2-D Optical Orthogonal Codes

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 22, NO. 11, NOVEMBER 2004 2409

High-Performance Optical CDMA System Based on2-D Optical Orthogonal Codes

Antonio J. Mendez, Senior Member, IEEE, Member, OSA, Robert M. Gagliardi, Fellow, IEEE, Vincent J. Hernandez,Corey V. Bennett, Member, IEEE, Member, OSA, and William J. Lennon

Abstract—Optical code-division multiple access (OCDMA) is aninteresting subject of research because of its potential to supportasynchronous, bursty communications. OCDMA has been investi-gated for local area networks, access networks, and, more recently,as a packet label for emerging networks. Two-dimensional (2-D)OCDMA codes are preferred in current research because of theflexibility of designing the codes and their higher cardinality andspectral efficiency (SE) compared with direct sequence codes basedon ON–OFF keying and intensity modulation/direct detection, andbecause they lend themselves to being implemented with devicesdeveloped for wavelength-division-multiplexed (WDM) transmis-sion (the 2-D codes typically combine wavelength and time as thetwo dimensions of the codes). This paper shows rigorously that 2-Dwavelength/time codes have better SE than one-dimensional (1-D)CDMA/WDM combinations (of the same cardinality). Then, thepaper describes a specific set of wavelength/time ( ) codes andtheir implementation. These 2-D codes are high performance be-cause they simultaneously have high cardinality ( 10), per-userhigh bandwidth ( 1 Gb/s), and high SE ( 0.10 b/s/Hz). The phys-ical implementation of these codes is described and their per-formance evaluated by system simulations and measurements onan OCDMA technology demonstrator. This research shows thatOCDMA implementation complexity (e.g., incorporating doublehard-limiting and interference estimation) can be avoided by usinga guard time in the codes and an optical hard limiter in the receiver.

Index Terms—Access protocols, code-division multiple access(CDMA), codes, encoding, multiaccess communication, numericalmodeling, optical fiber communication.

I. INTRODUCTION

OPTICAL code-division multiple access (OCDMA) has al-ways been of interest because of its inherent ability to sup-

port asynchronous bursty communications. As such, it was ini-tially pursued for local area [1] and then for access network ap-plications [2]–[5]. More recently, it is the subject of research forgeneralized multiprotocol label switching (GMPLS) versions ofemerging networks [6]–[8]. Generally, OCDMA can be dividedinto direct-sequence pseudoorthogonal (PSO) pulse sequences

Manuscript received December 16, 2003; revised June 24, 2004. This workwas supported in part by the U.S. Department of Energy under SBIR Phase IIGrant ER83277 and by the National Science Foundation under SBIR Phase IGrant 0319414. The joint collaboration between Mendez R&D Associates andthe Lawrence Livermore National Laboratory (LLNL) was carried out under Co-operative Research and Development Agreement (CRADA) TC-2051-02. Thiswork was performed under the auspices of the U.S. Department of Energy bythe University of California, LLNL, under Contract No. W-7405-Eng-48.

A. J. Mendez is with the Mendez R&D Associates, El Segundo, CA 90245-1856 USA (e-mail: [email protected]).

R. M. Gagliardi is with the Department of Electrical Engineering—Systems,University of Southern California, Los Angeles, CA 90089-2565 USA.

V. J. Hernandez, C. V. Bennett, and W. J. Lennon are with the Lawrence Liv-ermore National Laboratory, Livermore, CA 94551 USA.

Digital Object Identifier 10.1109/JLT.2004.837296

[9], which are frequently referred to as optical orthogonal codes(OOCs) [10], [11]; direct sequence bipolar codes [6]; frequencyor phase encoding codes [12], and so on; and two-dimensional(2-D) and higher dimensional codes. The 2-D codes, in turn, canbe divided into time-spreading frequency-hopping types [13],[14]; depth-first search types [15], [16]; 2-D prime code types[17], [18]; sonar codes [19]; and folded optimum Golomb rulertypes [20]–[26]. Examples of three-dimensional (3-D) codes aregiven in [27], using wavelength, space, and time for the codesand using wavelength, polarization, and time for the codes [28].

The 2-D codes typically combine wavelength and time asthe two dimensions of the codes. 2-D codes based on ON–OFF

keying (OOK) have better spectral efficiencies than one-dimen-sional (1-D) codes of the same cardinality [19]. Thus, 2-D codesmake better utilization of the bandwidth expansion associatedwith the codes.

This paper first shows that 2-D wavelength/time ( )codes have better spectral efficiency (SE) than wavelength-di-vision-multiplexed (WDM)/1-D-CDMA combinations (of thesame cardinality). It then describes a specific set of codesand their implementation. These 2-D codes are high perfor-mance because they simultaneously achieve the following:

1) have a high cardinality ( 10);2) lend themselves to high per-user data rates ( 1 Gb/s);3) have a high SE ( 0.10 b/s/Hz and potentially 0.5 b/s/Hz).

The paper decribes the physical implementation of these2-D codes and evaluates their performance by means of systemsimulations and measurements on an OCDMA technologydemonstrator (TD).

This research shows that implementation complexity (e.g.,double hard limiting with and without interference estimation[29]) can be avoided by using a guard time (GT) in the codes andan optical hard limiter (OHL) in the receiver. The OHL needs tobe enabled when the number of users exceeds one half of theavailable number of 2-D codes; for fewer users, the GT may besufficient.

II. THEORY, ANALYSIS, AND SIMULATION

A. Comparison of 2-D ( ) Codes and WDM/CDMASequence Codes

In OCDMA systems, multiple wavelengths can be used toproduce W/T matrix codes as well as products of WDMand OOCs (i.e., the combination WDM/CDMA sequencecodes). Either approach can be used to generate codes forsignaling. These two methods of using wavelength and timecan be described as 1) 2-D codes in which (the weight of

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2410 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 22, NO. 11, NOVEMBER 2004

the code) pulses are placed in an matrix to form an OOCmatrix code set or 2) WDM/CDMA codes, in which a set ofOOCs of weight is associated with each of wavelengths toform a code set. This section of the paper compares these twoalternatives in terms of SE and decoding bit-error probability,and it concludes that the 2-D codes have a significantly betterSE than WDM/CDMA codes.

WDM/CDMA: A set of OOCs of length and weightare selected. A set of wavelengths is selected, and the OOC setis used with each of these wavelengths. A WDM/CDMA codeis selected by assigning a wavelength and an OOC. Hence, thereare specific codes in the set.

If is the code bit time, then a code chip time in the se-quences is , and the sequence bandwidth is ,where is the code bit rate. The overall required band-width is then

BW (1)

The throughput of the entire code set is the number of codestimes the bit rate per code

TP (2)

The SE of the code set is SE BW, or

SE (3)

For OOCs with pulses, the code length satisfies

(4)

hence, SE satisfies

SE (5)

Thus, the bound on the SE of WDM/CDMA depends on onlythe code weight. For example, a weight-four code set has anSE .

The bit-error probability is that of sequence detection and de-pends on the assumption of the multiaccess interference (MAI),which is due, of course, to the crosstalk of the other codes (MAIonly; no noise is considered in this analysis). With only MAI, abit error occurs only if the MAI causes the correlation output toexceed threshold (which can be set high if no noise is involved).Since there are codes at any one wavelength, only codescan interfere with any specific code. For a code with weight ,and a threshold placed slightly below , no decoding error canoccur if . (The MAI cannot cause a bit error sinceit can only climb to a value of at most during correla-tion. This is particularly true if code acquisition and samplingwindow techniques are incorporated in the receiver. We havenot included the potential interference from beat noise.) Hence,WDM/CDMA has the theoretical potential for zero error prob-ability if the number of codes per wavelength does not exceed

.Matrix Codes: An matrix code, with wavelengths and

time slots, contains pulses to represent each code. A matrixset is formed by starting with OOCs (specifically, optimumGolomb rulers) of weight and adding dummy zeroesto obtain the code dimension CD and folding eachsuch (expanded) sequence into the matrix to form matrix

codes. The cyclic row shifting of each such matrix generatesnew matrix codes, producing a set of matrix codes.The pulsewidth of a matrix pulse placed in a time slot at any

wavelength is , and the overall bandwidth required is then

BW (6)

where is again the code bit rate. The total throughputfor the code set is

TP (7)

producing a spectra1 efficiency

SE (8)

The initiating code sequence must have length to supportOOCs, where . Since the matrix codedimension , it follows that

and in (8)

SE (9)

so that the upper bound of SE for matrix codes is times higherthan the for WDM/CDMA in (5). Hence, matrix coding al-ways has a higher SE than the corresponding WDM/CDMAsystem.

This analysis is well confirmed in practice. For example, thelinear codes (optimum Golomb rulers) of [26] have a cardinalityof four and a code length of 25. When combined with eightwavelengths for a WDM/CDMA combination, they produce 32hybrid codes with an SE of . On the otherhand, if we generate 32 codes with eight wavelengths andfour time slots according to the algorithm of [26], including thecyclic row permutations, then we have SE .This is slightly less than the factor of associated with (5) and(9) because of the filler zeroes that must be appended tothe optimum Golomb rulers as part of the procedure required toform matrix codes from the rulers.

In practice, the SE of OOCs is much poorer than that shownin (5) for the higher weight codes. The reason for this is shownin Fig. 1, where the actual code lengths of tabulated optimumGolomb rulers [9] (normalized by the cardinality of the set)are plotted along with the customary OOC code length lowerbound (i.e., ). The figure shows thatthe actual trend line for the normalized code lengths is a cubicfunction of the weight .

Similarly, the SE of the derived matrix code depends on thecode length of the OOC from which it is derived. This is shownin Fig. 2, where the computed SE, (8), is plotted for variouscases involving , , and . The actual lengths of the optimumGolomb rulers were used in the computation. The figure showsthat the SE is degraded with the higher and that a higher ma-trix code set cardinality and SE is achieved with using a larger

in combination with an intermediate (the dashed line in thefigure).

B. Example of the Matrix Codes

The kind of 2-D codes that we are developing are based onfolding the OOCs known as optimum Golomb rulers [26]. Ex-

MENDEZ et al.: HIGH-PERFORMANCE OPTICAL CDMA SYSTEM 2411

Fig. 1. Comparison of normalized optimum Golomb ruler lengths and the OOC length lower bound.

Fig. 2. SE of W=T matrix as a function of the cardinality n and weight w ofthe original linear code and number of wavelengths f in the matrix code.

amples of the rulers that were used in that reference to de-velop a set of 32 2-D codes are the set , ,of four rulers of weight four. These four rulers are shown in

the equations at the bottom of the page. After appending fillerzeroes to these rulers sufficient to form the code dimensionCD , the rulers can be folded into a rectangle [20], [26].The ruler thus generates the matrix , gen-erates ; generates , and generates

. Cyclic row shifting allows to produce ;produces ; produces ,

and produces .Simulations and measurements have shown that it is also nec-

essary to append a GT to the resulting matrices in order to avoidthe intersymbol interference (ISI) that results from the correla-tion process [23], [25], [26]. A 50% GT is considered ideal (thecode is applied to the first half of the bit, and the remainder ofthe bit consists of zero chips). The GT maximizes the numberof concurrent users and enables other functions such as opticalhard limiting in the correlator to sufficiently suppress MAI so asto permit all 32 codes to operate concurrently. Thus, the matrix

with the GT takes the form in Fig. 3, where the shaded por-tion is the folded ruler, and the unshaded portion is the GT. (Ofcourse, from a system viewpoint, the maximizing of throughputis at the expense of SE.)


Fig. 3. MatrixM1 showing the folded ruler and GT.

The square matrix form is very convenient because the cyclicrow shifting can be represented by the matrix operator givenby

(10)

and then the matrices are generated by

or

(11)

except in cases when shifts a “1” from the last row to the firstrow of the resulting matrix. In those cases, the resulting matrixis “fixed” by applying the cell shift operator

(12)

(where is a matrix element in the first row of any thatresults from the operator shifting it from the last row of thepreceding matrix). For example, is aresult that needs to be fixed that way and also ,

, , ,, , ,

, and (see Appendix for the full listof 32 valid OOC matrices). This cell shift operator is necessaryin the cases mentioned to be consistent with the shift algorithmof [26] and to preserve the rulers’ difference triangle property[9], which is, after all, the property that makes the rulers OOCs.

C. System Simulation

Accurate numerical modeling requires the capturing of all thecritical functions and transfer functions of the subassembliesand components of the system being simulated. The top-levelarchitecture of the optical CDMA TD that we are developing isshown in Fig. 4, and the design of the encoders and decoders ofthe 32 matrix codes based on eight wavelengths and eighttime slots (including GT) is shown in Fig. 5. (See Section III formore details on the system design.)

The emphasis in this paper, both in the simulations and themeasurements, is on the performance of the matrix codeswithout any signal processing such as optical hard limiting,double hard limiting, etc. [11], [23], [26], [29].

III. OCDMA TECHNOLOGY DEMONSTRATOR

We have designed and implemented a TD based on ma-trix codes. To reduce component count, component costs, pro-visioning requirements, and complexity, a network has been se-lected wherein a “central office” generates an encodable car-rier (EC) that is distributed to the users by means of a treetopology network (Fig. 4). The EC is a time-frequency combwith 100-ps (the chip time) return-to-zero (RZ) pulses, a repe-tition frequency of 1.25 GHz, and eight wavelengths (C35–C42on the ITU grid). Using the first four of the eight chips in the bitfor the coding gives a 50% GT to minimize ISI, as discussed pre-viously. Users encode the EC with their code and then impressnonreturn-to-zero (NRZ) GbE data. Encoded data is broadcastto the other users by means of a 32 32 star coupler (cur-rently implemented) or linear bus. Encoders/decoders are basedon arrayed-waveguide gratings (AWGs), 1 4 couplers, anddelay-line arrays (100-ps delay increments), as shown in Fig. 5.

Fig. 6 shows the TD installed in a 19 rack. The 18 AWGblades are in an 8U (1U 1.75 inches) enclosure at about mid-height of the rack. Sixteen of the AWGs are used to produce the32 encoders; one of the AWGs is used to combine the contin-uous-wave (CW) distributed feedback (DFB) laser outputs forproducing the multiwavelength light source that is used to gen-erate the EC; and one of the AWGs is reserved for producingtwo decoders (for two strictly orthogonal 2-D OOCs). The 481 4 couplers that are used to generate the tree topology net-work as well as to make the encoders and decoders are in four2U enclosures above and below the AWG enclosure. The 3232 star coupler is in a 1U enclosure at the top of the rack. Themainframe with the eight ITU wavelength DFBs is shown belowthe passive components, at the lower portion of the rack.

The devices and electronics for producing the RZ pulses(step recovery diode driving a Mach–Zehnder modulator) arenot shown in the figure.

The TD architecture defines the wiring diagram among theseenclosures and active components such as the multiwavelengthsource.

IV. SIMULATION AND MEASUREMENT RESULTS

The architecture and system concept of Fig. 4, includingall of the major subassemblies and/or their transfer functions,were captured in the R-Soft LinkSIM simulation program, fromwhich eye diagrams and bit-error rates (BERs) were generatedfor the cases of one user, four users, eight users, 12 users, and16 users. Previous analyses and simulations indicated that noadditional signal processing was required for up to 16 usersif a 50% GT was used; beyond 16 users, signal processing isrequired, and OHL was used as part of the (simulated) decoder.Where transfer functions were not available (e.g., the receiver),the LinkSIM default values were used.

The TD represents the system concept without OHL (to date,an OHL has not been implemented). Therefore, it can be prop-


Fig. 4. TD top-level architecture.

Fig. 5. Design of the 2-D W=T encoders based on AWGs, delay lines, andcouplers.

erly used to measure the eye diagram of up to 16 users. This wasdone at the same data rate as the simulation (corresponding to1 GbE, including the 8B/10B line coding). The comparison ofthe simulated and measured eyes is shown in Figs. 7–11, rep-resenting the canonical one, four, eight, 12, and 16 concurrentusers.

The figures show several results.

1) Simulation (two cycles) and measurement (three cycles)agree that the autocorrelation (single user case) exhibitsno sidelobes or “wings” in the eye (Fig. 7).

2) At four users, the eye is very open for either the simulatedor the measured case, and the signal to adjacent MAI is

4:1 for the simulation and somewhat less than that forthe measurements (the measurements suggest that there isa slight misalignment in some of the encoder delay lines,bunching up the MAI in some windows around the signaland reducing it in others (Fig. 8).

3) At eight users (Fig. 9), the simulated eye is still very open,whereas the measured eye is starting to show the effectsof receiver sensitivity (the simulation receiver sensitivityis greater than that of the TD); also some signal/MAI beat

Fig. 6. TD setup.

noise may be present (since the only MAI present isin-band of the code).

4) At 12 users (Fig. 10), the simulated eye is still quite open,but the adjacent MAI is starting to build up to the samelevel and the variance of the marks is starting to increase;the measured eyes are open but show more closure thanthe simulation (lower receiver sensitivity and possiblyfrom in-band beat noise). These data show the need to


Fig. 7. Eye diagram, single user: system simulation (left) and measured (right).

Fig. 8. Eye diagram, four users: system simulation (left) and measured (right).

Fig. 9. Eye diagram, eight users: system simulation (left) and measured (right).

incorporate sampling in a time window at the data rate,after code acquisition, as part of the system setup routine.

5) At 16 users (Fig. 11), the simulation shows an open eye,but the temporal region between eyes is starting to fill up(at greater than 16 users, the simulation is unable to finda BER; this is a property of the quantization of the MAI).

The simulation and the measurements agree very wellwith respect to the magnitude of the adjacent MAI versusthe peak of the signal. Again, the simulation and mea-surements suggest that, with sampling within a windowsynchronized with the data clock, it should be possible toretrieve the signal without requiring more complex signal


Fig. 10. Eye diagram, 12 users: system simulation (left) and measured (right).

Fig. 11. Eye diagram, 16 users: system simulation (left) and measured (right).

processing, but this contention needs more simulation andexperimentation.

Finally, we show the simulation results comparing one to 16asynchronous concurrent users (using only GT) and one to 32asynchronous concurrent users (using GT and OHL in the cor-relator) (shown in Fig. 12). The figure indicates that there is noadvantage (but a slight power penalty) to using OHL below16users; above 16 users, GT plus OHL permits the full set of usersto operate concurrently at BERs of to , sug-gesting that additional receiver complexity beyond GT and OHLmay be counterproductive.

Fig. 12 also shows a rapid increase in required received powerabove 24 users. This interesting phenomenon has two interre-lated causes. For (or ), the matrixcodes are characterized by time-slot reuse; e.g., the target code

can be represented as [ , ; ; , ; ;0;0;0;0], includingthe GT, where the semicolons denote the matrix columns or timeslots. Note that wavelengths and (as well as and ) are inthe same time slot. On the other hand, for (adding

), the added codes are represented by wavelengthreuse; e.g., can be represented by [ ; ; ; ;0;0;0;0], in-cluding GT. Note that wavelength appears in time slots one,two, and four. The two causes can then be explained as fol-lows: 1) codes with wavelength reuse like , when they have a

wavelength in common with , increase the average receivedpower (the OHL does not affect this because the common wave-length occurs in different time slots) and 2) the MAI due to thecommon wavelengths is distributed over several time slots, in-creasing the probability that the MAI will be coincident with theautocorrelation peak. It is evident that both causes will requirethat the receiver respond by increasing the decision threshold.

For completeness, the following are the codes added betweenand that contribute most to the increased

required received power above :

at

at

at and

at

V. DISCUSSION AND CONCLUDING REMARKS

R-Soft LinkSIM simulations and measurements with theOCDMA TD indicate that the visibility of the signal over theMAI is good enough to produce BERs of tofor up to 16 concurrent users (while using a 50% GT in thecodes), giving an SE of 0.25 b/s/Hz. For 16 users, addi-tional signal processing (e.g., OHL) is required, but additional


Fig. 12. Comparison of received power required to achieve BER’s of 10 � 9 and 10 � 12, with GT only and GT plus OHL; there is no advantage to usingOHL below 16 users; above 16 users, GT plus OHL permits all 32 users to operate concurrently and error-free.

complexities such as double hard limiting and interferenceestimation are probably not required. The OCDMA TD de-scribed in this paper is intended to explore and extend theboundaries of high-performance OCDMA in terms of numberof asynchronous users, associated data rates, and associatedSE. It is particularly designed to show that high-performance2-D intensity-modulated/direct-detection (IM/DD) OCDMA is

feasible without requiring any technical complexity beyond aGT and OHL.

APPENDIX ALISTING OF THE 32 2-D OOCS AND THEIR CONSTRUCTION

See equations that follow on the bottom of the page and theremaining pages.


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Antonio J. Mendez (M’88–SM’03), photograph and biography not available atthe time of publication.

Robert M. Gagliardi (F’93), photograph and biography not available at thetime of publication.

Vincent J. Hernandez, photograph and biography not available at the time ofpublication.

Corey V. Bennett (M’99), photograph and biography not available at the timeof publication.

William J. Lennon, photograph and biography not available at the time of pub-lication.

2-D Optical Orthogonal Codes

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