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534 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13, NO. 3, MARCH 1995

Optical Code-Division-Multiplexed Systems Basedon Spectral Encoding of Noncoherent SourcesM. Kavehrad, Fellow, IEEE, and D. Zaccarh

Abstract-In this paper, we present a new category of opticalCDMA systems which work based on spectral encoding. In suchsystems, that wewill referto asFrequency-Encoded CDMA (FE-CDMA) systems, the coding is done in the frequency domainwhile in the usual CDMA systems the code multiplies the mod-ulation signal in the time domain. We present a new type ofFE-CDMA system, based on encoding noncoherent broadbandsources. We discuss the advantages of our system compared toother optical CDMA systems and present its performance. Weshow that very efficient, low-cost, CDMA systems can be obtainedwith an aggregate throughput of many gigabits per second. Also,for th is system, the spreading gain of CDMA is independent ofthe modulation bandwidth. Hence, the system can accommodatevariable bit rates, naturally.

I. INTRODUCTIONN MOST REPORTS in the literature, CDMA systemsI esign is based on encoding the information signal in thetime domain by a pseudorandom sequence. Efficient systemsfor use in Local Area Network (LAN) environments can beobtained. However, no matter how the system is designed, itwill always suffer from a basic limitation. As the number ofsimultaneous active users is increased, the code length has tobe increased in order to maintain the same performance. Todo so, without sacrifying the bit rate, one is constrained touse shorter and shorter pulses. When coherent, the requiredoptical sources are likely to be mode-locked lasers producingtransform limited pulses, rendering the system expensive and

possibly not competitive when compared with those usingother access schemes. If an incoherent CDMA system isconsidered, it might be difficult, at some point, to find lasers forwhich the coherence time is much shorter than the chip period,a necessary condition for these systems to behave as expected.We should also note that as the pulses used become very short,the chip duration becomes incompatible with the bandwidth ofthe photodetector, and that optical nonlinear elements, such asAND gates have to be used as in TDMA systems, increasingthe cost and the complexity of the system.It is therefore necessary to find other types of optical CDMAsystems, for which increasing the multiple access capacity,i.e. the code length, will not necessarily mean using shorter

Manuscript received November 5, 1994; revised December 5, 1994 Thiswork was supported in part by the Telecommunications Research Instituteof Ontario TRIO), hotonics Networks and Systems Thrust and NSERC(Canada.).M. Kavehrad is with Department of Electrical Engineering, University ofOttawa, Ottawa, Ontario KlN6N5 Canada.D. accarin is with Bell Northern Research Ltd., Ottawa, Ontario KlY4H7Canada.IEEE Log Number 9409174.

pulses or lower bit rates. One possibility is to use differentdimensions for the code and for the information. In [l],Weiner et al., proposed coding mode-locked pulses in thefrequency domain. The information is transmitted using ASKin the time domain. However, the coding in the frequencydomain will affect the pulse in the time domain, placing moreconstraints on the bit rate. Moreover, short pulses are stillrequired and mode-locked lasers have to be used, making thesystem expensive.Inspired by their design, we propose an original solutionbased on encoding in the frequency domain noncoherent opti-cal sources such as edge-emitting LEDs (EE-LED) or Superluminescent diodes (SLD). Our system has the advantage ofbeing simple, inexpensive and has a spreading gain totallyindependent of the bit rate. Part of the following work hasbeen published in [2] and [3]. In the next section, we firstpresent how in practice encoding optical sources can be donein the frequency domain. The encoder is a well-known double-grating apparatus and is common to both our system and thesystem developed in [l]. In Section 111, we focus on FE-CDMA systems that employ noncoherent sources. In SectionIV, we present some examples of codes that are suitable forthis application. In Section V, we describe the transceiverdesign. In Section VI, we look at some practical issues inimplementation and applications of such a system. In SectionVII, we evaluate the performance of our proposed method.In Section VIII, we examine the possibility of using thistechnique for ATM switching. In Section IX, we discuss ourresults, and in Section X, we conclude the paper.

11. FREQUENCY ENCODINGF OPTICAL SOURCESA well-known frequency-encoder for optical sources isshown in Fig. 1. It consists of a pair of diffraction gratingsplaced at the focal planes of a unit magnification, confocallens pair. This apparatus has been used with high-efficiencyby many research teams for temporal shaping of short pulses,for example see [4]-[5]. The first grating spatially decomposesthe spectral components present in the incoming optical signalwith a certain resolution. A spatially patterned mask is insertedmidway between the lenses at the point where the opticalspectral components experience maximal spatial separation.

After the mask, the spectral components are re-assembled bythe second lens and second grating into a single optical beam.The mask can modify the frequency components in phaseand/or in amplitude, depending on the coherence property ofthe incident optical source. The number of frequency bandsthat can be resolved by the encoder will dictate the code length,0733-8724/95 04.00 1995 IEEE


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HAVEHRAD AND ZACCARIN: OpIlCAL. CODE-DIVISION MULTIPLEXED SYSTEMS BASED ON SPECTRAL ENCODING 535

ource7DATA

Fig. 1. Frequency encoder for optical sources.

and therefore the number of subscribers in the system. It canbe shown [4] that this number is given approximately by6 X TWX d . os e,)M 0.5-

where X is the center wavelength of the optical source, S isthe spectral width being encoded, w s the input beam radius,d is the grating period and 0, is the diffracted angle of thecentral wavelength. For S = 50 nm, = 1.55 pm, w = 3mm, l /d = 1200 lines/mm grating and 0, = 68 (for Littrowconfiguration), we compute N M 490 subscribers. Such aspectral width is easily obtained when using noncoherentoptical sources such as LEDs or superluminescent diodelasers. When using coherent optical sources, it requires a pulseduration of approximately 0.1 ps (100 fs), at that wavelength.

III. FE-CDMA SYSTEMSWITH O R A L L Y, INCOHERENT SOURCESSince FE-CDMA systems are based on encoding the spec-trum of optical sources, natural alternatives to mode-locked

lasers are noncoherent sources such as multimode lasers orLEDs. For these sources, the large frequency bandwidthis caused by photons being produced with different energy,and is independent of the modulating signal. It is then clearthat filtering the spec- of these sources will not affectthe temporal shape of the modulating signal. Therefore, themultiple-access capacity cannot be based on the differencesof intensity levels betweeh the and the uncoded waves.New coding strategic5 have to be found.Polychromatic spatially coherent or noncoherent sourceshave found many applications in the past in different areassuch as spectrography, holography [7], optical processing [8]and image transmission [9]-[ 103. In transform applications,spatial incoherence allows to avoid coherent noise while thelarge spectrum is divided into many wavelength channels toachieve parallel capacity. Much effort is still being spent by theresearchers to achieve achromatic transforms using broadbandsources.In communications applications however, broadbandsources such as LEDs were until recently, considered as being n fact the signal in the time domain will be only slightly modified [ 6 ] .

To Network

undesirable, laser diodes being the right choice. Mainly threereasons explain this: 1) Lasers couple more light into SMF, 2)they allow a wide variety of modulation types such as DPSKor FSK and 3) they can be modulated at higher bit rates. Anumber of recent experiments however have demonstratedthat light-emitting diodes can be used instead of diodelasers to satisfy many short to medium distance single-modeor multimode system requirements. When compared withdiode lasers, LEDs offer the advantage of higher reliability,reduced temperature sensitivity, less complicated drive circuitrequirements, immunity to optical feedback, and lower costdue to high yields in packaging technology. The cost factor isvery important in bringing the optical fiber with transmissioncapacity of up to 600 Mbt/s to customers in the SubscriberLoop applications [ll]. To answer this, extensive researchefforts are made to develop new types of LEDs suchas Edge-Emitting LEDs (EE-LED) and SuperluminescentDiodes (SLD). These LEDs are very strong competitors todiode lasers since they can couple high power levels intoSMF. As examples, SLDs with average output power of -5dBm at 1480 nm have been reported [12]. EE-LEDs coupling-6 dBm into SMF are available. Such high coupling poweris made possible by the fact that the output emission profileis a narrow beam, very similar to that of the lasers. Theirmodulation bandwidth is also very large compared to Surface-Emitting LED(SE-LED). The amplified spontaneous emissionnoise (ASE) emitted by erbium-doped fiber amplifiers, usuallycalled broadband Superluminescent Fiber Source [13], is alsoa good candidate for FE-CDMA systems. Recent experimentsshow that the ASE can be used as a broadband (more than30 nm) source with a total output power of 5 mW +7 dBm).The spectral density of the source has less than 5 dB variationover the 30 nm bandwidth. The coherence length is 210 pm.Recent experiments with EE-LED over 10 km and 20 km ofSMF have been conducted at bit rates of 1.2 Gbt/s and 600Mbt/s [ll]. The FWHM of these devices is from 50 nm to~ 1 2 0 o that for CDMA applications, the bahdwidth tobe encoded is also very large.

All these factors make us believe that EE-LED and SLDcould play an important role in future LAN applications.In the next section, we show how LEDs could outperformlaser diodes in LAN applications using CDMA. This is ac-

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complished by using the dimensionality of wavelength. Sincethe system configuration depends on the codes used, we firstdescribe suitable codes for amplitude coding of LEDs.IV. CODES FOR INCOHERENT FE-CDMA SYSTEMS

Since LEDs are temporally incoherent sources, they can notin general retain phase information and the weighting functionW(f) used to code the spectrum is constrained to be a unipolarreal function. Since the masks used are passive devices wemust have W(f) 5 1, and it is immediately apparent thatsome power loss will occur. Note that, although we considercomplete asynchronism between the users, only the periodiccorrelation parameters are of interest, since the frequency slotsof the different users will always be aligned.

Let X) x o , ~ ~ , . . . ,N-I) and Y )= YO,YI,..,y ~ - 1 )e two (0,l) sequences. The periodic crosscorrelationisN-1

@XY k) = xiyi+k. 2)i = O

Define the complement of sequence (X) by X) hoseelements are obtained from (X) by Zi = 1- xi.The periodiccrosscorrelation sequence between a) nd (Y) is similarlyN-1

@Ry k) = iiYi+k. (3)i = O

We look for sequences for which4)

A receiver that computes Oxy k)- Oxy k) will reject theinterference coming from user having sequence (Y).We firstlist some sequences that achieve this, and then explain howOxy k)- O,y k) can be computed optically.A . M-Sequences

A unipolar M-sequence of length N is obtained from thebipolar version by replacing each binary 1 by a 0 and each -by a 1. Consider the sequence (Y) as being TX) = X)kwhere T is the operator that shifts vectors cyclically to theleft by one place, that is (TX) = x 1 ,x 2 , . . ,ZN-I , xo . Inthat case5 )

i=O

which results in Oxy 0)= for k = 0 and to Oxy k)=for k = 1 to N - 1. The sum i + k is taken moduloN . These results come from the shift-and-add property ofM-sequences which says that the modulo-2 sum of an M-sequence and any cycle phase shift of the same M-sequenceis another phase of the same sequence. In other words, halfthe 1 s in X)kcoincide with the 1s of (X) while the otherhalf coincide with the Os, where X ) k s the k cycle shift of

X). receiver that computesN-1 N-1

= @ x y k ) @ x y k )= xixi+],- (1 - xi)x i+k ,i = O i = O

= 2Oxy - OXY (0)= 2 x N + 1)/4 - N + 1)/2= o 6)will reject the signal coming from the interfering user havingsequence X ) k .This is true for any k , and by assigning theN cycle shifts of a single M-sequence to N subscribers, wehave a network that can support N simultaneous users withoutany interference. Complete orthogonality between the users isachievable theoretically.

B. Hadamard CodesA Hadamard Code is obtained by selecting as codes therows of a Hadamard matrix. It is well known that an (N x N)Hadamard matrix of 1sand 0s has the property that any rowdiffers from any other row in exactly N/2 positions. All rowsexcept one contains N/2 zeros and N / 2 ones. As an example,

for N = 4/1 1 1 1\ /o 0 0 o \

Taking (X) as being row i and (Y) as being row j withi j it is easy to verify that

(7)where s from A&, therefore satisfying (4). In particular,we note that Hadamard codes allow orthogonal signaling inplace of ASK. This is possible because for Hadamard codeswe also have that

This is simply not true for M-sequences. This allows gainingback a 3-dB loss inherent to the previously designed system.Finally, note that for an N x N Hadamard matrix, N - 1 sub-scribers can be accommodated since the codeword containingall 1 s has to be rejected.C. Bipolar Codes

Any complex number can be represented as a combi-nation of real, unipolar components. For practical reasonswhen designing the masks, we limit ourselves to -1,l)codes. We recall that, one can represent a bipolar sequence(Y) = yo,y1,.. Y N - ~ ) by its unipolar version Y )=yg,yy,.. We note that

yyi = 1 yi = 1= o y . - - 1-

- 1 y; = -1y;i+l = 0 yi = 1-


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538 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 13,NO. , MARCH 1995

response time shorter than a bit period. For Rb in the Mbt/srange, this is still challenging with current technology.Looking at the architecture of the proposed system, we seethat it requires only low-cost broadband incoherent sources(compared to mode-locked sources) and simple direct de-tection receivers (no optical threshold element is needed).Furthermore, the spreading gain is independent of the bitrate since the coding in the frequency domain will not affectthe signal in the time domain, significantly. This is a majoradvantage for a network that supports different kinds ofservices at different bit rates. The bandwidth of the receiverand the associated electronics need only match the bandwidthof the information signal, and not the chip rate.

VI. PRAcncm CONSIDERATIONSIn this section, we address some practical concerns on theimplementation and application of the proposed FE-CDMAsystem.

A. Spectral Shape of the Optical SourcesIn the above discussion, it was implicitly assumed that all

the 1s in the sequence will appear as 1s at the photodetector.However, the spectrum of a LED is not flat. It might exhibitfor example a Gaussian shape, meaning that some 1s willbe seen as different values depending on the position theytake along the spectrum. The consequence of that will bea loss of perfect orthogonality among the users. There arebasically three ways to counter this effect. The first is touse programmable Spatial Light Modulators (SLM), such asliquid crystal devices, in order to obtain nonbinary amplitudetransmissions. Alternatively, one can assign different lengthsof frequency bands depending on the chips positions in thecodes, so that the power transmitted in each band will bethe same. This however increases thg complexity of maskfabrication. The second one is to equalize the LED spectrum,up to some degree, by using Acousto-Optical Tunable Filters,in the same way they have been used in optical systemswith optical amplifiers [15]. Finally, one can simply reducethe length of the total frequency band that is encoded tobe in the center of spectrum, which is flatter. In this paper,we concentrate on this solution. To see the effect of thespectral shape of the source, we have calculated the Signal-to-Interference Ratio (SIR) for different possibilities. We assumethe code used is an M-sequence of length N = 127, a differentcycle-shift of the same sequence is assigned to each subscriber.The SIR can be written as

(10)where z; depends on the spectral shape of the source. Weconsider three cases:

1) Gaussian shape1 112 J B I Z a + i + 1 ) B / N o )zi = e-f df (1 1)2 T f f 2 ) - B / Z a + i B / N a )

where B is the 3-dB bandwidth of the source (B =2.3540) , a is a design parameter related to the encodedbandwidth and a = 1 when we encode the 3-dBbandwidth of the source. As a is increased the encodedbandwidth is reduced and the code looks more binary atthe receiver.Cosinusoidal shape

where X represents the mean spectral height.This shape is chosen to see the effect of ripples of differentamplitudes Am and different period T , on the SIR. It mightcorrespond also to an unperfectly equalized spectrum.3) Sinusoidal shape

B P X + -sin( F ) d f .~ T f (13) = Lsj Am

In this case, the spectrum is assymmetric around the carrierfrequency, and as it will be seen, the SIR is different from thecosinusoidal shape.The results are shown on Fig. 3andFig. 4.On Fig. 3, theSIR (in dB) is plotted as a function of the number of activeusers for the three spectral shapes considered. Remember thatfor a perfectly flat spectrum the SIR would be infinite. Thefirst observation is that the cosinusoidal and Gaussian spectralead approximately to the same SIR, when Am = 4, althoughthey are very different shapes. The sinusoidal shape leads toa worse performance which might be an indication that anasymmetry around the carrier frequency is detrimental. As theperiod T of the cosinusoidal or sinusoidal shapes is changedfrom T = 1 to T = 9, the effect on the SIR is minor. However,as the amplitudes of the ripples is reduced, the SIR increasesby more than 5 dB, for 40 users and a cosinusoidal shape. Notethat, the value Am = 2 corresponds to a very badly equalizedspectrum since the amplitude of the ripples is the same as themean value X . On Fig. 4, the SIR is plotted as a function of a ,for 20, 60 and 100 active users, and for a Gaussian spectrum.As expected, increasing a leads to a higher SIR since thespectrum looks flatter. However, the power received would besmaller, since the encoded spectrum is reduced. This effect isnot seen here, but will be observed in the next section whenwe calculate the bit error probability.

B. Programmable Amplitude MasksIn a CDMA network, it will usually be required thateach user should be able to communicate with all othersubscribers. In the context of a FE-CDMA system this impliesthat the mask used to code the spectrum of the source atthe transmitter should be programmable. Alternatively, the

masks at the receiver could be made programmable. However,it is more convenient to make the mask at the transmitterprogrammable since there is only one mask, compared totwo at the receiver. Programmable Spatial Light Modulators(SLM), electrically addressed or optically addressed, are usefulin many applications in optics so that they have been availablefor a long time. Probably the most commonly used type of


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HAVEHRAD AND ZACCARLN: OPIlCAL CODE-DIVISION MULTIPLEXED SYSTEMS BASED ON SPECTRAL ENCODING

30 .539

rnU

0tuUal0CalalE

-c?-6c-tuC0n.-

Fig. 3.

30

25

20

15

10

5

0

Cos,T=l ,Am3e Cos,T=l,Am=4X Sin,T=l ,Am4m Sin,T=S,Am40 Gaussiarwl

A Cos,T=S,Am=4

20 4 0 60 80 100 120

Number o f Act ive usersSIR versusnumber of active users for different spectral shapes.

0tuU.-c

Fig. 4shape

25

20

15

10

C

c

K=lOO

1 . I . I . I . I

Parameter aEffect of the encoded bandwidth on the SIR for a gaussian spectral

electrically addressed SLM is the Liquid Crystal Television(LCTV) panel, as it offers simplicity and a low-cost. However,recent applications such as pulse shaping by spectral phasemodulation [16] and by spectral amplitude modulation [17]require lower losses and higher speeds, so they lead to thedevelopment of specially designed liquid crystal modulatorarray. One can find a summary of the state-of-the-art forsmart-pixels, SLM based on liquid crystal technology in [181.In our application, as well as in the case of coherent FE-CDMA, the main SLM parameters of interest are its speed andits optical contrast ratio, defined as the ratio of output opticalpower for a pixel being in the ON state to that of a pixel inthe OFF state. For current commercially available devices, thisratio is usually larger than 100.Qualitatively, a finite contrast ratio will reduce the desiredsignal power at the receiver since the power of the OFF pixelsat the transmitter will flow through the lower branch of thereceiver. In the upper branch nothing is changed, since themasks used at the receiver are fixed plates (transparencies orothers), having an infinite contrast ratio.For an interfering signal, the effect will be minimal ifapproximately half of the power in the OFF pixels of theinterfering code goes through the upper branch and half goes

through the lower branch. This will be indeed the case whenusing Hadamard codes, but not quite when using M-sequences(the number of 0s is odd in this case). If the spectrum is flat,it is easy to see that a finite contrast ratio would have littleeffect on the multiple-access capacity of the system. In thenext section, we will show the quantitative effects when oneis using an M-sequence of periode N = 127, and for a lowcontrast ratio value of 10.The other major concern is the switching time required fora pixel to go from one state to another. One future applicationof the FE-CDMA system designed in the paper is its useas a routing technique for ultra fast Asynchronous TransferMode (ATM) switches. We will discuss this application inSection VIII. For an ATM switch, a packet has a fixed lengthof 53 bytes and is called a cell. Assuming a bit rate of 500Mbt/s, a cell is transmitted in 0.85 ps so that the time toprogram a new address on the SLM should be a fractionof that value. For present SLMs, this is still challenging,although rapid progress is being made [19]-[20]. However,one should remember that SLMs are two-dimensional devices,having usually between 200 and 300 rows, most of them beingindependently programmable. Encoding the spectrum requiresonly one row. A possible solution to the speed limit, for a


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switch application, could be to program the other unused rowsin advance, by reading the address of the packets waiting inthe queue. An LED array whose elements are associated withdifferent rows of the SLM could be used, as done in the contextof a free-space optical interconnect.C . Dispersion

It is interesting to note that in the context of LAN's orswitches, the orthogonality of the codes tolerates dispersion.That is, locally, as long as the optical source spectrum isflat, the codes will remain orthogonal. Suppose one is to usesuch a technique over a wide area network as a mean ofmultiplexing. It is clear that in any LED system, dispersionwill limit the system length (10 s of kilometers at most) dueto intersymbol interference of adjacent data bits. However, theresulting degradation would not be more severe than that dueto a nonflat spectrum. We have already demonstrated that evenwith a nonflat spectrum, a substantial number of active userscan be supported. Therefore overall, this multi-access methodoffers a good deal of tolerance to dispersion, even over longerdistances.VII. PERFORMANCE VALUATION

In this Section, we will evaluate the bit error probabilitytaking into account the Multi-Access Interference (MAI), theshot noise and the thermal noise. Since for EE-LED's or SLD'sthe transmitted power can be limited, we will not just plot theBit Error Rate (BER) floors. We will rather seek the numberof required photonshit for a given value of Pe, as a functionof the number of active users.As in our work in [21], the entire system is linear in power,and the Moment Generating Function (MGF) can be easilyfound. We will therefore use the saddle point approximation tocalculate the average probability of error. However, as it willbe shown, the Gaussian approximation gives results almostidentical (it gives a tight upper bound) to those observed byusing the saddlepoint technique. The Gaussian approximationis used for most of the presented results. The results will bepresented assuming the spectral shape is Gaussian. Followingthe expressions in [21], the MGF of the decision variable zis simply

M z ( s )= n Mk(S)eXO(e -l)eu2s2/2. (14)k

For our calculations, we choose T o = 293, R = 100 and1/T = 500 Mbt/s. The MGF for one interfering signal iseasily expressed as

where

We will consider only Amplitude Shift Keying (ASK) modula-tion and therefore bo, I f , , E {0,1}. The delay T is uniformover the bit period. The factors A and A t are the meanintensities received on the positively and negatively biasedphotodetectors respectively, for the interfering user k. Theirexpressions, and the expression for Xo are

where variable zi was defined in (1 1).When using the Gaussian approximation, it is sufficient tofind the mean and the variance of the decision variable z .They are easily found to bel K

772 = X 6 + (A: - Ak = l= X bo + K A: +A )k = l

Note that, the second term in (20) comes from the fact that theshot noise processes produced by the two photodetectors areindependent, while the third term would be zero in the caseof perfect cancellation of the interfering signals. As it can beseen, this would occur for a flat spectral density z; = d e ) .The factor 1/4 in front of the third term in (20) is true if weassume that all users are bit synchronized, T k = 0) for allI C For a uniform T k over [O,T] t would be 1/6. The reasonfor assuming bit synchronized users is for the ATM switchingapplication discussed in Section VLII. In this case, the packetsat the input ports will be routed to their destination output portsat the same time, so that there is no random delay among them.VIII. FE-CDMA SYSTEMS FOR ULTRAFAST ATM SWITCHING

Before presenting the results obtained from the perfor-mance calculations, we will briefly discuss one applicationof our system: routing in packet switches. The AsynchronousTransfer Mode (ATM) is a promising technique for switchingdifferent kinds of services in future broadband ISDN B-ISDN).The required switch capacity depends strongly on theapplication and can range from several Gbt/s in small LocalArea Networks, to a few Tb/s in B-ISDN exchange offices.As an example, if 100 000 customers are served each witha STS-3c line (155.52 Mbt/s), a capacity of 1.5 Tb/s will beneeded for a ten percent traffic load [22].Electronic ATM switches have been extensively developedbut their throughput is limited by the operation speed limitof LSI's and signal transmission bandwidth limit. It is ex-pected that the bottleneck of large capacity switching systems

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HAVEHRAD A ND ZACCARIN: OPTICAL CODE-DIVISION MULTIPLEXED SYSTEMS BASED ON SPECTRAL ENCODING 541

- #1 I\\R bi t ls

I

R bl t ls rn n,lYKInputModules

Fig. 5. A growahle ATM switch architecture.

mOpticalStars

i4oooa

120000

100000

80000

60000

40000

20000

0

m Log Pe)=-70 Log Pe) = -5

I I . I . I . I 1 I I .10 20 30 40 50 6 0 7 0 80 90 100

Number of ports: KFig. 6. Number of photons needed for a fixed P,, N = 127 M-sequencesp-i-n photodetectors.made up of electronic components will arise first in theinterconnection of modules or boards. Optical interconnectswith self-routing ability may be an efficient solution to thisproblem [22]. Switch architectures that combine the strength

c.-U)E00cn

iic0

z

Fig. 7

R bitls

140000

120000

100000

80000

60000

40000

20000

0

III

bitls

KK

Modulesoutput

0 Log Pe)=-9W Log Pe)= -7

Log Pe)= -5

1 . I . I . I . I I . I . I .

10 20 30 40 5 0 6 0 7 0 80 9 0 100

Number of ports: KNumber of photons needed for a fixed P,,N = 128, Hadamardcodes p-i-n photodetectors.

of electronics for contention resolution and buffering andthe strength of optics for routing and signal transmissionare therefore suitable. Optical routing strategies include thosebased on wavelength [22-231 and time domain multiplexing


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c.-U)c00cc

n

t-z

140000

120000

100000

80000

60000

40000

20000

0 Log Pe)=-9Log Pe)=-7Log Pe)=-5

0 . 1 . 1 . , . 1 . 1 - , . 1 . 1 .

Number of ports: KFig. 8. Number of photons needed for a fixed P,, = 511 M-sequencesp-i-n photodetectors.[24], as well as CDMA. A new optical routing strategy canbe obtained from the incoherent FE-CDMA just discussed.Our routing technique can be used in many packet switcharchitectures, among them are the ones described in [22] andmore recently in [25].They both take the form shown in Fig. 5.In [25], m is larger than n and the structure generalizes theknockout principle to a group of n outputs. Buffering is onlydone at the output. In [22], n > m and the structure uses sharedinput and output buffers based on memory chips developed byHitachi [26]. Following is a list of the involved parameters:

1) L = nK input and output lines;2) K input and output modules;3) m optical stars, each with K input and output ports;4) m transmitters (receivers), e.g., number of LEDs in a5) R: bit rate used in the input lines;6) :bit rate for the optical signals in the optical inter-For n > m, a Contention Resolution Device (CRD) isneeded to resolve output contention. Its role is to choose onecell for each output module for each of the m optical stars.Detailed description of the CRD can be found in [22]. When

LED array, for each of the K input (output) modules;

connect ( R x n = Ro x m);

c.-mU)E00cn

t0

z

0 Log Pe)=-9A Log Pe)= -9 SLM)

Log Pe)= -7 SLM)\ a Log Pe)= -5 (SLM)100000

80000

60000

40000

20000

o . , . , . , , . . I I10 20 30 40 50 6 7 0 80 9 0 1

Number of ports: K0

Fig. 9. Numberof photons needed for a fixed P,, N = 127 hl-sequencescontrast ratio = 10 dB.the CRD is m times faster than the cell transmission timethrough one star, the m optical stars are busy at all times.Only up to m cells can be routed to the same output modulein one cell transmission time and therefore there is a Head ofthe Line Blocking (HOL) probability. This probability can bereduced by increasing m. However, for K fixed, m is limitedby the speed limit of the CRD. On the other hand, K is limitedby the power visioning occuring at the star couplers. Thenumber of photonshit (Ph) available at a receiver is given by

Ph = 21)where P, is the source power in dB, 10logK is the splittingloss due to the star coupler, a total of 6 dB of other losses andRo is the bit rate. This will be plotted on the figures of the Pshown in the next section, for P, values of 0 dBm, -2 dBmand -5 dBm. The crossing points of Ph with the P, curvesdetermine the maximum value of K that can be used.

1o PS-1O ogK-6)/10Rohf

Ix. REiSULTS AND DISCUSSIONThe results obtained are given on Figs. 6 to 11. Unlessotherwise specified, these results assume a Gaussian shape,


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HAVEHRAD AND ZACCARIN OPTICAL CODE-DIVISION MULTIPLEXED SYSTEMS BASED ON SPECTRAL ENCODING

0 Log Pe) = 9, PINA Log Pe)= -9, PIN, E0 Log Pe) = -9, APD

100000

80000

60000

40000

20000

10 20 30 40 50 60 7 0 80 90 100

Number of ports: KFig. 10. Number of photons needed for Log Pe) = -9 ,N = 127M-sequences.with a =1.3. The number of photonshit required to getP, =lo- and is given, as well as the numberof photonshit available, for three power source values, from(21). The reason for considering different P, values is thatP, =10^-5 might lead to an acceptable probability of packeterror. Unless otherwise stated, the results are calculated usingthe Gaussian approximation on the decision variable. Thefirst matter to note is the number of active users (K). Morethan one hundred users can be accommodated for P, =lo-.Note on Fig. 6 that, up to 70 interfering users, the powerpenalty is less than 3 dB. However, if the incoherent opticalsource can launch less than -2 dBm power, the multiple-access capacity will be limited to about 40. This is for avery reasonable code length of 127, for which a high-speedprogrammable SLM has already been developed for pulseshaping. On Fig. 7, Hadamard codes are considered insteadof M-sequences. As seen, a better performance is obtained.Less than 3 dB penalty is observed for up to 100 users.The better performance can probably be explained by the factthat for a Hadamard code, the distribution of the ones andzeros across the spectrum is more uniform than for an M-sequence of length N = 2T - 1, which always counts a run

4-4 --5 --6

-7

-8 --9 -

-2 a=0.8a = .0-3 a = .4. = .60 a= .2

543

-10 I I INumber of Photons / Bit

Fig. 1 1 Performance as the encoded bandwidth varies; N = 127M-sequences K = 40.of T ones and T - 1 zeros. On Fig. 8, we show the effect ofincreasing the code length N to 511. A code length N =127 is sufficient to accommodate 127 subscribers. However,by increasing the code length, the spectral length allocatedto each chip is smaller, and the allocated power is thereforemore uniform. As seen, the performance is better than withN = 127, but the requirement on the resolution of the spectralfiltering is more severe. Tolerance to misalignments would alsobe greatly reduced. ,,In Fig. 9 we show the effect of having a finite contrast ratio(labeled SLM), takeh to be 10dB.As seen, 70 photonshitare needed for K = 100, and P, = lo-, compared to 54photonshit needed when the contrast ratio is 0. For othervalues of P, there is little difference between a finite value,and an infinite valae of the contrast ratio. We therefore believethat a finite contrast ratio from a programmable SLM wouldnot be too harmful to our system. On Fig. 10, we compare theP, obtained when using the saddlepoint approximation andthe Gaussian approximation. As seen, the results of Gaussianapproximation are very close to the exact results (curvelabeled E). This yields a tight upper bound on the systemperformance. We also present the performance obtained when


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544 JOURNAL OF LIGHTWAVE TECHNOLO GY, VOL. 13, NO. 3, MARCH 1995

using an APD with a gain G and an ionization coefficient k =0.1. In this case, the expressions for the mean and varianceneed to be modified

An APD with the parameters considered would perform betteronly when the thermal noise dominates, which seems true forK 5 40. When there are more active users, the shot noisedominates and a p-i-n is the right choice. It is interestingto see that the Gaussian and the saddlepoint approximationsgive identical results in the range where the thermal noisedominates. Finally, on Fig. 1 1 we plot the P, as a function ofthe number of photons/bit for different values of the parametera, and for K = 40 active users. It was observed in Fig. 4that reducing the encoded bandwidth (increasing a) yields ahigher SIR. One can see that taking into account the shot noiseand the thermal noise, the highest a is not the best choice,since reducing the encoded bandwidth will reduce the receivedpower, and therefore the Signal-to-Noise Ratio SNR).Notethat, for a = 0.8, a floor is observed. In that case, the encodedbandwidth is too large and the spectrum is not put enough,therefore, multiple-access-interference dominates and the P,cannot be reduced by increasing the power.Let us now estimate a possible achievable throughput foran ATh4 switch based on our encoding technique. Let ussuppose f i = 500 Mbt/s as achievable by EE-LEDs. ForM-sequences with N = 511 in Fig. 8, the cell transmissiontime is 0.848 ps 53 bytes x 8/Ro).An arbitration cycle musttherefore be over 0.848 ps/m. A device that can achieve thisin less than 22 ns is described in [22]. Taking a conservativevalue of 22 ns, we get m 5 42. The total throughput TR ofthe switch is given by

TR= Ro x K x m. 24)Assuming P, = lo is needed and a value of P, = -2 dBm,K is limited to 72, from Fig. 8, and the achievable throughputis TR = 500 Mbt/s x 42 x 72 = 1.5 Tb/s. To reduce thenumber of transmitters and receivers needed per module, wemight choose m = 10 and the throughput decreases to TR=360 Gbt/s. Form =20, and assuming a P = is sufficient,one gets TR = 840 Gbt/s.

X. CONCLUSIONIn this paper, we have presented a new type of CDMAsystem based on frequency encoding of optical broadbandsources. Parts of this paper had been published by the sameauthors in [2]-[3]. We presented in detail a new design thatapplies to incoherent (broad-linewidth) sources. The proposedsystem has the advantage of using inexpensive optical sources,

and simple direct detection receivers with bandwidth require-ments equal to the bit rate. The spreading gain of this type ofCDMA system is independent of the bit rate since the spectralshaping of the sources does not affect the signals in the timedomain. It was shown that a large number (from 70 to 100)active users can be supported, for a moderate code length ofN = 127, with an operating average bit error rate of P =Application of such a system as a core module in anATM switch was also briefly discussed.

REFERENCESA. M. Weiner, J. P. Heritage, and J A. Salehi, Encoding and decodingof femtosecond pulses, Opt. Let., vol. 13, p. 300, 1988.D. Zaccarin and M. Kavehrad, An optical CDMA system based onspectral encoding of LED, IEEE Photon. Technol. Left., Apr. 1993.D. Zaccarin and M. Kavehrad, Ultrafast ATM switching using opticalCDMA based on spectral encoding of LED, in Proc. ICC New Orleans,May 1994.A. M. Weiner et al., High-resolution femtosecond pulse shaping, J.Opt. Soc. Am. B., vol. 5 , pp. 1563-1572, Aug. 1988.M. B.Danailov and I. P. Christov, Time-space shaping of light pulsesby fourier optical processing, J. Mod. Optics, vol. 36, pp. 725-731,1989.T. E. Chapuran, S. S. Wagner, and T. P.Lee, Wavelength-dependentpower penalties in broad band spectrally sliced WDM networks, inProc. OFC 92, Paper TuN4, 1992.G. D. Collins, Achromatic fourier transform holography, Appl. Optics,vol. 20, pp. 3109-3119, Sept. 1981.P. Anders, J. Lancis and W. D. Furlan, White-light transformer withlow chromatic aberration, Appl. Optics, vol. 31, pp. 46824687, Aug.1992.P. Cielo and C. Delisle, Transmission dimages par modulation duspectre, Can. J. Phys., vol. 54, pp. 2332-2339, 1976.A. Lacourt and P. Boni Transmission dimages et dhologrammespar une nappe de fibers optiques au moyen dun codage chromatique,Optics C o m u n . , vol. 27, pp. 57-60, Oct. 1978.T. Ohtuka et al., Single-mode fiber transmission using edge-emittingLED for broadband subscriber loops, Electron. Commun. Japan, partI, vol. 72, May 1989.Y. Kashima e? al.. Performance and reliability of InGaAsP superlu-minescent diode, J. Lightwave Technol., vol. l i , pp. 1644-1649,-Nov.1992.P. Wysocki eta l . , Spectral characteristics of high-power 1.5ern broad-band superluminescent fiber sources, IEEE Photon. Technol. Lett., vol.J Wolfmann, Almost perfect autocorrelation sequences, IEEE Trans.Inform. Theory,vol. 38, pp. 1412-1418, 1992.S. F. Su et al., Gain equalization n multiwavelength lightwave systemsusing aoustoopic tunable filters, IEEE Photon. Technol. Left., vol. 4,pp. 269-271, Mar. 1992.A. M. Weiner et al., Programmable Shaping of femtosecond opticalpulses by use of 128-element liquid crystal phase modulator, J.Quantum Electron, vol. 28, pp 908-920, 1992.M. C. Wefers and K. A. Nelson, Programmable phase and amplitudefemtosecond pulse shaping, Opt. Lett., vol. 18, pp. 2032-2034, 1993.K. M. Johnson, D. McKnight, and I. Underwood, Smart spatial lightmodulators using liquid crystals on silicon, J. Quantum Electron., vol.29, pp. 699-714, Feb. 1993.G. Andersson et al., Submicrosecond electro-optic switching in theliquid-crystal smectic A phase: The soft-mode ferroelectriceffect, Appl.Phys. Lett., vol. 51, pp. 640-642 1987.J. Gourlay, P. McOwan, and D. G. Vass, Time-multiplexed opticalhadamard image transformwith ferroelectric-liquid-crystal-over-siliconspatial light modulators, vol. 18, pp. 1745-1747, Oct. 1993.D. Zaccarin and M. Kavehrad, Performance evaluation of opticalCDMA systems using noncoherent detection and bipolar codes, JLightwave Technol., vol. 12, no. 1, Jan. 1994.A. Cisneros and C. A. Brackett, A large ATM switch based on memoryswitches and optical star couplers,IEEE J. Select Areas Commun., vol.N. Shimosaka et al., Wavelength-addressed optical network using anATM cell-based access scheme, in Dig. OFC, San Jose, Feb. 1993,Paper TuJ6, p. 49

2, pp. 178-180, Mar. 1990.

9, pp. 1348-1360, Oct. 1991.


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[24] A. Jajszcyk and H. T. Mouftah, Photonic fast ATM switching, IEEECommun.Mag. ol. 31, pp. 58-65, Feb. 1993.[25] K.Y. Eng., M. J. Karol, and Y. S. Yeh, A growable packet (ATM)switch architecture: Design principles and applications, IEEE Trans.Commun., ol. 40, p. 423430, Feb. 1992.[26] H. Kuwahara et al., A shared buffer memory switch for an ATMexchange, in Proc. ICC, June 1989, pp. 4.4.14.4. 5.

Mohsen Kavehrad (S75-S75-M784M86-F9 2) was born in Tehran, Iran, on January 1,1951.He received his Ph.D. degree from PolytechnicUniversity (Formerly: Brooklyn PolytechnicInstitute), Brooklyn, NY, n November 1977 inElectrical Engineering.Between 1978 and 1981, he worked for FairchildIndustries (Space Communications Group), GTESatellite Corp. and GTE Laboratories in Waltham-Mass. In December 1981 he joined AT&T BellLaboratories where he worked in Research,Development, and Systems Engineering areas as a member of technicalstaff. In March 1989 he joined the Department of Electrical Engineeringat University of Ottawa, as a full professor. He is the Leader of PhotonicNetworks and Systems Thrust and a Project Leader in the TelecommunicationsResearch Institute of Ontario (TRIO). Also, he is a project leader in theCanadian Institute for Telecommunications Research (CITR). Presently, heis the Director of Ottawa-Carleton Communications Center for Research(OCCCR). In the summer of 1991, he was a visiting researcher atLaboratories in Japan. He has worked in the fields of satelli te communications,point-to-point microwave radio communications, portable and mobile radiocommunications, atmospheric laser communications, and optical fibercommunications and networking. He has published over 150 papers andhas several patents issued in these fields.

Dr Kavehrad is a former Technical Editor for the IEEE TRANSACTIONSNCOMMUNICATIONS,EEE COMMUNICATIONSAGAZINE.nd the IEEE MAGAZINEOF LIGHTWAVEELECOMMUNICATIONSYSTEMS.

Denis Zaccarinwas bom in Qu6bec city, Canada, on November 24, 1964. Hereceived the B.Sc.A. and M.Sc. degrees in electrical engineering from LavalUniversity, Qukbec, Canada, in 1987 and 1989, respectively, and the Ph.D.degree in electrical engineering from University of Ottawa in 1994.In 1988 he served as Consultant for the Canadian government in the areaof satellite comuunication systems. In 1989-1990, he worked as a researchengineer for the Department of National Defense, Ottawa, where he wasinvolved in secure coumnication systems. He is a member of scientific staffat Bell-Northem Research, Ottawa, where he works in the area of high-speedoptical comuunication systems.

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