Photon Netw Commun (2010) 19:277–283DOI 10.1007/s11107-009-0232-8

Direct-detection synchronous O-CDMA system with interferenceestimation and cancellation

Kai Cui · Mark S. Leeson · Evor L. Hines

Received: 21 April 2009 / Accepted: 11 November 2009 / Published online: 28 November 2009© Springer Science+Business Media, LLC 2009

Abstract An M-ary coded synchronous optical code-divi-sion multiple-access (O-CDMA) system with pulse-positionmodulation (PPM) is investigated. One novel class of opticalspreading codes based on combinatorial designs is adoptedin the multiplexing process. Their ideal correlation proper-ties facilitate the discrimination between desired signals andjamming. However, the multiple-access interference (MAI)with high intensity significantly deteriorates the system per-formance even if the number of interferers is small. In thispaper, we present an interference reduction technique fordirect-detection O-CDMA to suppress the noise effect andincrease the system capacity. The MAI from reference sig-nals can be estimated by utilizing the uniform cross-corre-lation (CC) among its sequences and considerably cancelledout after the photodetection process. The upper bound onthe error probability of optical synchronous PPM-CDMA isthen derived. The proposed system is shown to be effective toimprove the bit error performance and to alleviate the errorfloor when the number of simultaneous users and the receivedoptical power are not appreciably small.

Keywords Optical code-division multiple-access(O-CDMA) · Pulse-position modulation (PPM) ·Combinatorial code designs · Multiple-access interference(MAI) · Interference reduction

1 Introduction

In recent years, the use of spread spectrum technologyhas been of continued interest in optical communication

K. Cui (B) · M. S. Leeson · E. L. HinesSchool of Engineering, University of Warwick Coventry,Coventry CV4 7AL, United Kingdome-mail: K.Cui@warwick.ac.uk

networks [1–3]. In contrast to wireless, fiber-optic sys-tems enjoy access to substantial available bandwidth andultra-high signal processing speed is possible in the opticalmedium. Optical code-division multiple-access (O-CDMA)is therefore evolving into a promising candidate for next-gen-eration broadband communications, due to its potential forall-optical processing, decentralized network management,service differentiation, as well as enhanced information secu-rity [2–4]. Conventional O-CDMA can be classified into syn-chronous and asynchronous systems depending on whethersynchronization is required [5–7].

In a bit-asynchronous, incoherent O-CDMA system, eachuser can transmit data simultaneously without any time slot-ting restrictions. Thus, no frame or chip synchronization isrequired and no overall network control is necessary. How-ever, a major obstacle in its implementation is the limitednumber of available code sequences and poor bit error perfor-mance compared to analogous time-division multiple-access(TDMA) or wavelength-division multiplexing (WDM) sys-tems [2,5]. It should be noted that O-CDMA schemes withsynchronous access can accommodate a larger number ofpossible subscribers than their asynchronous counterpartsunder a given throughput. This is because one code sequenceis extended to several by rotation and thus the same codewordcan be reused with different phases. Synchronous O-CDMAis then attractive in high rate applications where synchroni-zation is easily achievable, e.g., local area networks (LAN’s).

O-CDMA systems suffer from multiple-access interfer-ence (MAI), which results from the incomplete orthogonalityof the spreading codes used [2,6]. The number of simulta-neous users is then limited by the maximum tolerable MAIamong codewords. To alleviate this adverse impact, inter-ference cancellation techniques using modified prime codesequences have been widely studied [6,7]. These systems uti-lize the code grouping characteristic: codes within the same

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group do not interfere with each other but suffer from thesame amount of MAI via other groups.

In this paper, a novel MAI reduction scheme is proposedfor direct-detection synchronous O-CDMA with simpler sys-tem implementation. Padded-orthogonal codes [8,9] are uti-lized as spreading sequences, where the add-in padding ordercan be used to relax the correlation constraint and estimatethe amount of interference. To further improve the systemcapacity, M-ary pulse-position modulation (PPM) signalingis adopted instead of O-CDMA with on-off keying (OOK) [9,10]. The bit error performance of optical synchronous PPM-CDMA is then evaluated, and comparisons between systemswith and without MAI cancellation examined.

The rest of the paper is organized as follows. Section 2describes the code construction and evaluation. Systemdesign and discussion are detailed in Sect. 3. The opticalPPM-CDMA with MAI estimation and cancellation is theninvestigated in Sect. 4, where numerical results and per-formance comparison are also given. Finally, Sect. 5 brieflypresents the main conclusions of our study.

2 Code construction and evaluation

One of the primary goals of O-CDMA is to extract the desireduser data in the presence of other interfering signals. Thiscan be accomplished by utilizing a set of (quasi-) orthog-onal codes with good correlation properties [1]. The max-imum autocorrelation function facilitates the data recoveryand also enables a receiver to obtain synchronization. Theminimum cross-correlation (CC) then considerably elimi-nates the effect of mutual interference and preserves thequasi-orthogonality between network users.

Here, a novel class of optical spreading sequences,termed ‘padded-orthogonal codes’ [8,9] is introduced. Thiscode design is based on mutually orthogonal Latin squares(MOLS) [11,12], a special case of balanced incomplete blockdesigns (BIBD). Given a prime power Q, Q2 + Q codesequences are generated upon the use of Galois field. Eachcodeword from the same group has complete orthogonality,while those from different groups has a constant in-phase CCof ‘1’. To achieve unity CC for the entire family, the samesub-block of length Q + 1 is padded to each resolvabilityclass. Note that the padding order has to be unique for thesame group but differ from others. The CC function betweendistinct code m and n (m, n ∈ {

1, 2, . . . , Q2 + Q}) at syn-

chronized time is given by

Cmn ={

Q + 1 if m = n autocorrelation1 if m �= n, cross-correlation

(1)

As a result, a full set of number sequences is obtained as inTable 1.

Table 1 Padded-orthogonal codes for Q= 3

Lattice group Code sequence Padding order

1 1 0 0 0 1 0 0 0 1 0 0 1 0

0 1 0 0 0 1 1 0 0 0 0 1 0

0 0 1 1 0 0 0 1 0 0 0 1 0

2 1 0 0 0 0 1 0 1 0 0 1 0 0

0 1 0 1 0 0 0 0 1 0 1 0 0

0 0 1 0 1 0 1 0 0 0 1 0 0

3 1 1 1 0 0 0 0 0 0 0 0 0 1

0 0 0 1 1 1 0 0 0 0 0 0 1

0 0 0 0 0 0 1 1 1 0 0 0 1

4 1 0 0 1 0 0 1 0 0 1 0 0 0

0 1 0 0 1 0 0 1 0 1 0 0 0

0 0 1 0 0 1 0 0 1 1 0 0 0

Though padded-orthogonal codes can be used in asyn-chronous systems, undesirable out-of-phase CC may be ashigh as the code weight. In addition, more complex dynamicthreshold estimation and analysis is required. It is thereforerecommended that this code scheme is employed in synchro-nous O-CDMA with reserved code synchronization. It is easyto distinguish simultaneously active users, since the autocor-relation peaks always occur in distinct slots.

3 System design and discussion

3.1 Overview of interference cancellation techniques

Typically, MAI causes a penalty on the performance ofO-CDMA. This occurs randomly due to the pulse over-lapping in data modulation and the asynchronicity of themultiplexed signals. MAI reduction in optical OOK-CDMAstudies to date has been accomplished by one of two methods:either the statistical properties of the MAI are used to set thedecision threshold or the code interferer’s MAI is estimatedover long intervals with repeated updating [6,13].

However, the first scheme suffers from large variances inusers’ independent usage statistics and the second from longbit-decoding delays over the time intervals [13]. In addition,even if the received optical power is large enough, an errorfloor still exists and limits the number of accommodatablesimultaneous users. Thus, an M-ary PPM-coded system isproposed instead.

3.2 Optical PPM-CDMA with MAI reduction

At the transmitter in Fig. 1, the M-ary continuous data sym-bols are modulated by the laser pulse position to form thePPM signal. The frame time T is divided into M disjoint

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Photon Netw Commun (2010) 19:277–283 279

Fig. 1 Optical PPM-CDMAtransmitter system

Fig. 2 Direct-direction O-CDMA system with MAI reduction

slots each having a duration τ = T/M . The output signalis further spread into Q + 1 pulses by the sequence encodercomposed of tapped delay lines, where the correspondingspreading code determines the relative pulse positions. Theresulting waveform will be recombined and transmitted overthe optical channel.

Figure 2 shows the block diagram of the proposed syn-chronous O-CDMA receiver with interference reduction. Theoptical correlator consists of a set of delay lines inverselymatched to the sequence encoder. The correlation function ofthe pulse sequences is then traced out and at the end chip, thesum of received optical intensity locates in the same positionas that of the padded-orthogonal code.

At the receiver, the matched optical correlator is used torecognize the arrival of the desired sequence. The receivedsignal r (t) is then divided into three branches. The first signalis directed to the upper or main branch, where it is correlatedwith the spreading code [1 0 0 0 0 1 0 1 0 0 1 0 0] assigned tothe desired user. The correlator output is integrated after pho-todetection and sampled at the end of the time interval. Theother signals are directed to the lower branches to accomplishthe interference estimation process. The second correlator isthen correlated with the padded sequence [0 0 0 0 0 0 0 0 0 0 10 0] to estimate the influence from the same class. In the lastbranch, the signal is correlated with the sum of the paddingorder [0 0 0 0 0 0 0 0 0 1 0 1 1] of different groups, wheresimilar processing to that in the main branch is performed.The output of the first photodetector is the desired signal Zincluding the MAI. The reference signals from other photo-detector outputs have the same amount of the MAI as thatincluded in Z . This is because the desired user suffers from

MAI in proportion to the number of simultaneous users. Thereference components are then subtracted from Z to effec-tively eliminate noise effects. The received electrical signal Zis integrated at every slot interval and passed to the decisionmechanism. In contrast to conventional schemes [6,7], thistechnique does not require any code preservation for inter-ference estimation, and remarkably simplifies the receiverstructure by using substantially fewer optical correlators fordecoding.

4 Optical PPM-CDMA with interference estimation andcancellation

Since there are Q2 + Q available sequences in the pro-posed code family, the total number of subscribers is equalto Q2 + Q. We assume that K out of Q2 + Q are activeusers and the remaining users are idle. A random variableγn

(n ∈ {

1, 2, . . . , Q2 + Q})

is then defined as follows:

γn ={

0 if user n is idle.1 if user n is active.

(2)

Thus

K =Q2+Q∑

n=1

γn (3)

Assuming, without loss of generality, that user 1 is thedesired user, let the random variable T represents the num-ber of active users in the first group

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T =Q∑

n=1

γn (4)

The probability distribution of T , given that user 1 is activefor any t ∈ {tmin, tmin +1, . . . , tmax}, where tmin = max(K −Q2, 1) and tmax = min(K , Q) is [9]:

PT (t) =

(Q2

K − t

)(Q − 1t − 1

)

(Q2 + Q − 1

K − 1

) (5)

Let Dn be a vector of length M representing the data sym-bol for user n. If symbol i ∈ {0, 1, . . . , M − 1} is sent,then each entry in Dn is assigned as ‘0’, except the i thentry, which is equal to ‘1’, i.e., Dn, j = 0 and Dn,i = 1for every j �= i . Let Yn = (

Yn,0, Yn,1, . . . , Yn,M−1)and

Yr = (Yr,0, Yr,1, . . . , Yr,M−1

), n �= r , denote the photon

counts collected by the main and reference branches of theintended receiver, respectively. The average photon count dueto interference is the same for all users and thus

Yn = α · (Q + 1) · Dn + α · χ (6)

and

Yr = α · (χ + Dn) (7)

where α denotes the average received photon count per pulseand the interference random vector χ is given by

χ ≡Q2+Q∑

n=2

Dnγn (8)

Given T = t , it is easy to check that χ is a multinomialrandom vector with probability [6,10]

Pr{χ = (κ0, . . . , κM−1)|T } = 1

M K−t· (K − t)!κ0!κ1!, . . . , κM−1!

(9)

where∑M−1

i=0 κi = K − t .

4.1 Optical PPM-CDMA

Assuming equally likely data symbols, the following deci-sion rule is adopted, where symbol i is deemed to be thecorrect one if Y1,i > Y1, j for every j �= i . Because PPM isan M-ary orthogonal signaling scheme, the bit-error proba-bility of a coded O-CDMA system can be expressed as [6,7]

Pb = M

2 (M − 1)

tmax∑

t=tmin

PE ∗ PT (t) (10)

where the symbol error rate PE is

PE =M−1∑

i=0

Pr{Y1, j ≥ Y1,i , some j �= i |T = t , D1,i = 1

}

· Pr{

D1,i = 1}

= Pr{Y1, j ≥ Y1,0, some j �= 0

∣∣T = t, D1,0 = 1

}

≥ Pr{Y1,1 ≥ Y1,0 |T = t , D1,0 = 1

}(11)

Note that PE decreases as α increases, taking the limit asα → ∞, the lower bound of error probability is derivedfrom the weight distribution of codewords as [6,9]

PE ≥K−t∑

κ1=Q+2

(K − tκ1

)1

Mκ1·(

1 − 1

M

)K−t−κ1

·min(κ1−Q−2,K−t−κ1)∑

κ0

(K − t − κ1

κ0

)· 1

(M − 1)κ0

·(

1 − 1

M − 1

)K−t−κ0−κ1

+ 0.5 ·K−t+Q+1

2∑

κ1=Q+1

(K − tκ1

)

· 1

Mκ1·(

1 − 1

M

)K−t−κ1

·(

K − t − κ1

κ1 − Q − 1

)

· 1

(M − 1)κ1−Q−1 ·(

1 − 1

M − 1

)K−t−2κ1+Q+1

(12)

4.2 Interference cancellation in O-CDMA

In this system with interference reduction, the collection ofphoton counts Yr is subtracted from Yn to cancel the MAI

and shot noise. The mean vector{

Yn

}M−1

n=0is then defined as

Yn ≡ Yn − Yr (13)

Similar to the case without cancellation, symbol i ′ is deemedto be the correct one if Y ′

i > Y ′j for every j ′ �= i ′. The bit-

error rate (BER) is given by

Pb = M

2 (M − 1)

tmax∑

t=tmin

P ′E ∗ PT (t) (14)

As equally likely data symbol is assumed, we get

P ′E = Pr

{Y1, j ′ ≥ Y1,0, some j ′ �= 0

∣∣T = t, D1,0 = 1

}

= (M − 1) Pr{

Y1, j ′ ≥ Y1,0∣∣T = t, D1,0 = 1

}

≤ (M − 1)∑

χ

Pχ |T (κ |t )

· Pr{Y1,1 ≥ Y1,0

∣∣T = t, χ = κ, D1,0 = 1

}

≤∑

χ

Pχ |T (κ |t ) · �(t, χ) (15)

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Photon Netw Commun (2010) 19:277–283 281

Fig. 3 BER comparison between lower bound on the PPM-CDMAwithout cancellation and the upper bound of MAI reduction scheme forK =70 and M =16

where

�(t, κ) ≤ (M − 1) · exp

[

−α · (Q + 1)2

4 · (Q + 1 + κ0 + κ1)

]

thus error probability is upper bounded as [7,9]

P ′E ≤ (M − 1) ·

K−t∑

κ1=0

(K − t

κ1

)·(

1

M

)κ1

·(

1 − 1

M

)K−t−κ1

·K−t−κ1∑

κ0=0

(K − t − κ1κ0

)·(

1 − 1

M − 1

)K−t−κ0−κ1

·(

1

M − 1

)κ0

· exp

[

−α · (Q + 1)2

4 · (Q + 1 + κ0 + κ1)

]

(16)

4.3 Numerial results

In this section, numerical performance comparisons betweenoptical PPM-CDMA systems with and without cancellationare presented. In Fig. 3, the probability of error is plottedversus the average received photons per nat (υ), where υ =α · (Q + 1) / ln M . The pulse-position multiplicity (M) andthe number of simultaneous users (K ) are set as M = 16and K = 70. It can be seen that under the Poisson shot-noisemodel for the receiver photodetectors, the bit-error perfor-mance improves remarkably with our MAI reduction schemecompared to that without cancellation. The improvement ismore apparent as υ and/or Q increases. This scheme canthen operate effectively under both low- and high-load traf-fic, since the MAI from all other sequences are all suppressedwithout reducing the cardinality.

Fig. 4 A comparison of the BER for different PPM-CDMA systemsfor K =50 and Q =8

Fig. 5 BER variation versus the number of simultaneous users

Figure 4 shows the BER comparison for the two systems atdifferent modulation levels, when K = 50 and Q = 8. Thesystem with MAI reduction outperforms the conventionalscheme for moderate values of υ and M . The performanceimprovement is significant for high pulse-position multiplic-ity and optical received power. The greater the value of M ,the more signal allocation space and capacity are offered.The proposed optical PPM-CDMA system can then reachfull load and retain reliable transmission.

In Fig. 5, the BER variation versus number of simulta-neous users is shown, where M = 8 and υ = 200. It is clearthat, without interference cancellation, the systems provideunreliable communication as K increases. A larger numberof simultaneous users can then be accommodated in the pro-

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Fig. 6 BER performance of PPM-CDMA systems with and withoutinterference cancellation for the case of full capacity

posed optical PPM-CDMA system with relatively low errorprobability, as long as υ and/or M are large enough. It shouldbe noted that, as the value of M increases, the required opticalreceived power to alleviate the error floor becomes less. Thereis thus a tradeoff between the BER and the required opticalreceived power depending on the value of M .

Figure 6 illustrates the performance of the two systemsfor the case of full load K = Q2 + Q. A lower boundis evaluated at υ = ∞ for the system without cancella-tion, whereas an upper bound is evaluated at υ = 150for the proposed MAI reduction. Again, the conventionalscheme becomes unreliable as the prime power increases,where the BER is relatively constant for various Q val-ues. The performance improves with interference cancel-lation, so that an arbitrarily small error probability can beachieved. Furthermore, the probability of error is signifi-cantly reduced with greater M values, at the cost of systemcomplexity.

5 Conclusion

The main reason for performance degradation in O-CDMAsystems is eventually due to the MAI that reduces the practi-cal capacity and increases the bit errors [6,7]. In this paper, asynchronous optical PPM-CDMA system with interferencecancellation is investigated. A novel class of optical spread-ing codes is used in which their add-in padding orders areused to provide estimation on the MAI. The undesirable inter-ference can then be effectively eliminated from a scaled ver-sion of the received signal after photo-detection.

The bit-error performance of our proposed optical PPM-CDMA system and that without MAI reduction have beenevaluated and compared. The numerical results reveal that the

BER improves considerably with the adoption of the afore-mentioned techniques. As a result, padded-orthogonal codesalways exist to enable all subscribers to communicate simul-taneously with arbitrary small error probability.

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Author Biographies

Kai Cui was born in Shandong, China, in1984. He worked as Network Engineer fromlate 2003 to 2004, and then received the B.E.(Hons) degree in Electronic Engineering in2006. He is currently completing his Ph.D.degree in Communications Engineering atthe University of Warwick. His researchinterests include multiple access techniques,optical multiplexing and networking, wire-

less communications, and coding theory. Mr. Cui is a student memberof the Institution of Engineering and Technology (IET).

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Photon Netw Commun (2010) 19:277–283 283

Mark S. Leeson received a Ph.D. from theUniversity of Cambridge, UK, in 1990 andthen worked as a Network Analyst for a UKbank until 1992. After academic appoint-ments in London and Manchester, he joinedthe University of Warwick in March 2000,where he is now an Associate Professor. Hismajor research interests are optical receivers,optical communication systems, communi-

cation protocols, coding and modulation, ad hoc networking, and evo-lutionary optimization. To date he has over 140 publications in thesefields. Dr. Leeson is a Senior Member of the IEEE, a Chartered Memberof the Institute of Physics and a member of the EPSRC Peer ReviewCollege.

Evor L. Hines joined Warwick University in1984 and he is a Reader in the School of Engi-neering. He became a Fellow of the HigherEducation Academy (FHEA) in 2000 and wasawarded his DSc (Warwick) in 2007. He is achartered Engineer and a Fellow of IET. Hismain research interest is concerned with Intel-ligent Systems (also known by other namessuch as Computational Intelligence and Soft

Computing) and their applications. Most of his work have focused

on Artificial Neural Networks, Genetic Algorithms, Fuzzy Logic,Neuro-Fuzzy Systems, and Genetic Programming. Typical applica-tion areas include intelligent sensors (e.g., electronic nose), medicine,non-destructive testing of, for example, composite materials, computervision, telecommunications, amongst others. He has for example co-authored some 215 articles and supervised more 30 successful researchstudents. He currently leads the School’s Intelligent Systems Engineer-ing Laboratory which he established in 1990 and the School’s Informa-tion and Communication Technologies Research Group. His work hasbeen funded by numerous organizations including several EPRSC andEU and he acts as a referee for a range of journals.

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