However, heir generaion is no as simple, as an order-n coder has n saes and signals. Even he order- code uses signals ha can pu a burden on he elecronics as hey require a phase-shif jus in he middle of a signaling inerval. While an order- CAPS code can be very well approximaed by narrow filering a DBPSK signal [], no simple way for generaing or approximaing higher-order codes is acually known. In his paper a relaively simple echnique for generaing an order- CAPS code is presened and he obainable performance is compared o ha of an acual order- code for ransmiing a Gb/s over a sandard single mode fiber. he paper is organized as follows. In Secion II he CAPS codes are briefly reviewed and specific examples for an order- code are given; in Secion III a ransmier srucure able o approximae an order- code wihou using a DAC is inroduced; in Secion IV he performance obainable by such approximaion is compared o ha of an acual order- code; finally, conclusions are drawn in Secion V. II. CAPS CODING he main idea behind he CAPS codes is ha a sufficienly dispersive fiber approximaes a Fourier ransformaion, meaning ha i urns an inpu pulse s() wih Fourier ransform S(f) and bandwidh B ino an oupu pulse v() whose envelope can be approximaed as where v() πγ ( ) S πγ, for γ(πb ) () γ = λ R bd a /ω () λ being he opical wavelengh, R b = / he bi rae, D a he accumulaed dispersion (usually given in ps/nm), and ω he opical carrier angular frequency []. Moreover, his approximaion becomes exac when he inpu pulse s() is properly chirped []. his means ha, for γ = κγ, replacing he inpu pulse s() by s () = s(/κ)/ κ will produce he same oupu pulse v() (when properly chirped). his way, he same performance can be obained irrespecive of γ and Noe ha CAPS coding is no relaed o carrierless ampliude modulaion (CAP), which is a varian of quadraure ampliude modulaion (QAM). - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.

3 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of s () s () s () s () Σ s () s () s () s () s () s () s () Σ Σ Σ s () Σ s () s () s() Σ Σ Σ Fig. : Sae diagram of a code. s() g()= g I ()+ jg Q () α g I () g Q () Fig. : Supporing pulse for a code.. β hus any amoun of chromaic dispersion can be (heoreically) defeaed. As shown by (), he mos concenraed in frequency he inpu pulse, he less he broadening of he oupu pulse. Using a supporing pulse g() larger han he signaling inerval and also differenially encoding he informaion bis o obain a furher reducion of bandwidh, he following PAM signal could be ransmied where x() = k= w k g( k ) () w k = b k. () and he precoded symbols b k {, } are obained from he informaion symbols u k {, } by precoding as b k = u k + b k mod () When g() is chosen so ha is in-phase and quadraure componens are piecewise consan over a symbol ime, he signal () can be produced by a coder whose sae diagram and signals (of lengh ) are obained as explained in []. Using a supporing pulse g() of lengh (n + ) corresponds o an order-n CAPS code. For example, he sae diagram of an order- code is as shown in Fig. and he corresponding signals are given (for i =,,..., ) by (b i,k.)g ( + (k ) ), s i () = () k= oherwise i b i,k = mod () k he addiional delay in () is necessary only o make he sample x(k ) correspond o w k, because g() is considered o be cenered around he origin. Noe ha if g() is chosen as a recangular pulse of lengh (wih no quadraure componen), hen () would be a duobinary coded signal. In his case, in opics, () would be he driver signal of a Mach-Zehnder modulaor (MZM) and he average value. may also no be removed as done in (), so ha w k = b k and () would be a unipolar -level signal whose ampliude is adjused o properly drive he MZM beween wo ransmission maxima. Some MZMs allow o independenly adjus he bias, so ha () can also convenienly be zero-mean. In-phase componen Quadraure componen Fig. : signal for α =. and β =.. Here he inensiy of he signal componens is represened, bu wih he sign of he corresponding elecrical field. he pulse g() should have lengh and is in-phase and quadraure componens chosen in order o approximae he required chirp ha makes () an exac relaion. From a purely heoreical poin of view, he bes shape of g() should be relaed o ha of a prolae spheroidal waveform (mos similar o a Gaussian shape), and hus he in-phase and quadraure componens of g() and he employed filers should also be chosen such ha o approximae his shape []. A possible g() is shown in Fig., where he parameers α and β can be ailored o opimize he performance for differen amouns of accumulaed dispersion. An example of he signal generaed by a code is shown in Fig. for he given binary informaion sequence. In order o show he effec of he code, he inensiy of each signal componen is represened wih he sign of he corresponding elecrical field. he eye diagram obained afer propagaing such signal hrough a sandard single mode fiber a Gb/s, igh filering and phoodeecion is insead shown in Fig. for hree differen fiber lenghs, namely km (backo-back), km, and km. he eye diagrams on he righ side correspond o he case in which only he in-phase componen is ransmied. As can be seen, i is he quadraure componen ha allows o keep he eye open unil well afer km. he effeciveness of he code has been experimenally demonsraed in [] using a DAC for implemening he code hrough is -sae diagram and signals (Fig. ). I was found ha he ransmission disance can be increased by a facor of and. in comparison o OOK and PAM-, respecively. However, in order o be suiable for shor-reach opical - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.

4 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of... Boh componens. In-phase componen only.. (a) Back-o-back Precoded daa LPF B' g g Laser Fig. : IQ-duobinary ransmier. MZM MZM π / I Q Boh componens Boh componens... (b) Afer km... (c) Afer km In-phase componen only In-phase componen only Fig. : Eye diagrams of he signal in Fig. afer filering and phoodeecion. Only he in-phase componen was ransmied for he diagrams on he righ side. Precoded daa / (a) g g I Q Precoded daa LPF B' Fig. : Block diagrams for he generaion of in-phase (I) and quadraure (Q) componens. he duobinary in-phase componen is ideal in (a) and obained by filering in (b). inerconnecs applicaions, a much simpler implemenaion is required, preferably wihou he use of a DAC. In he following i will be shown ha coding can be implemened by using a ransmier whose complexiy is comparable o ha of a DQPSK ransmier, while sill allowing for using an OOK receiver. Here we only deal wih heoreical aspecs, deferring experimenal resuls (o be sill obained) o a laer publicaion. (b) III. APPROXIMAING HE CODE As eviden from Fig., given α =. and β =. (which is a good choice, as shown in he following), he in-phase g g I Q componen is very similar o a duobinary coded signal, and indeed i would be a duobinary signal for α =. hus, saring wih non-reurn-o-zero (NRZ) pulses p() of lengh, we could approximae he signal () as shown in Fig. a, where he gains g and g are o be properly chosen (in his case, wih reference o Fig., i has o be g = βg ). However, he / delay may be hard o implemen, because i would require a clock a double he bi-rae in a digial implemenaion or a precision increasing wih he bi-rae in an analog one. We can solve his issue by noing ha he Fourier ransform of p()+p( ) is equal o e jπf P (f) cos πf, being P (f) he Fourier ransform of p(). Hence, using a filer whose ampliude response approximaes cos πf a leas in he Nyquis bandwidh f R b /, we could resor o he mehod in Fig. b. his akes care of he / delay issue hanks o he omission of he e jπf facor. However, now g = βg, due o he omission of he facor and under he hypohesis of using a filer wih uni DC gain. he required cosine shape can be approximaed by choosing a filer whose bandwidh B is in he order of R b / [9]. he kind of filer is no of primary imporance, even hough a filer wih an almos Gaussian shape (such as a Bessel-ype filer) gives bes resuls. Anyway, his mehod sill has a delay issue, namely he delay inroduced by he filer iself, so we would be simply exchanging he / delay issue wih a filer-dependen delay one. We can avoid his problem by using he same ype of filer also in he quadraure branch or, beer, using a single filer as shown in Fig., where also he required nesed Mach- Zehnder modulaor (MZM) is depiced. As will be seen, using a single filer for boh componens may slighly modify he value of is opimum bandwidh. We found ha he opimum bandwidh depends on he amoun of accumulaed dispersion, alhough only marginally, and a bandwidh of R b / produces good resuls for any fiber lengh. he main pracical issue in he implemenaion of he mehod in Fig. is relaed o signal addiion, due o he qualiy of elecrical couplers. However, a dedicaed inegraed circui design could improve he overall performance keeping he complexiy very low. Our approximaion of a signal is obained by associaing a quadraure componen o a duobinary coded signal. Inspecion of Fig. reveals ha such a componen is simply given by wo aenuaed replicas of he duobinary signal iself, respecively anicipaed and delayed by a symbol ime. For his reason we named his modulaion scheme IQ-duobinary. he nesed MZM s elecrical drive signals for (wih α =. and β =.) and IQ-duobinary (wih g = g ) normalized o he MZM V π are shown for - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.

5 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of : : IQ-DUO DBPSK x Laser Precoded daa H(!) MZM Fig. : IQ-DBPSK ransmier. β : : (a) In-phase drive signals. (b) Quadraure drive signals. IQ-DUO Fig. : Nesed MZM elecrical drive signals for (α =. and β =.) and IQ-duobinary (g = g ) for he given binary sequence. he IQ-duobinary elecrical filer is Gaussian shaped wih bandwidh R b /, while a bandwidh of R b was assumed for. he ampliudes are relaive o he bias volage and are normalized o he MZM V π. IQ-DUO (a) In-phase componens. IQ-DUO (b) Quadraure componens. Fig. 9: Elecrical fields a he oupu of he nesed MZM corresponding o he drive signals in Fig.. he MZM is aken o have infinie exincion raio. comparison in Fig., while he corresponding oupu elecrical fields are repored in Fig. 9. Looking a his las figure, i is ineresing o noice ha he IQ-duobinary in-phase componen approximaes an order- CAPS code, as he low signal levels are fa wih a phase-shif in he middle []. However, he raio beween he maximum ampliudes of low and high levels is abou, which is somewha higher han he opimum value of., so ha narrow filered DBPSK allows a beer approximaion []. In he lieraure, here has always been a bi of confusion abou wha a duobinary signal is. According o a by he book definiion, a duobinary signal is he in-phase componen in Fig. a, while he in-phase componen in Fig. b is only an approximaion. However, his approximaion is mos commonly referred o as i iself being a duobinary signal. We hink ha i has o be also considered as an approximaion o differen formas such as PSB or CAPS-. We canno say how much closer o a PSB signal i is, given is loose definiion [], bu we can say how much beer i approximaes CAPS-. So, in he case of chromaic dispersion limied ransmission, comparing he performance of CAPS- and he by he book (ideal) duobinary we find ha he firs one is he bes of he wo, whereas he laer is only marginally beer han OOK []. he performance of wha is commonly referred o as duobinary lies in beween he wo. x() H f (f ) (a) Sysem model. H o (f ) H e (f ) n() (b) Lowpass equivalen model. Fig. : Block-diagram of a direc-deecion opical sysem. he previous observaion suggess ha we can also ry o approximae a signal by properly filering a DBPSK signal in he opical domain, as shown in Fig., where he opical filer has ransfer funcion H(ω) = e jω + j β ( + e jω ) () and could also be employed a he receiver side, insead of he ransmier one. However, such kind of filering is difficul o realize in he opical domain. For example, in an inegraed silicon phoonics implemenaion, he necessary delays would require oo long waveguides wih oo large losses. For his reason we will no invesigae furher his possible realizaion here, even hough i would be able o provide a slighly beer performance when properly adjusing he aenuaion parameer β. IV. BER PERFORMANCE he sysem model used for performance evaluaion is depiced in Fig. a. he generaed opical signal is launched in a sandard single mode fiber and a he receiver end i is opically filered prior phoodeecion. he opical filer models he operaion of an opical demuliplexer ha exracs he desired channel from a DWDM signal. he phoodeecor and he following elecronic circuiry will add sho and hermal noise, respecively. he deeced signal is hen lowpass filered and sampled. he only impairmens aken ino accoun will be he inersymbol-inerference due o finie bandwidh of elecroopic componens and chromaic dispersion, and receiver hermal noise, which is assumed o be dominan over sho noise. Hence, he lowpass equivalen model in Fig. b can be used, where x(), H f (f), and H o (f) are he (lowpass equivalen) ransmied opical signal, fiber frequency response, he generaed opical signal has also o be filered by a narrowband opical filer which is no shown. I mus be noed ha in his case he filer H(ω) would be able o approximae he inverse of he fiber ransfer funcion, and hus no sricly a signal. - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.

6 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of (a) Back-o-back (b) km (a) Back-o-back (b) km (c) km (d) 9 km (c) km (d) 9 km (e) km (f) km Fig. : conour plos of E b /N penaly a BER = vs elecrical (B e ) and opical (B o ) filer bandwidhs for six fiber lenghs (reference is he performance of an OOK sysem in back-o-back configuraion) (e) km (f) km Fig. : IQ-duobinary conour plos of E b /N penaly a BER = vs ρ = g /g and he bandwidh B of he elecrical filer a he ransmier (same fiber lenghs and reference as in Fig. ). and ransfer funcion of he opical filer, respecively, while H e (f) is he ransfer funcion of he pos-deecion elecrical filer modeling he response of he elecronic circuiry. he hermal noise n() is modeled as addiive, whie and Gaussian wih monolaeral power specral densiy N. he elecrical performance will be given in erms of he raio E b /N, E b being he average elecrical energy per bi. hus, denoing by B n he noise-equivalen bandwidh of H e (f), he corresponding signal-o-noise raio is SNR = (E b /N )R b /B n. All resuls will be given for a sandard single mode fiber wih chromaic dispersion parameer β = ps /km and MZMs wih an opical exincion raio of db. A fixed bi rae of R b = Gb/s is used for all considered formas and a de Bruijn sequence of suiable lengh adoped ( for he binary formas and for PAM-). he elecrical E b /N penaly is referred o a BER arge of, aking as a reference an OOK sysem in a back-o-back configuraion. In all cases, he opical and elecrical filers were considered o be ndand s-order Gaussian, respecively. For OOK and PAM-, he opimum db bandwidhs of hese filers, denoed hese values were deermined by increasing he sequence lengh unil no significan change was observed compared o he previous run. as B o and B e, 9 urned ou o be loosely dependen on he accumulaed dispersion, he opimum B e slighly increasing while he opimum B o slighly decreasing wih increasing dispersion. A conour plo of he E b /N penaly a BER = as a funcion of B o and B e can be found in [] for OOK and PAM-, while Fig. repors he resuls for an acual code wih α =. and β =. for six fiber lenghs. In his case, while he opimum B e urns ou o be almos independen of dispersion, he opimum B o firs decreases wih increasing dispersion and hen increases again bu only slighly. Anyway, he value of boh bandwidhs is no criical, as can be seen from Fig.. According o hese findings, whaever he amoun of accumulaed dispersion, in he following B o R b and B e R b / will be assumed for boh and IQduobinary, as he laer approximaes he former. In his way, he E b /N penaly wih respec o he opimum bandwidhs is always less han abou. db for disances greaer han km. As regards IQ-duobinary, given his choice we only have o selec proper values for he raio ρ g /g and he bandwidh B of he lowpass filer in Fig.. As already 9 hus, he bandwidh of he lowpass equivalen filer H o(f) is B o/. - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.

7 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of menioned, he ype of he employed filer is no of paramoun imporance, alhough phase lineariy is a desirable propery. No significan difference was found using eiher Gaussian or Bessel-like filers, including some commercially available filers. Hence, we repor here only he resuls obained wih a Gaussian filer. Fig. shows he conour plos of he E b /N penaly a BER = vs ρ and B for he same fiber lenghs as in Fig.. As can be seen, he opimum range for B is R b < B <.R b unil abou 9 km, and B >.R b for higher disances. However, choosing a value slighly larger han he opimum produces only a negligible penaly. So, choosing B = R b / allows for bes resuls a higher disances (larger accumulaed dispersion) while keeping he penaly wihin abou. db for shorer ones (smaller accumulaed dispersion). As regards parameer ρ, in order o mainain he penaly wihin. db, i mus be chosen no larger han. unil abou 9 km, and hen increased for larger disances. aking an OOK sysem in back-o-back configuraion as a reference, boh elecrical and opical penalies are repored in Fig. for IQ-duobinary wih hree differen values of parameer ρ and for an acual code wih wo differen choices for parameers α and β. For comparison, also he penalies of he reference OOK and a PAM- sysem are repored in he same figure. For hese laer formas, he opimum bandwidhs for a fiber lengh of km were used []. I can be seen ha IQ-duobinary performs even beer han for fiber lenghs in he range from o km, bu he laer fares beer for larger disances. Indeed, for a given penaly allows o bridge abou km more han IQ-duobinary. Finally, Fig. b shows ha, allowing for a db opical power penaly wih respec o OOK, PAM- allows o bridge abou km, while IQ-duobinary almos km. However, PAM- is a mulilevel signal and hus allows for a beer specral efficiency and for half he elecronics speed required by IQ-duobinary, alhough i also requires a DAC a he ransmier and an ADC a he receiver, which are he dominan source of power consumpion. Insead, as regards power consumpion, boh and IQ-duobinary are equivalen o OOK a he receiver side, because exacly he same receiver can be used for all hese las hree schemes. As regards he ransmier side, he in-phase componen for and IQ-duobinary requires he same elecrical power as OOK, while he power required by he quadraure componen can be considered almos negligible, is ampliude being abou % of he in-phase one. However, requires a DAC while IQ-duobinary does no, such ha i is almos equivalen o OOK also in his case. V. DISCUSSION AND CONCLUSIONS In shor-reach opical inerconnecs up o km, opical amplificaion can be avoided and direc deecion is employed for cos effeciveness. In his scenario, chromaic dispersion is he main impairmen and, wih he consrain of avoiding DSP, only mulilevel PAM formas are able o bridge his disance, seemingly. However, given a bi rae of Gb/s, PAM- can only bridge abou km when acceping an opical Elecrical Eb/N penaly BER= Opical power penaly BER= OOK PAM- IQ-DUOBINARY Bi-rae = Gbps ρ=: ρ=: ρ=: α=: β=: α=: β=: Fiber lengh (km) OOK PAM- IQ-DUOBINARY (a) Elecrical penaly Bi-rae = Gbps ρ=: ρ=: ρ=: α=: β=: α=: β=: Fiber lengh (km) (b) Opical penaly Fig. : Penaly vs fiber lengh. power penaly of db wih respec o a back-o-back OOK sysem. he disance could be increased o abou km bu wih a furher db penaly. On he oher hand, increasing he modulaion order does no help wih opical power link budge. Indeed, a leas PAM- would be required o achieve a reach of km bu sill requiring abou db more opical power wih respec o OOK []. Moreover, while PAM- is pracical as a soluion, PAM- is no because of is higher suscepibiliy o ransmission impairmens [9]. As shown here, a possible alernaive o PAM is using CAPS codes for combaing chromaic dispersion. Given a db penaly wih respec o back-o-back OOK, a CAPS- code operaing a a bi rae of Gb/s is able o bridge km a he cos of using a complex ransmier bu sill using he simples direc deecion receiver. By significanly simplifying he ransmier, he IQ-duobinary forma allows bridging km for he same penaly wihou requiring addiional DSP. Alhough PAM- a Gb/s (i.e., a Gbaud) is being considered for a wo-wavelengh Gb/s channel soluion, in applicaions wih reach significanly greaer han km i would require digial equalizaion [], [], []. In his regard, we would like o poin ou ha, as chromaic - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.

8 his aricle has been acceped for publicaion in a fuure issue of his journal, bu has no been fully edied. Conen may change prior o final publicaion. Ciaion informaion: DOI.9/JL.., Journal of dispersion inroduces severe nonlinear disorion o he signal due o he square-law phoodeecion, elecronic equalizaion canno be really effecive unless special echniques ruled ou for shor-reach applicaions due o heir complexiy are employed []. In any case, he use of elecronic (or opical) equalizaion would provide similar benefis o any modulaion scheme. In his paper, aking ino accoun a reasonable opical power penaly (say no greaer han db compared o a back-o-back OOK), a possible DSP-free alernaive for bridging disances up o abou km a Gb/s wih a single-wavelengh soluion or a Gb/s using wo wavelenghs has been proposed. While he ransmier is slighly more complex han for PAM-, neiher a DAC nor an ADC are necessary, and he receiver is very simple. REFERENCES [] C. Kachris, K. 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Lighw. echnol., vol., no., pp. 9, 99. [] B. eipen, N. Eisel, A. Dochhan, H. Griesser, M. Eisel, and J.-P. Elbers, Invesigaion of PAM- for exending reach in daa cener inerconnec applicaions, in Proc. In. Conf. ransparen Opical Neworks (ICON),, paper Mo.D.. [] G. Colavolpe,. Foggi, E. Foresieri, and G. Prai, Mulilevel opical sysems wih MLSD receivers insensiive o GVD and PMD, J. Lighw. echnol., vol., no., pp., May. - (c) IEEE. Personal use is permied, bu republicaion/redisribuion requires IEEE permission. See hp:// for more informaion.