Throughput/Delay Analysis of Spectrally Phase- Encoded Optical CDMA over WDM Networks

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Archibald Hodges
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1 Throughput/Delay Aalysis of pectrally Phase- Ecoded Optical over etwors K. Putsri *,. ittichivapa * ad H.M.H.halaby ** * Kig Mogut s Istitute of Techology Ladrabag Departmet of Telecommuicatios Egieerig, Bago, Thailad ** Uiversity of Alexadria, Departmet of Electroic Egieerig, Alexadria, Egypt idsaapog.pu@rmuti.ac.th, ssuvepo@mitl.ac.th, shalaby@ieee.org Abstract-This paper presets a performace aalysis of spectrally phase-ecoded optical over etwors. Radom access protocol is adopted to assig wavelegths. The discrete time Marov chai model is used to build aalytical model of multi-chael radom access protocol. We measure several performace characteristics, amely, steady-state throughput ad average pacet delay time. Additioally, the efficiecies of the system, which are based o both the processig gai ad the umber of wavelegths, are cosidered. Expoetial retrasmissio is used for solvig pacet collisio problems. I our umerical results, system performace is give i terms of both average throughput ad delay time. Keywords: Optical,, Expoetial retrasmissio, pectrally phase-ecoded optical (PE-O) I. ITRODUCTIO I the middle of 8 s, O (Optical code divisio multiple access) has bee widely developed as high-rate optical commuicatio etwor systems, where ecodig ad decodig are all performed i optical domai [-]. The advatageous fuctio of the optical is the fact that it lets each user access the etwor asychroously ad simultaeously without strict wavelegth cotrol ad timig sychroizatio. I additio, optical local area etwors allow shared access to a broadcast medium. However, multiple access iterferece (MAI) i O icreases as the umber of users icreases. Additioally, Optical ca be operated o Etheret passive optical etwors (EPO) which architecture is the ey fuctio i local area etwors (LAs) i future. Moreover, it ca also be upgradeable to either Gigabit or Gigabit Etherets. I fact whe usig O i EPO, both capacity ad badwidth will highly icrease [-,6]. This ca oly be achieved by mixig two techiques together, e.g., hybrid optical / techique []. I this paper, we propose a spectrally phase-ecoded optical (PE-O) over etwor via radom access protocol. PE-O or coheret ultrashort light pulse techiques seems to be a good techique, sice it offers high bit rates [8]. PE-O techique is used to ecode/decode data with the O code sets. Each simultaeous user or ode is assiged a differet uique code. The ecoded data is the set to wavelegth divisio multiplexig () chaels. Multi-chael slotted Aloha is used to coted free wavelegths for each O code (each ode coteds the available wavelegths for sedig pacets out). We assume that the umber of chaels is equal to the umber of wavelegths. Pacet collisio occurs if more tha two active users choose the same wavelegth ad same code at the same time. Therefore, to resolve this problem, expoetial retrasmissio is used. We measure our system performace usig both average system steady-state throughput ad average system pacet delay time. Both are based o discrete time Marov chai model. The rest of this paper is orgaized as follows. I sectio A, the system model descriptio is preseted. The mathematical aalysis is illustrated i sectio II, where we give more details about discrete time Marov chai. I sectio III, the umerical results are show i terms of both system throughput ad delay time versus the umber of active users. Fially the coclusios are preseted i sectio IV. A. Model Descriptio λ λ w λ λ tar Couple Figure. ystem model descriptio of optical over etwors ode ode ode ode Figure. Architecture of optical code over chael Figure shows the system model. It composes of a set of trasmitters (data sources ad tuable lasers, optical ecoders), star couplers ad a set of receivers (optical decoders). The data is ecoded/decoded with the set of spectrally phase-ecoded

2 optical (PE-) techique [8]. Each ecoded data is assiged a wavelegth by usig multichael radom access MAC protocol. That is, o each wavelegth, users ca be accommodated by idividually assigig each user with a differet optical code. Therefore, the same code sequece ca be reused o all chaels. We use Multi-chael slotted Aloha radom access protocol to assig wavelegths λ i, i =,,,... w [5-6], as show i Fig.. We assume that the pacet is received successfully if o collisio has occurred (o termials or odes have chose the same wavelegth ad same code at the same time to trasmits pacets out). I reality, this problem is uavoidable, therefore, i this paper, the expoetial bacoff retrasmissio with probability of retrasmissio p = r is used to solve this problem, =,,,..., is level of retrasmissio. II. MATHEMATICAL AALYI A. Pacet error rate of PE-O We assume that if the data bit to be trasmitted is, the o spectral-phase ecoder eergy is trasmitted. O the other had, if the data bit is, a ultrashort pulse is set out to the spectral-phase ecoder [8]. The receiver declares a was set if the decoded itesity exceed the threshold ad declares a otherwise. Therefore, the probability of error P e for PE optical is give by [8-9], P = e l = l l ( ( γ () l ρ() l ))] l K K l Where K = T / b T is the processig gai, T b is period of the data source, T is the ecoded pulse duratio, as: ad () l = exp ( I lp ) th / () γ () () Ith ρ l = Q, () l lp Here ( a b) Q, is the Marcum s Q fuctio, expressed a + b Q ( a, b) = x exp I ( ax) dx b P is the pea power of the ultrashort pulse, is the umber of chips i the coded sequece, ad I th is the itesity threshold of the receiver comparator for detectig ad. Therefore, from the probability of pacet error i (), the success probability of L bits legth ca be give i (5), (4) Ps ( ) = K l l + l = l (5) K K L ( ( γ () l ρ() l )) B. ystem Performace Aalysis I this sectio, we aalyze the performace of our system usig discrete Marov chai model [9,]. We assume that the umber of chaels equal to the umber of wavelegths. Pacet collisio occurs if more tha oe active user chooses the same wavelegth ad the same code at the same time. Therefore, to resolve this problem, the expoetial retrasmissio is used. However, if more that oe active user select oly same wavelegth (but differet codes) at the same time, there will be multiple access iterferece (MAI), o collisio. q P P P P - q q q q P Figure. tate trasitios of Marov chai model of expoetial retrasmissio level The discrete time Marov chai is show i Fig.. Let p (t) be the retrasmissio probability i the t-th slot (equal period of a pacet legth). p (t) is updated accordig to acowledgmet feedbac. There are idle ad busy statuses, i the busy statuses correspod to both success ad collisio of the curret time slot, it could be expressed as p ( t + ) = mi( pmax, p( t) / r), if umber of idle wavelegths x M ad p( t + ) = max( pmi, p( t) r), if umber of wavelegths < x M Where x deotes the largest iteger ot greater tha x. < x < be the factor of wavelegths remai i system, < r < be the probability of retrasmissio whe collisio occurred, < p max, ad p mi = r ad be the maximum value of retrasmissio level. oted that, icreasig the level guaratees system stability but with large system delay time. The system state trasitio probability from state to j, P (, j) is preset i [] q, = j = p, = j = P(, j) = p, j = + ad q, j = ad< whe =,,,... q P (6)

3 Here, by applyig biomial distributio, we get the probability that umber of idle wavelegths p whe system state is M x < p j M j M x M r r = j= j M M (7) Where, is the umber of statios or odes M, is the umber of wavelegths ad q is the probability that umber of idle wavelegths > M x is q = (8) p Let π ad P be the limitig probability vector ad the trasitio probability matrix, respectively. Therefore, the limitig probability ca be satisfied the steady-state probability from, π = πp, ad i= π = (9) the overall system throughput oa () give by, oa ( ) = j = j M j j i Ps ( ) j ( r ) ( r ) Ad throughput per wavelegth pc (), pc j () ( ) = oa ( ) () M the steady-state system throughput with spectrally phase-ecoded optical is give i () [-5,] ad P was give i A of ectio II, s Here, ( ) s = ( ) = π s () pc ( ), for throughput per wavelegh = oa ( ), for overall throughput Fially the system pacet delay is, () D = + π (4) = III. UMERICAL REULT I this sectio, we preset some umerical results i terms of system throughput ad system delay time for the spectrally phase-ecoded optical over etwors via radom access protocol. I all of our calculatios of system performace, we select same parameters as give i [-5,8-9], amely, pacet legth L = 8 bits, =, I th / P / 4 o, x =. ad r =.9. I Fig. 4, we have plotted the system throughput per wavelegth versus the umber of active users. We vary the umber of wavelegths from 8, to. The throughput icreases up to a maximum value at a umber of active users about 5 to 7. Additioally, we foud that if the umber of wavelegths icreased, from 8 to, the maximum throughput of 8 wavelegths is still higher tha ad. This is because the utilizatio of 8 wavelegths is more tha the wavelegths of ad. However, the overall system performace of wavelegths show better performace tha 8 wavelegths, illustrated i Fig. 8 ad 9. Figure 5 the system pacet delay time per wavelegth has bee show versus the umber of active users. We also vary the umber of wavelegths from 8 to wavelegths. It ca be see that, the delay time decreases whe the umber of wavelegths are icreased. Therefore, if the umber of wavelegths icreased, from 8 to wavelegths, the maximum delay time is decreased whe we compare the results at the same umber of active users as well as the system throughput. I Fig. 6 ad 7, we have compared the system throughput ad system pacet delay time while varyig the processig gai K from to 4, respectively, ad holdig the wavelegths fixed at wavelegths. From Fig. 6 we see that, the throughput of processig gai with is more tha that of K = by.5 times. I this case, the maximum throughput is about.8, but for K = the maximum throughput is about.. It meas that, the processig gai ( K ) strogly affects the system. Figure 7 shows that the system pacet delay time with is less tha K =, correspodig to system throughput i Fig. 6. Therefore, we see that, whe the processig gai is icreased the system delay time decreases, ad the system throughput icreases as well. I Fig. 8 ad 9, we have bee compared the over all system throughput ad system pacet delay time while varyig the umber of wavelegths of 8, ad by usig (). We agai observe both the maximum throughput i Fig 8 ad miimum delay time i Fig 9, respectively. From Fig 8 ad 9, the over all system performace icreased whe the umber of wavelegths icreased. It is clear that, the processig gai ( K ) ad the umber of wavelegths strogly affect the overall system performace whe the PE-O is used. I Fig. ad, we plot the system throughput ad system pacet delay time per wavelegth while varyig the probability of retrasmissio r. It could be see that whe the umber of r icreased, the system throughput decreases but system delay time icreases cause traffic o etwor is icreased.

4 wavelegths L = 8 bits Ith/Po = /4 o = r = wavelegths L = 8 bits I th/p o = /4 o = r =.9 ystem Throughput.5 wavelegths wavelegths ystem Throughput 4 wavelegths 8 wavelegths umber of Active User Figure 4. ystem throughput per wavelegth versus umber of active users with various wavelegths umber of Active User Figure 8. ystem throughput versus umber of active users with various wavelegths 4 L = 8 bits Ith/Po = /4 o = r =.9 8 wavelegths L = 8 bits Ith/Po = /4 o = r =.9 8 wavelegths ystem Delay Time wavelegths wavelegths ystem Delay Time 4 wavelegths wavelegths umber of Active User Figure 5. ystem pacet delay time versus umber of active users with various wavelegths umber of Active User Figure 9. ystem pacet delay time versus umber of active users with various wavelegths ystem Throughput.5.5 umber of wavelegths = L = 8 bits IthP o = /4 o = r =.9 ystem Throughput r =. r =.9 Ith/Po = /4 o = L=8 bits umber of Wavelegth = 8 r =.7.5 K = umber of Active User Figure 6. ystem throughput per wavelegth versus umber of active user with various K (Processig gai) Active of User Figure. ystem throughput versus umber of active users with various probability of retrasmissio ystem Delay Time umber of wavelegths = L = 8 bits IthP o = /4 o = r =.9 K = ystem Delay Time I th/po = /4 o = L=8 bits umber of W avelegth = 8 r =. r =.7 r = umber of Acive User Figure 7. ystem pacet delay time versus umber of active user with various K (Processig gai) Active of User Figure. ystem pacet delay time versus umber of active users with various probability of retrasmissio

5 IV. COCLUIO We propose a performace aalysis of spectrally phaseecoded optical over etwors via radom access protocol. The PE-O techique is used to ecode/decode data with the O code sets. Each simultaeous user or ode is assiged a differet uique code. Additioally, multi-chael lotted Aloha is used to coted the available wavelegths. The two characteristics of system performace are cosidered. Oe is system steady-state throughput ad aother is average system pacet delay time. The results show that, the processig gai, probability of retrasmissio ad the umber of wavelegths have more effects i system. Therefore, whe we use E-O techique for optical fiber commuicatio, these factors ad effects should be cosidered. REFERECE [] Chao-Chi Yag. Hybrid wavelegth-divisio- Multiplexig/pectral-Amplitude-Codig Optical ystem, IEEE Photoics Techology Letters, 5, vol. 7. [] Kitayama, K, Xu Wag, aoya Wada. O over PO-solutio path to gigabit-symmetric FTTH, Joural of Lightwave Techology, 6, vol. 4, Issue 4: [] H.M.H. halaby. Optical radom access protocols with ad without pretrasmissio coordiatio, IEEE J. Lightwave Techol.,, vol. : [4] H.M.H. halaby. Performace Aalysis of a Optical Radom Protocol, IEEE J. Lightwave Techol., 4, vol., o. 5:-4. [5] to, A., arget, E.H. ystem performace compariso of optical ad A i a broadcast local area etwor, IEEE Commuicatios Letters, 4, vol. 6, Issue 9: [6] Galli,., Meedez, R., Toliver, P., Bawell, T., Jacel, J., Youg, J., Etemad,. D-compatible spectrally phase ecoded optical, GLOBECOM '4. IEEE, 4, Vol.: [7] Kamath, P., Touch, J.D., Baister, J.A. The eed for media access cotrol i optical etwors, IFOCOM 4, vol. 4, March 7-, 4: 8-9, [8] J. A. alehi, A. M. Weier, ad J. P. Heritage, Coheret ultrashort light pulse code-divisio multiple access commuicatio systems, IEEE J. Lightwave Techol., vol. 8, pp , Mar. 99. [9] K. ia, K. alma, ad J. Kambiz. Aalysis of Throughput ad Delay i a pectrally Phase-Ecoded Optical Pacet etwor, the WOC '7 Coferece, 7, -4 July 7. [] D. Behaddou, A. Al-Fuqaha, ad G. Chaudhry. ew Multiprotocol /-based Optical witch Architecture, the 4th Proceedigs of imulatio ymposium, April: [] M.. Alam, A.Z.M.E. Hossai. Throughput Aalysis of a Multichael lotted-aloha Protocol i hort-haul Commuicatio Eviromet for a Expoetial Bacoff Retrasmissio cheme, The Proceedigs of ICIC 997, vol., ept. 9-, 997: 4 8.

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